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ModelingAndSimulation

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‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﺍﻟﻨﻤﺬﺟﺔ ﻭﺍﻟﻤﺤﺎﻛﺎﺓ‬
‫ام‬
‫‪Excel, SIMAN, Arena and General Purpose‬‬
‫)‪Simulation System (GPSS WORLD‬‬
‫ﺗﺄﻟﻴﻒ ﺩ‪ .‬ﻋﺪﻧﺎﻥ ﻣﺎﺟﺪ ﻋﺒﺪﺍﻟﺮﺣﻤﻦ ﺑﺮﻱ‬
‫ﺃﺳﺘﺎﺫ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ ﺍﻟﻤﺸﺎﺭﻙ‬
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‫‪Arena and General Purpose Simulation System (GPSS‬‬
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‫و‪ M/O & I‬و‪ &/O MN‬ا@‪/‬و‪ 3‬ه‪.‬ا ‪ 30‬أ‪ :‬ان ا"‪2‬م وا‪,:‬‬
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‫‪ Microsoft Excel‬و ‪G6‬م ا ‪ /‬ة ‪ SIMAN‬و ‪ Arena‬و ‪GPSS World‬‬
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‫اا ] ا `‪2H ,‬د‪ UI‬آ أن ‪ GPSS‬أ'‪ Y ! a‬ت ا آ ة ذات ا ‬
‫ا‪ Object-Oriented 3bO‬وه‪.‬ة ‪G‬ة ‪- , N‬ا ‪0‬ي ‪ ,-. ,Y‬و آ ة‪،‬‬
‫‪ ,; [email protected]‬إ و‪2-‬د ‪7 , H d‬ب ا@‪.W‬‬
‫إن إام ا ] '` ت ا‪ 3; Excel M[ O‬ا ‪ ,-.‬وا آ ة ا'‪O a‬ا‬
‫;‪ 3‬آ[ ! ا‪ " H‬ت‪ ،‬وا' ‪ `' ,-. W‬ت ا‪Spreadsheet O‬‬
‫‪ ! Modelling‬ا ‪2‬ا‪ RV‬ا ‪- , U‬ا وا‪f‬ور‪ 3; ,9‬ا"‪ %‬ا‪ 3" H‬و ‪&J‬‬
‫‪2‬رة ‪;2 !/I %‬ة ! ‪MJ‬‬
‫وذ‪: g‬ر‪ UI‬ا‪ ,H " ,? U‬ا ت ‪ M/‬أ‪U /‬‬
‫إ‪ O‬ر ا ت ا‪ ،,h‬و‪0‬دل ذ‪ eH : g‬ا ‪2[6‬ن ا‪0‬وا?‪ 3; M‬أوا?‪ M‬ا‪:‬ن‬
‫ا"‪ 3; ) !9O‬ا`ة ! ‪ 1920‬م‪ 1960 -‬م( إ إام ‪C‬ق ‪,9:I‬‬
‫‪ Approximation Methods‬و‪ :I‬ر ‪ Asymptotic Methods ,‬و‪-‬اول‬
‫ور‪ 2‬ت ‪ M ,‬ا@‪" 3? 6‬م و‪2-‬د أو ‪C ;2I‬ق ‪ , 6‬أو‪،,/I 2I‬‬
‫و‪ _q‬ا‪G9T 9O‬ال ا‪ ! [/‬ا@‪ !? 6‬وا‪ M/O !V 9‬م ‪ !:Y‬‬
‫ا‪7‬ق ا‪ , 9:‬ا‪2C 3‬رت ‪.6‬اك و‪2Y9 %‬ا ا‪:‬رات ا‪ ,? U‬ت ا ‪،,[9‬‬
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.‫ ة‬,b ‫ ; رغ‬
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‫ ذج ام‬M6‫ و‬927I %I ‫ة‬0‫اء ا‬G-0‫ ا‬3;‫ و‬Excel ‫ آ ة ام‬
W "‫ أ‬Microsoft Excel ] 3 ‫ إا‬3; . GPSS World ‫ و‬Arena
‫'ارات‬z‫ ! ا‬M‫ آ‬3; ‫;ة‬2 ‫ ا‬Minimal Excel U ‫ أ‬3‫وا واوال وا‬0‫ا‬
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3; [email protected]‫ ا‬,/ -‫ا‬2 ‫ن‬2/‫ و‬% S C ‫ي‬0 3 H ‫ ب‬/‫ا ا‬.‫ن ه‬2/
http://www.abarry.ws/books/SimulationBook.pdf RJ2 ‫ا‬
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‫د‬2" g ‫ ا‬," ‫ هـ‬1423 3 [‫ ا‬R ‫ر‬
‫ م‬2002 ,29
5
:‫ ات‬
3
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....................................................................................... , : ‫ا‬
................................................................................ ‫ا اول‬
........................................................................ ‫ دة ا آ ة‬, :
.............................................................................. , ‫_ ا‬9‫" ر‬I
............................................................................ Model ‫ذج‬2 ‫ا‬
................................................................................. ‫اع ا ذج‬2‫أ‬
.............................................................................. ‫_ ا آ ة‬9"I
........................................................................ ‫ م ا آ ة‬
...................................................................... ‫ات إاد ا آ ة‬27
.................................................................................. ‫ا ا‬
................ Hand Simulation Examples :,[ 0‫ " ا‬,9‫ ة او‬/ ‫ا‬
........................ Single Channel Queue 6‫ا‬2‫ر ا _ ا‬2 C : 1 ‫[ ل‬
....................................................... ,"9‫ ا‬, / ‫ و‬6‫ أ‬:2 ‫[ ل‬
................................................................ _ ‫ ا‬R? ,/O :3 ‫[ ل‬
.................................................................. !9G‫ ا‬3; ,/O :4 ‫[ ل‬
.................................................................. S7‫ ا‬9 I ,/O 5 ‫[ ل‬
..................................................... (M,N) !9GI ‫ م‬N ‫ آ ة‬:6 ‫[ ل‬
.................................................................................. ‫ا ا‬
........................................................... O‫ا آ ة ام '` ت ا‬
............................................. Excel ‫ ام‬3 6‫ إ‬R9‫ز‬2I ! ,9 " ‫ا‬
............................................................ Excel ‫ آ ة ام‬,[ ‫أ‬
.................................................... 3/I 2I‫ أو‬R ,‫ آ ة آ‬:1 ‫[ ل‬
.............................................. Excel ‫ ت ا آ ة ام‬- M I
............................... Excel ‫ ام‬6‫ا‬2‫ر ا _ ا‬2 C ‫ آ ة‬:2 ‫[ ل‬
...................… Excel ‫ ام‬,"9‫ ا‬, / ‫ و‬6‫ آ ة أ‬:3 ‫[ ل‬
.......................................... Excel ‫ ا _ ام‬R? ,/O :4 ‫[ ل‬
.............................. Excel ‫( ام‬M,N) !9GI ‫ م‬N ‫آ ة‬
:5 ‫[ ل‬
.................................................................................. ! ‫ا اا‬
.......................................................................... ,?‫ا‬2O ‫ م‬J‫ أر‬2I
................................................................... ,?‫ا‬2O"‫ م ا‬J‫ر‬0‫اص ا‬2
.................................................................... ,?‫ا‬2O & ‫ م‬J‫ أر‬2I
......................... Linear Congruential Method 37‫ ا‬7‫ ا‬,:9C
.................................................................. ,?‫ا‬2O"‫ م ا‬J‫ر‬q ‫إ رات‬
.................................................................... ‫ ا وي‬R9‫ز‬2‫إ ر ا‬
............. Kolmogrov-Smirnov Test ‫ف‬2 – ‫روف‬2-2 2‫إ ر آ‬
‫ ام‬Kolmogrov-Smirnov Test ‫ف‬2 – ‫روف‬2-2 2‫إ ر آ‬
......................................................................................... Excel
.................................................... Chi-square Test ‫ آ ي‬R ‫إ ر‬
.....................................................… Excel ‫إ ر ع آ ي ام‬
........................................................................... ‫ل‬:@‫إ رات ا‬
.................... Runs Up and Runs Down M`0 ‫ي‬H‫ وا‬0 ‫ي‬H‫ا‬
6
77
80
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........................................ Excel ‫ ام‬M`0 ‫ي‬H‫ وا‬0 ‫ي‬H‫ا‬
............ Runs above and below the mean w2 ‫ ا‬W I‫ق و‬2; ‫ي‬H‫ا‬
......................................… Excel ‫ ام‬w2 ‫ ا‬W I‫ق و‬2; ‫ي‬H‫ا‬
.......................................................................... 3I‫ا‬.‫ ا‬w ‫إ ر اا‬
...............................................… Excel ‫ ام‬3I‫ا‬.‫ ا‬w ‫إ ر اا‬
............................................................................... :"#$‫ا ا‬
..................................................................... ,?‫ا‬2O ‫ات‬Y 2I
..................... Inverse Transform Technique 3/"‫ ا‬M92 ‫ ا‬,:9C
................................ 30‫ ا‬R9‫ز‬2‫ ا‬R9 3?‫ا‬2O Y ! ‫ هات‬O 2I
................................... Excel ‫ ام‬30‫ ا‬R9‫ز‬2‫ هات ! ا‬O 2I
....................................... (a,b) ! ‫ ا وي‬R9‫ز‬2‫ هات ! ا‬O 2I
..........................................… Weibull M9‫ و‬R9‫ز‬2I ! ‫ هات‬O 2I
........................ Excel ‫ ام‬Weibull M9‫ و‬R9‫ز‬2I ! ‫ هات‬O 2I
................... Triangular Distribution 3[[ ‫ ا‬R9‫ز‬2‫ هات ! ا‬O 2I
‫ ام‬Triangular Distribution 3[[ ‫ ا‬R9‫ز‬2‫ هات ! ا‬O 2I
......................................................................................... Excel
................................... Empirical Distributions ,9H‫" ت ا‬9‫ز‬2‫ا‬
............................... Excel ‫ ام‬M ` ‫ ا‬39H‫ ا‬R9‫ز‬2‫[ ل ا‬
............................... Excel ‫ ام‬M ‫ ا‬39H‫ ا‬R9‫ز‬2‫[ ل ا‬
.......................................... M ` ‫ ا‬39H‫ ا‬R9‫ز‬2‫ هات ! ا‬O 2I
...................... Excel ‫ ام‬M ‫ ا‬39H‫ ا‬R9‫ز‬2‫ هات ! ا‬O 2I
............ Direct Transformation 3"7‫ ا‬R9‫ز‬2 ‫ ا‬M92 ‫ ا‬,:9C
.............................................................................. :‫ا ا دس‬
.................................................... Input Modeling ‫ ا ت‬,-. ...................................................... ‫ هات‬O ‫ ! ا‬R9‫ز‬2‫ا"ف ا‬
........................................... ‫اري‬/‫ ا‬R9‫ز‬2‫ ا‬M/ ‫ ت‬b`‫ د ا‬XeI
........................................... ‫ هات‬O ‫ ! ا‬R9‫ز‬2‫ا"ف وإ ر ا‬
........................................................… Binomial !9 ‫ ذات ا‬R9‫ز‬2I
..................................... Negative Binomial S ‫! ا‬9 ‫ ذات ا‬R9‫ز‬2I
......................................... Geometric Distribution 3U‫ ا‬R9‫ز‬2‫ا‬
...............................................................… Poisson ‫ن‬2‫ا‬2 R9‫ز‬2I
.............................................................… Normal 3"7‫ ا‬R9‫ز‬2‫ا‬
........................................… Lognormal 3 X‫^ ر‬2‫ ا‬3"7‫ ا‬R9‫ز‬2‫ا‬
........................................................… Exponential 30‫ ا‬R9‫ز‬2‫ا‬
...................................................................… Gamma - R9‫ز‬2I
..........................................................................… Beta R9‫ز‬2I
...................................................................… Erlang ]T‫ إر‬R9‫ز‬2I
..................................................................… Weibull M9‫ و‬R9‫ز‬2I
Discrete or Continuous Uniform M ` ‫ أو ا‬M ‫ ا وي ا‬R9‫ز‬2‫ا‬
..........................................................… Triangular 3[[ ‫ ا‬R9‫ز‬2‫ا‬
........................................................… Empirical 39H‫ ا‬R9‫ز‬2‫ا‬
.............................................. Parameters Estimation % " ‫ ا‬9:I
............................................. ‫" ت‬9‫ز‬2‫ " ا‬,6: ‫رات ا‬: ‫" ا‬
7
113
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190
...................... Goodness of Fit Tests 7‫دة ا‬2- ‫! أو‬6 ‫إ رات‬
........................ Quantile-Quantile Plots ‫ا " ت‬-‫ ت ا " ت‬2‫ر‬
.... Excel ‫ ام‬Quantile-Quantile Plots ‫ا " ت‬-‫ ت ا " ت‬2‫ر‬
....... Chi-square Goodness of Fit Test 7‫دة ا‬2H ‫ آ ي‬R ‫إ ر‬
Chi-square Goodness of Fit Test 7‫دة ا‬2H ‫ آ ي‬R ‫إ ر‬
............................................................................. Excel ‫ام‬
K-S Goodness of Fit 7‫دة ا‬2H ‫ف‬2 -‫روف‬2-2 2‫إ ر آ‬
........................................................................................... Test
K-S Goodness of Fit 7‫دة ا‬2H ‫ف‬2 -‫روف‬2-2 2‫إ ر آ‬
.................................................................... Excel ‫ ام‬Test
:! ‫ا ا‬
................................................ SIMAN ‫ ا آ ة‬,Y ‫ا آ ة ام‬
................................................................... SIMAN ‫اء‬-‫ات إ‬27
............................................................ SIMAN 3; ,-. ‫أ ت ا‬
......................................................................... SIMAN ,Y ‫ا‬2J
................................................................................. ‫ذج‬2 ‫ ا‬S‫ا‬2J
............................................................................... , H‫ ' ا‬
........................................................................ ‫ة‬6‫ا‬2‫ ا‬,‫ ا آ‬,/O
............................................................... ‫رة‬27 ‫ة‬6‫ا‬2‫ ا‬,‫ ا آ‬,/O
................................................ M 37 ‫ƒ ?_ و‬2‫! ! ا‬2 ,/O
:#‫ا ا‬
...........................… ARENA ‫ ا آ ة‬, G6 ‫ وا آ ة ام‬,-. ‫ا‬
................................................................................... ‫ذج‬2 ‫ ء ا‬
..................................................................... 9:‫ ا آ ة وا‬,H
.............................................................. ‫ذج‬2 ‫ ت ا‬I ‫إد ل‬
...................................................................... 9:‫ ا آ ة وا‬,H
................................................... Output Analysis ‫ ت‬- ‫ ا‬M I
................................................................................ :!'‫ا ا‬
................................... GPSS ‫ ا آ ة‬, G6 ‫ وا آ ة ام‬,-. ‫ا‬
................................................................................ GPSS ‫أوا‬
..................................................................... GPSS S‫ا‬2J ‫ رات‬
............................................ GPSS 3; ‫;ة‬2 ‫ م ا‬N ,9‫ا ` ت ا"د‬
............................................ GPSS 3; , ‫ ا‬Operators ‫ا" ل‬
......................................... ‫ آة ا*)م‬-./# 0)# )12 ‫اآ‬34 ‫ك‬67 ‫آة‬#
................................................................................ ,/O ‫ض ا‬
.............................................................. GPSS ,Y ] ‫ض ا‬
........................................................................ ‫ذج‬2 ‫ ا‬M _'‫و‬
............................................................................... ‫اء ا آ ة‬-‫إ‬
................................................................................. ]? ‫ ا‬,OJ ................................................................................ ‫ ا آ ة‬M‫دا‬
.................................................................... 8 94‫آة ;م ه‬#
............................................................................... ,/O ‫ض ا‬
............................................................. GPSS ,Y ] ‫ض ا‬
8
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫إ‪-‬اء ا آ ة ‪...............................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪.................................................................................‬‬
‫دا‪ M‬ا آ ة ‪................................................................................‬‬
‫‪#‬آة ;م ‪ >$4‬ا=‪ .‬دور ‪.......................................................‬‬
‫ض ا ‪............................................................................... ,/O‬‬
‫ض ا ] ‪.............................................................. GPSS ,Y‬‬
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫إ‪-‬اء ا آ ة ‪................................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪.................................................................................‬‬
‫دا‪ M‬ا آ ة ‪................................................................................‬‬
‫‪#‬آة ور‪>/4 @ /4 7‬ن ‪..............................................................‬‬
‫ض ا ‪............................................................................... ,/O‬‬
‫ض ا ] ‪............................................................. GPSS ,Y‬‬
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫إ‪-‬اء ا آ ة ‪................................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪.................................................................................‬‬
‫دا‪ M‬ا آ ة ‪................................................................................‬‬
‫‪#‬آة ;م ا‪= A B‬دة‪...............................................................‬‬
‫ض ا ‪............................................................................... ,/O‬‬
‫ض ا ] ‪............................................................. GPSS ,Y‬‬
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫إ‪-‬اء ا آ ة ‪................................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪..................................................................................‬‬
‫دا‪ M‬ا آ ة ‪.................................................................................‬‬
‫‪#‬آة ;م ‪............................................................ -/C D*1 >$4‬‬
‫ض ا ‪............................................................................... ,/O‬‬
‫ض ا ] ‪.............................................................. GPSS ,Y‬‬
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫إ‪-‬اء ا آ ة ‪................................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪..................................................................................‬‬
‫دا‪ M‬ا آ ة ‪.................................................................................‬‬
‫‪#‬آة ;م ‪ !D ! 14‬إ‪B‬و ‪........................................................‬‬
‫ض ا ‪............................................................................... ,/O‬‬
‫ض ا ] ‪.............................................................. GPSS ,Y‬‬
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫إ‪-‬اء ا آ ة ‪...............................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪..................................................................................‬‬
‫دا‪ M‬ا آ ة ‪.................................................................................‬‬
‫‪#‬آة 'ق ‪#‬آ>ي ‪........................................................................‬‬
‫ض ا ‪............................................................................... ,/O‬‬
‫ض ا ] ‪.............................................................. GPSS ,Y‬‬
‫و'_ ‪ M‬ا ‪2‬ذج ‪........................................................................‬‬
‫‪9‬‬
‫‪191‬‬
‫‪193‬‬
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‫‪199‬‬
‫‪199‬‬
‫‪199‬‬
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‫‪204‬‬
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‫‪205‬‬
‫‪208‬‬
‫‪208‬‬
‫‪208‬‬
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‫‪213‬‬
‫‪213‬‬
‫‪213‬‬
‫‪217‬‬
‫‪217‬‬
‫‪217‬‬
‫‪218‬‬
‫‪223‬‬
‫‪223‬‬
‫‪224‬‬
‫‪227‬‬
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‫‪227‬‬
‫‪227‬‬
‫‪228‬‬
‫‪230‬‬
‫‪230‬‬
‫‪232‬‬
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‫‪232‬‬
‫‪232‬‬
‫‪234‬‬
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‫‪234‬‬
‫‪237‬‬
‫‪237‬‬
‫‪237‬‬
‫‪238‬‬
‫إ‪-‬اء ا آ ة ‪...............................................................................‬‬
‫ ‪ ,OJ‬ا ?] ‪.................................................................................‬‬
‫دا‪ M‬ا آ ة ‪.................................................................................‬‬
‫ )‪2J (1‬ا‪.................................................................... GPSS S‬‬
‫ )‪ (2‬أوا ‪................................................................… GPSS‬‬
‫ )‪ (3‬ا ` ت ا"د‪ N ,9‬م ‪..........................................................‬‬
‫ )‪ (4‬ل ‪.................................................................... GPSS‬‬
‫ )‪ (5‬أ‪ /‬ل ‪2J M[ I‬ا‪................................................... GPSS S‬‬
‫ )‪ (6‬أ‪ ,b‬ا@ رات ا ‪ ,:‬وأ‪............................................ U 2-‬‬
‫‪ I‬ر‪.......................................................................................... !9‬‬
‫‪..................................................................................‬‬
‫ا ا‪R-‬‬
‫‪10‬‬
‫‪241‬‬
‫‪241‬‬
‫‪241‬‬
‫‪244‬‬
‫‪262‬‬
‫‪269‬‬
‫‪272‬‬
‫‪274‬‬
‫‪275‬‬
‫‪407‬‬
‫‪421‬‬
:‫ا اول‬
:‫آ ة‬
‫ دة ا‬, :
,2‫ ا‬3‫ وه‬Problem Solving Techniques M‫ آ‬O ‫ ا‬M , U ‫ ا‬M? 2‫ ا‬6‫ ا‬3‫آ ة ه‬
‫ او‬Analytic Methods , ‫ق ا‬7 U6 "‫إ‬
Resampling
,9 " ‫ق إ دة ا‬C 3 ‫آ ة‬
‫ا‬
‫ إذا‬,/O ‫ أي‬M ‫ة‬0‫ة وا‬62‫ا‬
‫" ا‬I‫ و‬.Numerical Methods ,9‫ا"د‬
‫ م‬N‫_ ا‬9" T‫ف أ أو‬2 .," ‫ '` ت‬U ,?‫ا‬2O ‫ات‬Y ‫ م و‬J‫ أر‬2I‫ و‬Methods
:,I 2/ ‫و‬
: ‫ او‬9‫ر‬.4
: System ‫;م‬1‫ا‬
."‫ ا‬Uf" "I‫ و‬M `I ‫ ء‬0‫ ! ا‬,2 H
: Entity ‫آ‬
.‫ إه م ص‬U ‫ م‬N‫ ا‬3; ,2‫ † أو آ‬2‫وه‬
: Attribute H
.!? / ,' 2‫وه‬
: Activity ‫ط‬J
.‫ م‬N‫ ا‬3; YI SI , ‫أي‬
: State of the System ‫;م‬1‫ ا‬
.," ,N ‫ م‬N‫ ا‬3; ,7O0‫ وا‬UI `'‫ ? ت و‬/‫ ا‬M‫ _ آ‬I ‫ات‬Y 3‫وه‬
.& 6 3; ‫ات‬Y‫ ا‬R ‫ م‬N‫ر ا‬27I ‫رس‬9‫و‬
:‫ل‬#
R ‫ ا‬%J 3‫ م ه‬N‫ا ا‬.‫ ه‬3; , 0‫اء ا‬G-0‫ ا‬. U"7J R H9‫ و‬, f ]9 R
"
‫ي‬.‫ ت ا‬9O ‫ ا‬%J‫ و‬, f‫ @ ج ا‬R7:‫ ا‬5.‫ ه‬R H9 ‫ي‬.‫ ا‬R H‫ ا‬%J‫ و‬R7:‫ ا‬R 9 ‫ي‬.‫ا‬
M:9 ‫ي‬.‫ ا@ ج ا‬,J‫ ا‬%J‫ ! و‬O , f‫ ا‬GUH9 ‫ي‬.‫ ! ا‬O‫ ا‬%J‫ و‬, ‫اد ا‬2 ‫ ! ا‬A9
.‫ م‬J0‫ ا‬,: 3 M "‫ ا‬%:9‫ و‬, f‫ ا‬3 ‫ ت‬7‫ا‬
:‫ م‬N‫ا ا‬.‫ ه‬3;
d‫ ا‬R? f‫ ا‬،‫اء‬G-0‫ ا‬،‫ ت‬7‫ ا‬،‫ م‬JT‫ ا‬:3‫ ? ت ه‬/‫ا‬
11
‫ا‪ C O‬ت ه‪ , :3‬ا ‪ R‬و ‪ ,‬ا‪ R H‬و ‪ ,‬اء ا ‪2‬اد ا م و ‪ ,‬ا‪GUH‬‬
‫وا‪ ! O‬ا‪.d‬‬
‫ا ` ت ه‪ :3‬ا‪2 ،SC M/ , /‬ع ا‪ ،,"7:‬د ا ‪ 3; !? /‬آ‪ %J M‬ا‪d‬‬
‫وا‪H‬ول ا ‪ 37"9 3‬ا [‪ ," , N0 ,‬و " ‪: UI 2/‬‬
‫ا‪ N‬م‬
‫آ ? ت‬
‫'` ت‬
‫ا‪,7O‬‬
‫ور‬
‫ رات‬
‫‪,; ،,‬‬
‫‪2‬ا‪,J‬‬
‫‪g‬‬
‫ز ?!‬
‫دا?!‪ ،‬ر‪ %J‬ا ب‬
‫ ‪SC ،: S‬‬
‫‪J‬ض‬
‫إ‪I‬‬
‫‪T‬ت‬
‫‪ /‬ت‪ ،‬ر ?‪M‬‬
‫‪2C‬ل ا ‪,U- ،, /‬‬
‫ا@‪I‬‬
‫‪2‬ق آ‪G‬ي‬
‫ز ?!‬
‫إر ل‪M'2I ،‬‬
‫ل‬
‫‪ , ? J‬ا‪92‬‬
‫د;‪ , J R‬ا ‪ 9O‬ت‬
‫وه‪.‬ا ا‪H‬ول ‪ 6 37"9T‬آ ‪ R H M‬ا‪ ? /‬ت وا ` ت وا‪ 5.U ,7O0‬ا‪0 , N0‬ن ذ‪g‬‬
‫‪ ,;" S79‬ا‪0‬هاف ا‪ ! 3‬ا‪ U-‬رس ا‪ N‬م‪ .‬وإ دا ‪ 3‬ا‪0‬هاف ا ‪!/ 9 , 27‬‬
‫‪ 9 I‬و'_ أدق ‪ N‬م و ‪.,I 2/‬‬
‫‪ K‬ا‪;1‬م‪:‬‬
‫‪ Xe9‬ا‪ N‬م ‪Y‬ات ا‪ I 3‬ث ر‪ &-‬آ ا& ‪ 3 XA9‬ا ‪ M[ &26 ! w‬ه‪ 5.‬ا‪Y‬ات‬
‫‪ ,b 3 XAI‬ا‪ N‬م‪ ! ; .‬ا ‪- %U‬ا ‪ ,-.‬ا‪ N‬م ان ‪ G‬ا ود ! ا‪ N‬م و ‪ &b‬وه‪.‬ا‬
‫‪ 9‬د ";‪ ,‬ا‪0‬هاف ! وراء درا‪ ,‬ه‪.‬ا ا‪ N‬م‪.‬‬
‫;`‪ [ 3‬ل ا‬
‫‪ R‬ا"‪2‬ا ‪ M‬ا‪ 7 %/ I 3‬ت ‪ 3‬ا ‪ H‬ت ‪ "I‬رج ‪ XeI‬ا‪ N‬م و‪.U‬ا‬
‫;‪G- 3U‬ء ! ‪ ,b‬ا‪ N‬م و‪ !/‬إذا آ ن "ض ‪ 3 XeI‬ا‪ SH; S7‬ا‪ .‬ذ‪ 0 g‬ر إذ ان‬
‫ه ك ‪ - ! ,J‬ت ا‬
‫‪ R‬وو'‪2‬ل ا‪ 7‬ت و‪ 9‬ه‪.‬ا ‪ Feedback ,` ,9.YI‬و‪"I‬‬
‫ه‪.‬ة ا"‪ O ,J‬ط ! ا‪ ,7O‬ا‪ N‬م‪.‬‬
‫ا‪ DJ‬ا)ا‪ :Endogenous Activities /0‬و‪ _ I‬ا‪ ,7O0‬دا‪ M‬ا‪ N‬م‪.‬‬
‫ا‪ DJ‬ا‪$‬ر= ‪ :Exogenous Activities‬و‪ _ I‬ا‪ ,b 3; ,7O0‬ا‪ N‬م وا‪3 XAI 3‬‬
‫ه‪.‬ا ا‪ N‬م‪ .‬ا‪ N‬م ا‪.‬ي ‪ ,7Oe Xe9T‬ر‪ N 3 9 ,-‬م ‪ ˆ/" Y‬ا‪ N‬م ا‪.‬ي ‪Xe9‬‬
‫‪ ,7O0‬ا ر‪ ,-‬وا‪.‬ي ‪ N &e _'29‬م `‪2‬ح‪.‬‬
‫‪12‬‬
‫ا‪ DJ‬ا)دة ‪ :Deterministic Activities‬وه‪ 3‬ا‪UH? 9 I !/ 9 3‬‬
‫‪ I M/O‬م !‬
‫‪. UI‬‬
‫ا‪ DJ‬ا‪J.‬ا ‪ : Stochastic Activities‬وه‪ 3‬ا‪XeI Y9 3‬ه ‪2O M/O‬ا?‪ 3‬و‪2/I‬ن‬
‫ ?‪ UH‬إ ‪ /‬ت "دة ‪2 _'2I‬ز‪ R9‬إ‪ [ ; 3 6‬ا‪ WJ2‬ا‪.‬ي ‪_'29 R H ,( &JYI‬‬
‫‪2‬ز‪ R9‬إ‪ 3 6‬آ ان ا‪ ! ! G‬إ‪ 7‬ل (‪2O M/O Y9 ,‬ا?‪.3‬‬
‫ا; ا‪:Continuous Systems L/‬‬
‫وه‪ 3‬ا‪ , 6 U; YI 3‬ا‪ N‬م ‪ M M/O‬و ; [ إ‪6 5 HI‬آ‪? C ,‬ة ;‪ 3‬ر ‪2-‬ي‬
‫‪ %/ I W I‬ا‪ 7‬ر ا‪ I 3h‬ث ‪ Smooth % M/O‬‬
‫‪ a‬ا@‪.5 HI‬‬
‫ا; ا‪:Discrete Systems /1‬‬
‫وا‪ , 6 U; YI 3‬ا‪ N‬م ‪ R R7: M/O‬ا‪ [ ; ! G‬إآ ل ‪ 3; , f‬ا‬
‫‪ 9 R‬ث‬
‫‪ ،R7: M/O‬و'‪2‬ل ‪ 3 SC‬ا‪ 9 R? f‬ث ‪ R7: M/O‬ا‪.d‬‬
‫‪ =3‬ا‪;1‬م ‪:System Modeling‬‬
‫ا‪1‬ذج ‪: Model‬‬
‫ه‪ N 9HI 2‬م ‪2/9‬ن ! ‪ 2" R HI‬ت ‪26‬ل ا‪ N‬م ‪Y‬ض درا&‪ .‬ورا‪ N ,‬م‬
‫‪SH9‬‬
‫ان ‪2/‬ن او ‪2 3‬ذج ‪ _'2 Model‬ه‪.‬ا ا‪ N‬م ‪Y‬ض إ‪-‬اء ‪ HI‬رب ‪ 3 , -z‬أ‪,b‬‬
‫وإ;ا‪ V‬ت ‪ !/ 9T‬إ‪-‬ا?‪ 3 U‬ا‪ N‬م ة وذ‪7f9T 36 g‬ب ا‪ N‬م ا‪ 3'0‬و‪ 9‬ث‬
‫إر‪ I‬ك ;‪A9 & 3‬دي ا‪ YI 3‬ا‪ N‬م و;‪:‬ا& ‪2‬ا'& ا‪ ,'0‬آ ان درا‪ ,‬ا ‪2‬ذج ‪! T‬‬
‫ا‪ N‬م ‪ , HI ! !/ I‬ة ‪26‬ارات ‪26‬ل ا‪ N‬م وذ‪ g‬دة ا ‪2‬ذج ا‪ 3‬ا ‪ ,‬ا‪ ,'0‬‬
‫إ‪-‬اء آ‪26 M‬ار "‪ ˆ/‬ا‪ N‬م ا‪ 3'0‬ا‪.‬ي إذا ‪ !/ 9T YI‬إ د‪ ,I‬ة اى ‪ ,‬ا‪,'0‬‬
‫; [ را‪ N ,‬م إ‪J‬‬
‫دي ‪ Y‬ت ا"ض وا‪A9 J S7‬دي ا‪. U/ !/ 9T ]? 3‬‬
‫آ أن ا ‪2‬ذج ‪ !/ 9‬ان ‪9‬رس ;‪ 3‬أز ‪ ,‬إ;ا‪ !/ 9 [ ; ,V‬إ‪-‬اء‬
‫آ ة ‪ N‬م ام‬
‫ا ‪2‬ذج و ";‪ ; I " ,‬ت ا‪ N‬م `ات ة ا‪ U‬او ! ;‪ 3‬د‪ .,J ? J‬وآ‪!/ 9 g.‬‬
‫! ‪ 9C‬ا ‪2‬ذج درا‪ ,‬ا‪ N‬م ‪ MJ‬إ‪ &? O‬وو‪2-‬د‪ 5‬ا' ; [ ‪ 9‬ء‬
‫ رات ء ; ‪ 9‬اي ر ا;‪2/ Mf‬ن ‪2‬ذج ‪ M/‬ر و آ‪ I 3‬ف ا‬
‫‪ R‬و‪ 9‬ة‬
‫‪ W I R‬ه‪5.‬‬
‫ا رات‪.‬‬
‫أاع ا‪1‬ذج‪:‬‬
‫‪# ) > A‬د ( ‪ :Physical Models‬وه‪ 3‬ا‪2 3I 3‬اد ‪ M[ ,6‬ء ‪2‬ذج ‪? 7‬ة ;‪3‬‬
‫‪ ,6‬ا‬
‫‪ %‬وذ‪ @ g‬ر ه‪ƒ W I U/‬وف "‪.,‬‬
‫‪13‬‬
:Mathematical Models ( )T4 ‫ او‬/ /4 ) S‫ر‬
(d‫ ت ا‬2‫ ر‬،‫اول‬- ،‫ دوال‬،, 6‫" ت إ‬9‫ز‬2I ) ,V 9‫ ت ر‬J U? ‫ م‬3‫وا‬
‫ ! وا ذج‬G‫ ا‬R U 6 YIT 3‫ وا‬Static Models ‫ ة‬H‫ _ ذج ا‬I f9‫ه ك ا‬
.! G‫ ا‬R U 6 YI 3‫ وا‬Dynamic Models ,/ 9‫ أو ا‬,‫ا آ‬
3; ‫ ?ة‬C ‫ او‬,` ‫ذج‬2 ،‫ ا ام‬H ‫ذج ء ا‬2 ‫ ة‬H‫ ا‬,? 9G`‫ ا ذج ا‬3 ‫وآ [ ل‬
,‫ ور‬3; 3‫اق اا‬[email protected]‫ ا‬,( ‫ ذج‬3‫آ‬6 3? 9G; ‫ذج‬2 ‫ وآ [ ل‬d‫ ا‬36 S/ ‫ة‬.; .‫م‬2"‫ ا‬,/ ‫ ء‬9G`‫ ا‬%J M " 3; ,‫ ا آ‬,? 9G`‫ وآ[ ! ا ذج ا‬,U‫ ا‬,‫آ‬
3‫اه ا‬2N‫ ا‬:‫" ذ‬9‫) إ‬.,‫ ا آ‬g.‫ ة وآ‬H‫ ا‬,V 9‫ " ا ذج ا‬,[ ‫ أذآ أ‬:!9 I
(,‫آ‬6 ‫ن‬2/I ,J‫ أو ;و‬,V `I ‫ت‬T‫'_ " د‬2I
:3 ‫اع ا ذج آ‬2‫ ا‬M[ I !/ 9‫و‬
MODELS
MATHEMATICAL
PHYSICAL
STATIC
STATIC
DYNAMIC
NUMERICAL
ANALYTICAL
DYNAMIC
NUMERICAL
SIMULATION
,9‫ و د‬Analytical , I ‫ إ‬,‫ ا آ‬,V 9‫ ا ذج ا‬J ‫ ا‬aV2‫ ا‬3;
‫آة‬
‫ و‬Numerical ,9‫ و د‬Analytical , I ‫ إ‬,‫ ا آ‬,V 9‫ وا ذج ا‬Numerical
‫ ام‬g‫ وذ‬I U6 !/ 9 ,V 9‫ا ! ا ذج ا‬- M:‫ن ا‬0 g‫ وذ‬Simulation
‫ق‬7‫ام ا‬
9‫ د‬U6 !/ 9 U^‫ وأ‬،,:7 ‫ ت ا‬- @‫ وا‬,V 9‫ ت ا‬9N‫ا‬
.‫آ ة‬
‫ ا‬,7‫ا‬2 U6 !/ 9 U" -‫ و‬،,9‫ارز ت ا"د‬2‫وا‬
:‫ اآة‬9.4
9‫و‬9 ‫آ ة‬
‫ ا‬9-‫اء ا‬2‫ و‬.," , ‫ ;ة ز‬3::6 ‫ م‬N M " M[ I ‫ او‬:I 2‫آ ة ه‬
‫ض إ ج‬Y g‫ م وذ‬N R7
‫ا‬
d9‫ ر‬I 2I M OI U; S ‫او ام ا‬
.3:: ‫ م ا‬N ,YO‫اص ا‬2‫ا‬
14
‫وا‬
‫آ ة ‪2 927I "I‬ذج ‪ N‬م ا ‪ .3::‬ه‪.‬ا ا ‪2‬ذج ‪2/9‬ن ‪! ,2 H M/‬‬
‫ا`‪ V‬ت ا‪ M " "I 3‬ا‪ N‬م وه‪ 5.‬ا`‪ V‬ت ‪2/I‬ن ‪ J M/‬ت ر‪ ,V 9‬او ‪,:7‬‬
‫او ر ‪ ! Symbolic ,9G‬آ ? ت ا‪ N‬م‪ 927I " .‬و‪ validate M"`I‬ا ‪2‬ذج & @‪-‬اء‬
‫" ا‪ H‬رب ا‪ !/ 9T 3‬إ‪-‬ا?‪ U‬ا‪ N‬م ا ‪ 3::‬وذ‪Y g‬ض ‪ ,N6‬وإ ج‬
‫ا‪Y‬ات وا` ت ا `‪ ,‬ا‪7I J 3‬أ ا‪ N‬م ;‪ , 6 3‬إ‪-‬ا?‪ 3; , U‬ا ‪.,::‬‬
‫‪)$ U#‬م اآة‪:‬‬
‫ا‪27‬ر ا‪ 3; /‬ا ت وو‪2-‬د ا ]‬
‫ا@ام ‪ ! M"-‬إام ا‬
‫آ ة در‪ ! , ,-‬ا و‪ ,‬و‪,2U‬‬
‫آ ة ;‪ M6 3‬ا ‪ O‬آ‪ M‬ا ‪ ,‬وا@‪J‬‬
‫د‪ ,9‬وا@‪, -‬‬
‫وا‪ ,7‬وا‪ ,b‬ا‪ 0‬ا‪ MU‬ر‪ ,-‬ان ه ك ا‪ ! [/‬ا" ء ا‪ !9.‬ا دوا ' ^‪ ,‬ا‪! [/‬‬
‫ا"‪2‬م ا‪ !9 " ,:7‬ا "‪ 2‬ت ا ‪ , f‬ورا‪ Inherited Information X‬دا‪M‬‬
‫ا ‪ O‬هات ا ‪ " ,N6‬او ا و ون ا@;اض ‪e :‬ي ;‪ V‬ت ‪2/IT J‬ن ' ‪,‬‬
‫[‪ M‬ان `ض ان اوزان ;‪b‬ان ا‪ H‬رب ا ‪2I U ,‬ز‪ 3"C R9‬و;‪ , 6 3‬م ‪ : I‬ه‪5.‬‬
‫ا`‪2: ,V‬م ‪-‬اء ‪ Transformation M92 I‬ا ت ا ‪ O‬هة ‪ ,"C U"H‬و‪M/O 2‬‬
‫‪ R H‬ا‪ &9 ,9.60‬ا‪ : ,9.6‬س وا‪e; w:; 6‬ي ز ‪2‬ن ‪2/I‬ن ‪& J‬‬
‫‪ 39:I‬وه‪.‬ا ‪I &O9‬‬
‫‪ 2O‬ا ‪.‬اء ‪ ! R7:‬ا‪ : a 9 6 !7:‬س ا‪:‬م أ إذا‬
‫أ'‪ ! Y‬ا ‪.‬اء ‪2:9‬م ا ?‪R‬‬
‫آ ‪ W‬ا‪:‬م اآ ! ا ‪.‬اء ;ن ا ?‪ 9 R‬إ'" او إ'"! ‪ MI 6‬ا‪:‬م ;‪ 3‬ا ‪.‬اء )ه‪.‬ا‬
‫[‪ M‬إ;ا‪ .(3V‬و‪.U‬ا ;ن ا@‪ HI‬ة ا ‪ P9‬ه‪ " 2‬دع ا ت ا ‪ O‬هة ‪ " U` ! %/I‬وه‪./‬ا‬
‫‪27I‬رت ‪C‬ق إ دة ا " ‪ Resampling Methods ,9‬وا‪I 3‬م ا‬
‫و‪I‬م ا‬
‫آ ة ا‪h‬ن ‪ M/O‬آ و ‪ 3; _[/‬آ[ ! ا‪ 0‬ث ا" ‪ ,‬ا‪ ,9N‬أو ا‪,:7‬‬
‫وه‪ ! 3‬أه‪ %‬ا ‪2‬اد ا‪I 3‬رس أآ د ‪! V‬‬
‫‪ (1‬ا‬
‫آ ة ‪._[/ M/O‬‬
‫‪2‬ث ا" ت و‪ M I‬ا‪ %N‬و !‬
‫‪G‬ا‪: UI‬‬
‫آ ة ‪ ! !/ I‬درا‪ ,‬وإ‪-‬اء ‪ HI‬رب ا` ت اا‪0 ,‬ي ‪ N‬م "‪ :‬او‬
‫ ‪G-‬ء ! ذ‪ g‬ا‪ N‬م‪.‬‬
‫‪ (2‬ا‪Y‬ات ا@‪J‬‬
‫د‪ ,9‬وا ‪ ,‬وا@‪ , -‬وا‪ !/ 9 ,b‬ان ‪ I‬آ و ‪ ,N6‬ه‪.‬ا ا"‪M9‬‬
‫ ‪ I‬ف ا ‪2‬ذج‪.‬‬
‫‪ , ! (3‬ا ‪ ,-.‬وا‬
‫آ ة ‬
‫‪ 2" M‬ت `ة ‪-‬ا ! إداء ا‪ N‬م‬
‫ا ‪.3::‬‬
‫‪ Y (4‬ت ا‬
‫آ ة و ‪ ,N6‬ا ‪ -‬ت ا ‪ 9 I / 9 ,HI‬ا ‪Y‬ات ا ‪3; , U‬‬
‫ا‪ N‬م ا ‪ 3::‬و ";‪ ,‬ا‪ ,:97‬ا‪. U M `I 3‬‬
‫‪I (5‬م ا‬
‫آ ة "‪ f‬ا‪ ! [/‬ا ?] ا [‪ ,‬ا‪.,9N‬‬
‫‪15‬‬
‫‪I (6‬م ا‬
‫آ ة ‪I , H‬‬
‫‪ %‬و ت ‪9-‬ة ‪I %‬م ! ‪MJ‬‬
‫‪ 9‬‬
‫;‪ U U‬و‪6 U:I‬و‪. UX‬‬
‫‪ (7‬و‪I‬م ‪ ! :‬ا ‪2‬ل ا ‪ ,‬وا‪e‬آ ! ' ‪0 . U‬ن ذج ا‬
‫‪ Run‬و‪2-2; M IT‬د ‪,2 H‬‬
‫‪-‬اء ا‬
‫دة ! ا ت و‪2‬اص‬
‫آ ة ‪HI‬ى‬
‫دة ‪2‬ذج ‪ :9‬م‬
‫آ ة و ‪ ,N6‬ا ‪ -‬ت‪.‬‬
‫و‪ !/‬ه ك " ا"‪2‬ب او ‪6T‬ى ا "‪ 2‬ت [‪:M‬‬
‫‪ (1‬ء ‪2‬ذج ‪ 9‬ج ا ة و‪I‬ر‪ S9‬ص ‪ M‬ان ا" ‪2:9‬ل ان ء ‪2‬ذج ه‪ !; 2‬إذ‬
‫ˆ آ‪ %"9 ! M‬آ ‪ ,‬ا‪ 7 a 9 w‬ط‪ ،‬آ‬
‫‪ 39 J !` ! O‬آ‪U M‬‬
‫ان ;‪ , 6 3‬إ‪ 7‬ء `ˆ ا ‪,/O‬‬
‫ ‪2‬ذج ‪ g.‬و‪2/I‬ن ه ك ا ء ‪O‬آ‪! ,‬‬
‫ا ‪2‬ذ‪ !-‬ا ‪ !HI‬و‪ !/‬ا@; ت آة و! ‪2/9‬ن ا ‪2‬ذ‪.!:7 !-‬‬
‫آ ة او ‪2/9 J UI -‬ن ! ا "‪`I S‬ه و '‪ ,‬إذا آ ‪ W‬ا ت‬
‫‪ ]? (2‬ا‬
‫‪2O‬ا?‪,‬‬
‫‪ - , ]9‬ت ‪2O‬ا?‪ ,‬و ‪2/9 3‬ن ! ا "‪; ,;" S‬‬
‫إذا‬
‫آ ‪ W‬ا@; ت ا ‪ ,HI‬ه ! ا"‪2O‬ا?‪ ,‬ام ! ‪ ! 3::6 M `I‬ا ‪Y‬ات‪.‬‬
‫‪ (3‬ا ‪ ,-.‬وا ‪ M‬و‪ R -‬ا ت ‪Y‬ض ا‬
‫ا‪ 6‬آ ان إ‬
‫ر او ‪ " R7J‬ا‬
‫آ ة ‪Y9‬ق و‪- M92C J‬ا و‪2/9‬ن ‪_/‬‬
‫در ;‪ , 3‬ء ا ‪2‬ذج ‪2 U ]9‬ذج‬
‫ ‪ 79T ‹J‬ا‪ N‬م ا ‪ 3::‬و‪ , 9 &H? a I‬ا` ?ة‪.‬‬
‫و‪ " -2I 6 !/‬اا ] ا‪.‬آ‪ ,‬ا‪2 I 3‬ى ذج ‪ -‬ه‪G‬ة ‪ ! [/‬ا‪ , N0‬ا ‪,::‬‬
‫ا‪ ,"? O‬وه‪ 5.‬اا ] ‪.YI‬ى ت ;‪- ]? 37"; w:‬ة‪ ،‬آ ان ه‪ 5.‬اا ] ‪2 I‬ي ‬
‫ا ] ة ‪ M‬ا ت وا ‪ -‬ت ‪2:I‬م ‪ M/‬ا" ‪ M‬ا‪ O‬ق ا‪.‬ي ‪ &7I‬ه‪ 5.‬ا‪,7O0‬‬
‫و‪- ]? 37"I‬ة و ‪ ،,‬آ ان ه‪ 5.‬اا ] ‪2:I‬م ‪-‬اء ا‬
‫آ ة ذج ا "‪:‬ة ;‪ 3‬او‪ J‬ت‬
‫‪ : , J‬ر‪ ,‬ا ] ‪2C‬رت ‪ : MJ‬او ‪.!9:‬‬
‫‪D0‬ات إ‪)2‬اد اآة‪:‬‬
‫ه ك ‪27‬ات ‪ !/ 9 ,f9‬ا@هاء ‪@ U‬اد درا‪2 ,‬ا‪ ,7‬ا‬
‫‪2‬ف `‪U‬‬
‫‪ w7‬ا@ ب ا ‪:3‬‬
‫‪16‬‬
‫آ ة و ء ‪2‬ذج ‪S‬‬
Problem formulation
Setting of objectives and overall
project plan
Model conceptualization
Data collection
Model translation
No
Verified?
Yes
No
No
Validated?
Yes
Experimental design
Production runs and analysis
Yes
Yes
More runs?
No
Documentation and
reporting
17
Implementation
‫و‪2‬ف ‪O‬ح آ‪ ,6 M‬آ ‪:3‬‬
‫‪ B4‬او ‪ BJ4‬ا‪: Problem formulation /BJ‬‬
‫وه‪ 5.‬ا‪27‬ة ه‪ 3‬اه‪ %‬ا‪27‬ات ;‪ 3‬ء ‪2‬ذج‬
‫آ ة و‪" %I‬ض وا‪ aV‬وآ ‪ ,/O M‬او‬
‫ا‪ N‬م ا اد درا& و‪ " %I‬ون ‪ R‬وا‪ 3"V‬ا‪:‬ارات وا‪ M6 %U UI !9.‬ه‪ 5.‬ا ‪%X ,/O‬‬
‫و‪2 M/ 3; U"V‬ذج ر‪ 3V 9‬او‪. :6T 927 M J 3‬‬
‫و‪ !S‬اه)اف وا‪ D$‬ا‪: Setting of objectives and overall plan /#J‬‬
‫ا‪0‬هاف ‪2/I‬ن ! ا‪ ,b0‬ا اد ا@‪2 U , -‬ا‪ ,7‬ا‬
‫;‬
‫إذا آ ‪ W‬ا‬
‫آ ة وه ‪ SH9‬ا‪ 3; .0‬ا@ ر‬
‫آ ة ه‪ 3‬ا‪ ,:97‬ا ‪ M ,‬ه‪ 5.‬ا ‪ 3; !9.( ,/O‬ا@ ر ا‪0‬هاف‬
‫ا ‪ 52-‬و‪ !92/I‬ا ‪ ,/O‬ا ‪ ! ]I‬ا‪27‬ة ا ‪ ,:‬و ‪2V‬ء ذ‪ g‬إذا ‪:I‬ر أن ا‬
‫ا‪ ,:97‬ا ‪ SH; M ,‬و‪ RV‬ا‪ ,7‬ا‪, O‬‬
‫وا ‪2‬ارد ا ‪ M 9; ! ,6‬و ‪2‬اد و‬
‫آ ة ه‪3‬‬
‫‪ !/ 9 P‬درا‪ ,‬اا?‪ M‬ا ‪ N ,/‬م‬
‫در ‪ ,‬ا‪.d‬‬
‫‪ W4‬و ‪1‬ء ا‪1‬ذج ‪: Model conceptualization and Building‬‬
‫ ء ‪2‬ذج ‪ N‬م ‪ ,; [email protected] ; "9‬ا ا& ‪ %‬وذ‪ ! ˆ ,0 g‬ا ‪ !/‬ا‪ 7‬ء ‪! ,2 H‬‬
‫ا" ت وا‪2: 3‬د ‪f‬ورة ا ء ‪2‬ذج ;‪ 3‬آ‪ , 6 M‬و‪ !/‬ه ك ‪27‬ط ر?‪!/ 9 ,‬‬
‫ا@هاء ‪ . U‬إن ;! ا ‪ّG"ُ9 ,-.‬ز ‪:‬رة ‪ 9HI‬ا‪2‬اص ا‪ @ ,/O , 0‬ر‬
‫و‪ 927I‬ا`‪ V‬ت ا‪ , 0‬وا‪ G I 3‬ا‪ N‬م و ! ‪ %X‬إ^ ء وز‪ 9‬دة ‪ M' `I‬ا ‪2‬ذج ‪6‬‬
‫‬
‫‪ N - S9:I M‬م و ?] ‪ ,2:‬و‪ ،7 , J‬و‪.U‬ا ; ! ا‪f‬وري اء ‪2‬ذج‬
‫‪ %X w‬ز‪ 9‬دة ا` '‪ M‬ا ‪ S6 , U‬ا‪f‬ورة ه ‪ M‬إ در‪ ,-‬ا"‪ :‬ا ‪ , 27‬وا‪3‬‬
‫‪ SH9T‬ان ‪ ! 9GI‬ا‪U‬ف ا اد ‪ R‬ا‪ 3; .0‬ا@ ر ا& ˆ ! ا‪f‬وري ان ‪2/9‬ن‬
‫ا ‪2‬ذج '‪2‬رة ‪ C‬ا‪ N M'0‬م ا ‪ M 3::‬ان روح ا‪ N‬م ا ‪ 3::‬ه‪ 3‬ا ‪ ., 27‬آ ‪a 9‬‬
‫‪e‬ن ‪2/9‬ن ا ` ! ا ‪2‬ذج ‪ O‬رآ ;‪ R - 3‬ه‪ 5.‬ا ا‪ M6‬وذ‪ .0 g‬و‪N ,U-‬ة ;‪3‬‬
‫ا@ ر و ‪ %U; &I‬وإام ا ?]‪.‬‬
‫=! ا‪ 6‬ت ‪: Data collection‬‬
‫ه ك ‪ ! 3::6 M `I‬ء ا ‪2‬ذج و‪ R -‬ا ت ا‪f‬ور‪ ,9‬ت ;‪:‬ر د‪ ,J‬و' ‪,‬‬
‫ا ت ا ‪:9 ,‬ر ' ‪ ,‬ود‪ ,J‬ا ‪2‬ذج و ‪ 3‬ا ‪ -‬ت وا ?] آ ‪ R - SH9‬ا ت‬
‫ ت أ‪ X‬ء و‪ RV‬ا‪27‬ط ا?‪2 ,‬ذج وز‪ 9‬د‪27I S6 UI‬ر ‪ :"I‬ا ‪2‬ذج آ ان‬
‫ا‪0‬هاف ا ‪ I ,2V2‬د ‪2‬ع ا ت ا ‪27‬ب ‪ [ ; U" -‬درا ‪ N‬م ‪2 C‬ر ‪Y‬ض‬
‫";‪2C ,‬ل ‪2 C‬ر ا@‪ N‬ر و ‪ w2‬ز ! ا@‪ N‬ر ! اه‪ %‬ا ت ا ‪27‬ب ‪ U" -‬أز ‪,‬‬
‫! ا‪2'2‬ل ‪ !? G‬ا ‪2 7 !:‬ر @‪ H9‬د ‪2I‬ز‪ R9‬ز !‬
‫‪18‬‬
‫! ا‪2'2‬ل وأز ‪ ,‬ا ‪,‬‬
‫@‪ H9‬د ‪2I‬ز‪ R9‬ز ! ا ‪ ،%U ,‬و ! ا‪f‬وري ";‪ ,‬ا‪2‬ز‪ "9‬ت ا ر‪) ,9‬ا ‪ (,:‬ا‪f9‬‬
‫ ‪2 Validate 9‬ذج ا‬
‫آ ة‪.‬‬
‫‪ =4‬ا‪1‬ذج ‪: Model translation‬‬
‫ان "‪ %N‬ا‪ , N0‬ا ‪ U ]I ,::‬ذج ‪ I‬ج إ ‪ !9GI‬آ‪ %‬ه ?‪ ! M‬ا "‪ 2‬ت وإ‬
‫‪:‬رة ‪.U; ,92J , 2 6‬ا ‪ , -I SH9‬ا ‪2‬ذج إ ‪2U` M/‬م ! ا ‪ S‬إ‬
‫ا ‪ , 27‬أو إام ‪ , G6‬ا ]‬
‫‪ SIMPROCESS‬و ا ] ا‬
‫‪ , /‬اا ]‬
‫آ ة [‪ GPSS/PC M‬او ‪ SIMAN‬او ‪ ARENA‬او‬
‫آ ة ا ‪.‬آ‪2‬رة أآ[ ‪2J‬ة و و‪ ! ,‬اا ] ا ‪., 2/‬‬
‫[ ؟ ?‪: Verified‬‬
‫‪ّ *ُ#‬‬
‫ا ‪ :‬ه ص ` ‹ إذا‬
‫وا‬
‫آ ن ا ] ا ‪2 %-‬ذج ‪2:9‬م ;" ‪@e‬داء ا ‪27‬ب‬
‫‪ 3`; ، a‬ا ذج ا "‪:‬ة ! ا "‪ ! M S‬ا ‪ , -I M‬ا ‪2‬ذج ‪ &/O‬ا‪M /‬‬
‫‪ a‬وا‪ 3U 6 S9H‬إ ] ‪ -‬و ‪! :‬‬
‫‪ H‬ح ‪ S79 M‬ا‪ 0‬ا‪ ! [/‬ا‬
‫'‪.&6‬‬
‫‪ّ)ُ#‬ق؟ ?‪: Validated‬‬
‫ا ‪2/9 9‬ن ‪ ; 9‬إذا آ ن ا ‪2‬ذج ‪ M/O M[ 9‬د‪ J‬ا‪ N‬م ا ‪ 3::‬و‪9 " %I‬ة ا ‪2‬ذج‬
‫وذ‪ : g‬ر& ‪ R‬ا‪ N‬م ا ‪ 3::‬و‪ ,9"I‬إذا ‪G‬م ا‪ 0‬وه‪/I , 3‬ار‪2/I 6 I ,9‬ن‬
‫ا@; ت ! ا ‪2‬ذج وا‪ N‬م ا ‪ , U 3::‬أو ^ ‪ ،, U‬آ ان ه‪ 5.‬ا" ‪N " 37"I ,‬‬
‫و;‪ %U‬ا ‪ N‬م ا ‪ 3::‬وا ‪2‬ذج‪.‬‬
‫‪ 4‬ا‪T‬رب ‪: Experimental design‬‬
‫;‪ 3‬ه‪ 5.‬ا‪27‬ة د اا?‪ M‬ا اد ;‬
‫@‪-‬اء ا‬
‫آ ة ا?‪ M‬ا‪T‬ى‪ ،‬آ‬
‫‪U‬‬
‫ ‪2‬ذج‪ ،‬و^ ‬
‫‪ "I‬ا ?] ا ‪,:‬‬
‫‪:9‬ر ;‪ 3‬ه‪ 5.‬ا‪27‬ة ‪2C‬ل ;ة اء ‪Initialization‬‬
‫‪ period‬و‪2C‬ل إ‪-‬ا? ت ‪ Simulation runs‬ا‬
‫آ ة ود ا‪/‬ارات ‪ M/‬إ‪-‬اء‪.‬‬
‫ا^=ات ا^= وا‪: Production runs and anaysis /‬‬
‫و‪I‬م ه‪ 5.‬ا‪27‬ة ‪ ˆ9 : 9:‬ا‪0‬داء ‪ N Performance Measures‬م ا‬
‫آ‪.‬‬
‫ه *م _=ات اآ؟ ?‪: More runs‬‬
‫إ دا ‪ M I‬ا@‪-‬ا? ت ا ‪: ,:‬ر ; إذا آ ن ه ك ‪[email protected] ,- 6‬ا? ت إ‪ ,; V‬و ه‪3‬‬
‫اا?‪ M‬ا ‪ !/‬إا & ;‪ 3‬ه‪ 5.‬ا@‪-‬ا? ت‪.‬‬
‫ا` [ وا* ‪: Documentation and reporting‬‬
‫وه‪27 5.‬ة ‪- , U‬ا ‪2:‬م ;‪ X2 U‬اا ] ا ‪ , 2‬و‪ X2I‬ا ‪2‬ذج `& ‪!/ 9 6‬‬
‫إا ‪ ! U‬اي ‪ :6T P6‬آ ا‪` U‬ة ‪-‬ا ! و‪ RV‬ا ‪2‬ذج ا' ‪.9 3/‬آ ‪M' `I‬‬
‫‪19‬‬
‫ & " ز !‪ .‬ا‪ 9:‬ه‪ 2‬ا ‪ ]I‬ا‪ M " 3? U‬آ& وه‪ 2‬ا‪.‬ي ‪:9‬م إ ' ‪ R‬ا‪:‬ار و‪2/9‬ن !‬
‫ا ?] ا ‬
‫‪ R - ! U M‬ا‪27‬ات ا ‪ ,:‬و‪ SH9‬ان ‪2 9‬ي ‹ ‪ Summary‬و‪,H‬‬
‫‪ Conclusion‬وا‪ ! V‬‬
‫‪ R‬ا‪:‬ار‪.‬‬
‫ا‪: Implementation [ 6D‬‬
‫و‪ H‬ح ه‪ 5.‬ا‪27‬ة ‪ H "9‬ح ا‪27‬ات ا ‪ ,:‬و ى ا@‪G‬ام ‪ .- M/O U:7‬و‪SH9‬‬
‫ا‪ ,J‬و ا‪ ,"-‬ا‪ N‬م `ة ‪e 3/‬آ ! ى ‪ H‬ح ا‪ '2‬ت ا‪.,? U‬‬
‫أ‪(4) R- N‬‬
‫‪20‬‬
:‫ا ا‬
Hand Simulation Examples :/#‫ ا‬a.6 ‫ة ا )و‬B‫ا‬
, [
U0 JC‫ إ‬M`YIT‫ ا‬SH9‫آ ة و‬
‫ ا‬M' `I 3; N " 37"I ,9‫آ ة او‬
‫ا‬
.‫ راة‬S‫ او ا‬,‫ي "آ‬H‫† ا‬U9 ‫ وا@اد آ‬,bU‫ا‬
M‫ آ‬O ‫ ا‬M ‫داة‬e‫آ ة آ‬
‫ة ا‬2J ‫ "ض ى‬3/ ,[ ‫ "ة أ‬,9‫و‬9 ‫آ ة‬
‫اء‬- ‫م‬2: ‫ف‬2
:‫ارات‬:‫ ا‬R ‫و‬
Single Channel Queue )‫ اا‬9‫ ر ا‬C : 1 ‫ل‬#
U M `9 3?‫ا‬2O M/O R;‫ ا‬,7: ‫ ?! إ‬G‫ ا‬M 9 .6‫ وا‬S
ˆ` U ‫ل‬2'‫! و‬
& Y' , : M
, ‫ز‬0‫ ا‬5.‫ ? وه‬J‫ د‬8 ‫ و‬1 ! Interarrival times ‫ل‬2'‫! و‬
, ‫أز‬
:3 ‫ول ا‬H‫ ا‬3; ‫ ل آ‬[email protected]‫ا‬
:‫ل‬2'2‫! ا‬
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Time between
Arrivals
(Minutes)
Cumulative
Probability
Probability
Random Numbers
Assignment
1
0.125
0.125
0.0000-0.1250
2
0.125
0.250
0.1251-0.2500
3
0.125
0.375
0.2501-0.3750
4
0.125
0.500
0.3751-0.5000
5
0.125
0.625
0.5001-0.6250
6
0.125
0.750
0.6251-0.7500
7
0.125
0.875
0.7501-0.8750
8
0.125
1.000
0.8751-1.0000
:3 ‫ول ا‬H‫ ا‬3; ‫ت آ‬T 6 ? J‫ د‬6 ‫ و‬1 !
‫اوح‬I Sevice times , ‫ ا‬, ‫أز‬
:, ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬-
Service Time
(Minutes)
Cumulative
Probability
Probability
Random Numbers
Assignment
1
0.10
0.10
0.000-0.100
2
0.20
0.30
0.101-0.300
21
‫‪0.301-0.600‬‬
‫‪0.60‬‬
‫‪0.30‬‬
‫‪3‬‬
‫‪0.601-0.850‬‬
‫‪0.85‬‬
‫‪0.25‬‬
‫‪4‬‬
‫‪0.851-0.950‬‬
‫‪0.95‬‬
‫‪0.10‬‬
‫‪5‬‬
‫‪0.951-1.000‬‬
‫‪1.00‬‬
‫‪0.05‬‬
‫‪6‬‬
‫ا" ‪2‬د‪ !9‬ا‪ 3; !90‬ا‪H‬اول ا ‪2 ,:‬ف `ه ‪ . :6T‬ا ‪27‬ب ‪ M I‬ا‪ N‬م‬
‫آة‬
‫و'‪2‬ل و ‪ 20 ,‬ز ‪. 2‬‬
‫@‪-‬اء ا‬
‫آ ة ‪9‬و‪ 9‬ج إ ‪ 2I‬أز ‪,‬‬
‫! و'‪2‬ل وأز ‪ M/ , ,‬ز ‪2‬ن وذ‪g‬‬
‫ " ‪ ! ,9‬ا‪2‬ز‪ UI "9‬ا "‪ 7‬ة ;‪ 3‬ا‪H‬و! ا ‪ M"` 3/ .!:‬ذ‪ ,:9C ! ` g‬ا ‪M92‬‬
‫ا"‪ Inverse Transform Technique 3/‬وا‪O 3‬ح ` ‪ 3; M‬ب ‪ 2I‬ا ‪Y‬ات‬
‫ا"‪2O‬ا?‪.,‬‬
‫‪2/ -1‬ن ا‪2‬ز‪ R9‬ااآ ‪ 3‬آ ;‪ 3‬ا" ‪2‬د ا[ ‪ ! P‬آ‪- M‬ول‪.‬‬
‫‪ ! -2‬ا‪2‬ز‪ R9‬ااآ ‪; -2 3‬ات ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا "‪.e9 , J M/ ,‬ه ا ‪Y‬‬
‫ا"‪2O‬ا?‪.3‬‬
‫‪ 2 -3‬ر‪2O %J‬ا?‪ 3‬ام (‪., 6 ,‬‬
‫‪ N -4‬إ ا`ة ا‪ U; R:9 3‬ا‪ %J‬ا"‪2O‬ا?‪ ! 3‬ا" ‪2‬د اا ‪ 3; R‬ا‪H‬ول‪ ،‬ا‪%J‬‬
‫ا‪.‬ي ‪ 3; R:9‬ا" ‪2‬د ا‪0‬ول ا ‪ 5.U R‬ا`ة ه‪ 2‬ا ‪ Y‬ا"‪2O‬ا?‪ 3‬ا ‪27‬ب‪.‬‬
‫ام (‪ , 6 ,‬و‪ -‬ا ‪:3‬‬
‫‪-‬ول از ‪,‬‬
‫! ا‪2'2‬ل ‪ !? G‬اـ ‪20‬‬
‫‪Time between‬‬
‫‪Random Number‬‬
‫‪Arrivals‬‬
‫‪Generated‬‬
‫)‪(Minutes‬‬
‫‪Customer‬‬
‫‪8‬‬
‫‪0.8879‬‬
‫‪1‬‬
‫‪4‬‬
‫‪0.4065‬‬
‫‪2‬‬
‫‪1‬‬
‫‪0.0799‬‬
‫‪3‬‬
‫‪7‬‬
‫‪0.8029‬‬
‫‪4‬‬
‫‪8‬‬
‫‪0.9915‬‬
‫‪5‬‬
‫‪1‬‬
‫‪0.0381‬‬
‫‪6‬‬
‫‪6‬‬
‫‪0.7456‬‬
‫‪7‬‬
‫‪5‬‬
‫‪0.5014‬‬
‫‪8‬‬
‫‪2‬‬
‫‪0.1786‬‬
‫‪9‬‬
‫‪22‬‬
10
0.2481
2
11
0.4027
4
12
0.2708
3
13
0.9065
8
14
0.6057
5
15
0.7184
6
16
0.4033
4
17
0.8510
7
18
0.3966
4
19
0.6224
5
20
0.7386
6
:3 ‫ن آ‬2 ‫ ز‬M/ , ‫ ت ا‬J‫و‬0 ‫ول‬- ‫ن‬2/ ,:97‫و `ˆ ا‬
20 ‫ ?! اـ‬G , ‫ ا‬, ‫ول از‬Random Number
Customer
1
Sevice Times
Generated
(Minutes)
0.869
5
2
0.878
5
3
0.623
4
4
0.251
2
5
0.074
1
6
0.952
5
7
0.440
3
8
0.496
3
9
0.878
5
10
0.665
4
11
0.954
5
12
0.627
4
13
0.087
1
14
0.628
4
15
0.354
3
16
0.366
3
17
0.763
4
23
18
0.598
3
19
0.902
5
20
0.302
2
! ‫ول & ز‬0‫ن ا‬2 G‫ أن ا‬,N6 R ،‫ م‬N %‫ ء وره‬X‫ ?! أ‬G‫ ا‬R9 ‫ول‬- ‫ن‬2/ ‫ن‬h‫ا‬
, ! ‫ول آ ان ز ! ;اغ ا دم‬H‫ ! ا‬S 9 ‫آ ة‬
` ‫ ا‬, ! ‫ل‬2'‫! و‬
:‫ '`ا‬S 9 ‫ول‬0‫ن ا‬2 G‫ل ا‬2'‫ و‬6 ` ‫ا‬
:‫آ ة‬
Custom
er
Interarri
Arrival
Servi
Start
of
val
Time
ce
service
End
of
service
Time
‫ ا‬," ‫ول‬-
Time
Time in
Idle time
in
system
of server
Number
Time
queue
1
8
8
5
8
13
0
5
0
2
4
12
5
13
18
1
6
0
3
1
13
4
18
22
5
9
0
4
7
20
2
22
24
2
4
0
5
8
28
1
28
29
0
1
4
6
1
29
5
29
34
0
5
0
7
6
35
3
35
38
0
3
1
8
5
40
3
40
43
0
3
2
9
2
42
5
43
48
1
6
0
10
2
44
4
48
52
4
8
0
11
4
48
5
52
57
4
9
0
12
3
52
4
57
61
5
9
0
13
8
60
1
61
62
1
2
0
14
5
65
4
65
69
0
4
3
15
6
71
3
71
74
0
3
2
16
4
75
3
75
78
0
3
1
17
7
82
4
82
86
0
4
4
18
4
86
3
86
89
0
3
0
19
5
91
5
91
96
0
5
2
20
6
97
2
97
99
0
2
1
Totals
96
23
94
20
71
24
‫ م‬N ‫داء‬0‫ˆ ا‬9 : -2 ‫ول ا‬H‫! ا‬
,:J‫ د‬1.15= 23/20 = !? G‫د ا‬/‫ ر‬[email protected]‫ ر=ز ! ا‬[email protected]‫ ز ! ا‬w2 -1
0.4= 8/20=!? G‫ د ا‬/‫وا‬N‫! ا‬9.‫ ?! ا‬G‫ر =د ا‬2 7‫ ا‬3; ‫ ر‬[email protected]‫ ل ا‬6‫ إ‬-2
%78 ‫ أي‬0.78= 20/91 -1= 3/‫ ! ا‬G‫ا‬/‫ ز ! ا`اغ‬-1=‫ ا دم‬, "; -3
,:J‫ د‬3.55=71/20=!? G‫د ا‬/, ‫ ا‬, ‫ع از‬2 H =, ‫ ز ! ا‬w2 -4
4.8= 96/20=!? G‫ د ا‬/‫ل‬2'2‫! ا‬
, ‫ع از‬2 H =‫ل‬2'2‫! ا‬
, ‫ از‬w2 -5
,:J‫د‬
23/8=‫وا‬N‫! ا‬9.‫ ?! ا‬G‫ د ا‬/‫ ر‬[email protected]‫وا= ز ! ا‬N‫ ر ! ا‬[email protected]‫ ز ! ا‬w2 -6
,:J‫ د‬2.875=
,:J‫ د‬4.7= 94/20=!? G‫د ا‬/‫ م‬N‫ ا‬3; ‫ث‬2/ ‫ م= ز ! ا‬N ‫ث‬2/ ‫ ز ! ا‬w2 -7
:. ‫ ا‬#)$/ B ‫ أ) و‬:2 ‫ل‬#
.‫ر‬2 C _' ‫د اآ[ ! ر او‬2-‫آ ة و‬
‫ ا‬,:9C ‫ ض‬2‫ا ا [ ل ه‬.‫ض ! ه‬Y‫ا‬
‫ رات‬S7‫ ا‬M'2I‫ و‬.0 ! ‫ ت د‬7‫ ا‬,I ‫م‬2:9 ‫ رات‬,"9 , %"7
:, ‫ل ا‬2'2‫! ا‬
, ‫ از‬R9‫ز‬2I S6 %"7 ‫ ا رات إ ا‬M I .%"7 ,'‫ا‬2‫ا‬
:‫ل‬2'2‫! ا‬
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Time between
Arrivals
(Minutes)
Cumulative
Probability
Probability
Random Numbers
Assignment
1
0.25
0.25
0.000-0.250
2
0.40
0.65
0.251-0.650
3
0.20
0.85
0.651-0.850
4
0.15
1.00
0.851-1.000
S^‫ ا‬,f`9 g.‫ )و‬/ ! ‫رة وة‬J [‫ اآ‬6‫ ا‬،/ 3 [‫ وا‬6‫ ا‬%‫ه‬6‫ ا‬9 ! ‫ا د‬
3‫ ه‬/ ‫ و‬6‫ ! ا‬M/ , ‫ ا‬, ‫ از‬R9‫ز‬2I ،!? G‫ ا‬, 3; ‫ ?!( آ ا& اع‬G‫ا‬
:3‫ا‬2‫ا‬
: 60 , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
(Minutes)
Cumulative
Probability
Probability
25
Random Numbers
Assignment
2
0.30
0.30
0.000-0.300
3
0.28
0.58
0.301-0.580
4
0.25
0.83
0.581-0.830
5
0.17
1.00
0.831-1.000
:/ , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
Cumulative
(Minutes)
Probability
Random Numbers
Probability
Assignment
3
0.35
0.35
0.000-0.350
4
0.25
0.60
0.351-0.600
5
0.20
0.80
0.601-0.800
6
0.20
1.00
0.801-1.000
.&?‫ أدا‬,;" ‫ م‬N‫آ ة ا‬
‫آة‬
‫ب‬27 ‫ا‬
‫ ا‬M6‫! ا‬9 3 ‫ول ا‬H‫ا‬
Ahmad
Bakur
_______________________________________________
Cus
Random
Tomer Number
Time
Clock
Random
between Time of Number
Time
Time
Sevice Service Service
No.
for Arrivals Arrival Arrival
for Service Start
1
0.99284
4
4
0.398244
2
0.463490
2
6
0.485853
-
3
0.654933
3
9
0.018479
9
4
0.008010
1
10
0.375450
-
5
0.017539
1
11
0.380226
11
6
0.027118
1
12
0.071695
7
0.294307
2
14
0.794733
8
0.703278
3
17
9
0.305171
2
10
0.029153
11
0.294875
12
13
Time
Sevice
Time
Sevice Service
Time
in
Time
Ends
Start
Time
Ends
3
7
-
-
-
-
-
6
4
10
0
2
11
-
-
-
0
-
-
10
4
14
0
3
14
-
-
-
0
14
2
16
-
-
-
2
-
-
-
14
5
19
0
0.048615
17
2
19
-
-
-
0
19
0.744830
19
4
23
-
-
-
0
1
20
0.082780
-
-
-
20
3
23
0
2
22
0.913267
23
5
28
-
-
-
1
0.846545
3
25
0.625406
-
-
-
25
5
30
0
0.991276
4
29
0.987133
29
5
34
-
-
-
0
14
0.684252
3
32
0.641578
-
-
-
32
5
37
0
15
0.642370
2
34
0.416842
34
3
37
-
-
-
0
16
0.369203
2
36
0.916370
37
5
42
-
-
-
1
17
0.222240
1
37
0.712437
-
-
-
37
5
42
0
18
0.437991
2
39
0.770969
42
4
46
-
-
-
3
4
Queue
0
19
0.119146
1
40
0.061159
-
-
-
42
3
45
2
20
0.662990
3
43
0.934648
-
-
-
45
6
51
2
21
0.288916
2
45
0.923251
46
5
51
-
-
-
1
26
‫‪2‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪54‬‬
‫‪3‬‬
‫‪51‬‬
‫‪0.355554‬‬
‫‪49‬‬
‫‪4‬‬
‫‪0.903758‬‬
‫‪22‬‬
‫‪0‬‬
‫‪58‬‬
‫‪5‬‬
‫‪53‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪0.682907‬‬
‫‪53‬‬
‫‪4‬‬
‫‪0.948593‬‬
‫‪23‬‬
‫‪0‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪58‬‬
‫‪3‬‬
‫‪55‬‬
‫‪0.379748‬‬
‫‪55‬‬
‫‪2‬‬
‫‪0.375286‬‬
‫‪24‬‬
‫‪1‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪60‬‬
‫‪2‬‬
‫‪58‬‬
‫‪0.273077‬‬
‫‪57‬‬
‫‪2‬‬
‫‪0.273955‬‬
‫‪25‬‬
‫‪0‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪63‬‬
‫‪3‬‬
‫‪60‬‬
‫‪0.358811‬‬
‫‪60‬‬
‫‪3‬‬
‫‪0.664870‬‬
‫‪26‬‬
‫‪0‬‬
‫‪67‬‬
‫‪6‬‬
‫‪61‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪0.831475‬‬
‫‪61‬‬
‫‪1‬‬
‫‪0.125086‬‬
‫‪27‬‬
‫‪0‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪68‬‬
‫‪4‬‬
‫‪64‬‬
‫‪0.736537‬‬
‫‪64‬‬
‫‪3‬‬
‫‪0.804005‬‬
‫‪28‬‬
‫‪1‬‬
‫‪72‬‬
‫‪5‬‬
‫‪67‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪0.755743‬‬
‫‪66‬‬
‫‪2‬‬
‫‪0.431573‬‬
‫‪29‬‬
‫‪0‬‬
‫‪-‬‬
‫‪-‬‬
‫‪-‬‬
‫‪72‬‬
‫‪3‬‬
‫‪69‬‬
‫‪0.389873‬‬
‫‪69‬‬
‫‪3‬‬
‫‪0.785686‬‬
‫‪30‬‬
‫‪16‬‬
‫ة ا‬
‫‪56‬‬
‫‪61‬‬
‫‪Totals‬‬
‫‪69‬‬
‫آ ة ‪ 72‬د‪,:J‬‬
‫‪ , "; -1‬أ‪ 0.847 = 61/72 = 6‬أو ‪%85‬‬
‫‪ 0.777 = 56/72 = / , "; -2‬أو ‪%78‬‬
‫‪ -3‬د ا‪ %U !9.‬أ‪ 30 ! 18 = 6‬أي ‪ ! %60‬ا‪!? G‬‬
‫‪ w2 -4‬ز ! ا ‪ 3.39= 61/18 = 60 ,‬د‪ J) ,:J‬ر‪ , : U‬ا ‪(,::‬‬
‫‪ -5‬د ا‪ 30 ! 12 =/ %U !9.‬أو ‪ ! %40‬ا‪!? G‬‬
‫‪ w2 -6‬ز ! ا ‪ 4.67 = 56/12 = / ,‬د‪ J) ,:J‬ر‪ , : U‬ا ‪(,::‬‬
‫‪ w2 -7‬ز ! ا@‪ N‬ر ‪ 0.53 = 16/30 = R H‬د‪,:J‬‬
‫‪ w2 -8‬ز ! ا@‪ N‬ر ! ا‪N‬وا ;"= ‪ 1.6 = 16/10‬د‪,:J‬‬
‫‪ w2 -9‬ز !‬
‫! ا‪2'2‬ل= ‪ 2.3 = 69/30‬د‪ J) ,:J‬ر‪ , : U‬ا ‪(,::‬‬
‫‪ -10‬إ‪ 6‬ل ان ا‪2 G‬ن ‪0.33 = 10/30=N9‬‬
‫‪ w2 -11‬ز ! ا ‪2/‬ث ;‪ 3‬ا‪ N‬م= ‪ 2.4 = 72/30‬د‪,:J‬‬
‫‪#‬ل ‪ ! /BJ# :3‬ا‪:9‬‬
‫ه‪ N 3; ,9:I ,/O 5.‬م ا ‪G‬ون و‪O "I‬اء و ‪ R? ._ ' R‬ا‬
‫ا‪2‬ا‪6‬ة ـ ‪ 150‬ه‪ ,‬و‪ U"9‬ـ ‪ 200‬ه‪ ،,‬ا‬
‫" ‪ 10‬ه‪ ,‬‬
‫_ ‪O9‬ي ا‬
‫_ ا ‪ ,9 U ,:‬ا‪2‬م ‪ I‬ع ‬
‫`‪ ,‬ا‪2‬ا‪6‬ة‪O9 .‬ي ا ?‪ R‬ا‬
‫`‪,‬‬
‫‪J R‬ا‪ˆC‬‬
‫_ ! ا ‪2‬زع ;‪G6 3‬م ‪2/I‬ن ! ‪10‬‬
‫' _ )أي ‪ &/ 9‬اء ‪ 10‬او ‪ 20‬او ‪ 30‬وه‪./‬ا‪ 3; ,` ' ...‬آ‪ M‬ة(‪ .‬ا‪ S7‬ا‬
‫_‬
‫‪2 "9‬ع ا‪ 0‬ر ;‪ 3‬ذ‪ g‬ا‪2‬م ;‪ U‬ك ‪29‬م أ ر ‪ -‬و‪29‬م أ ر ‪ w2‬و‪29‬م أ ر‬
‫‪T 6 _"V‬ت ا‪2‬ا‪ 0.35 3‬و ‪ 0.45‬و ‪2I 0.20‬ز‪ R9‬ا‪ S7‬ا‬
‫‪2 S6‬ع أ‪ 0‬ر ه‪ 3; 2‬ا‪H‬ول ا ‪:3‬‬
‫‪27‬‬
‫_ ‪29 M/‬م‬
Demand Probability Distribution
___________________________________________
Demand
Good
Fair
Poor
40
0.03
0.10
0.44
50
0.05
0.18
0.22
60
0.15
0.40
0.16
70
0.20
0.20
0.12
80
0.35
0.08
0.06
90
0.15
0.04
0.00
100
0.07
0.00
0.00
._
‫ ا‬R? U9O9 3‫_ ا‬
‫ "د ا‬M[ 0‫ ا"د ا‬9 I ‫ب‬27 ‫ا‬
:,J"‫ ! ا‬S 9 ‫ي‬.‫ وا‬3 2‫ ا‬a ‫ و د ا‬29 20 ‫ م ة‬N‫ ا‬3‫ف آ‬2
Revenue
Profit =
Cost of
Lost profit from
-
-
From Sales newspapers
Salvage from sale
+
excess demand
‫ آ ع‬.: ‫ ا‬+ S7‫ دة ا‬9‫ ! ز‬R? f‫ ا‬a ‫_ – ا‬
of scrap papers
‫ – "ا‬R‫ ا‬3; ' = a ‫ا‬
ˆC‫ا‬:
:‫ ان‬H ,/O ‫! ح ا‬
, ‫_ ا‬
‫اة‬O ‫_ ا‬
(‫اة‬O ‫_ ا‬
‫ – د ا‬, 27 ‫_ ا‬
‫ اآ ! د ا‬, 27 ‫_ ا‬
‫اة – د ا‬O ‫_ ا‬
., 27 ‫_ ا‬
‫آة‬
%X 29 _
(‫اة‬O ‫_ ا‬
.!/ 9
‫ * د ا‬150 = _
‫" ا‬
‫ * )د ا‬50 = S7‫ دة ا‬9‫ ! ز‬R? f‫ ا‬a ‫ا‬
‫اة‬O ‫_ ا‬
‫( ان‬, 27 ‫_ ا‬
‫ * د ا‬200 = R‫ ا‬3; '
‫ن د ا‬2/I ‫ان‬
‫ * ) د ا‬10 = ˆC‫ا‬: ‫ آ ع‬.: ‫ا‬
‫اة اآ ! د ا‬O ‫_ ا‬
‫ اء د "! ! ا‬, 3I SH9 ‫آ ة‬
,/O ‫ ا‬5.‫ ه‬M ‫ د ا‬3‫ )وه‬, ‫ ا‬،3 2‫ ا‬a ‫ ا‬9 I‫ و‬29 20 ‫_ ة‬
‫ ه اآ‬a ‫ن ا‬2/9 3‫اة ا‬O ‫_ ا‬
‫ د ا‬M
‫ن د ا‬2/I
‫ ا‬S7‫ا‬
6 YI 5.‫ه‬
:‫ ر‬0‫م ا‬29 ‫ع‬2 R9‫ز‬2 , ‫اول ا‬H‫ا‬
28
Cumulative
Type of Newsday
Probability
Probability
Random Numbers
Assignment
Good
0.35
0.35
0.000-0.350
Fair
0.45
0.80
0.351-0.800
Poor
0.20
1.00
0.801-1.000
:‫ ر‬0‫م ا‬29 ‫ع‬2 S6 _
Cumulative Probability
‫ ا‬S7‫ ا‬R9‫ز‬2 3 ‫ول ا‬H‫وا‬
Random Numbers Assignment
__________________________________________________
Demand Good Fair Poor
Good
Fair
Poor
40
0.03
0.10 0.44
0.000-0.030 0.000-0.100 0.000-0.440
50
0.08
0.28 0.66
0.031-0.080 0.101-0.280 0.441-0.660
60
0.23
0.68 0.82
0.081-0.230 0.281-0.680 0.661-0.820
70
0.43
0.88 0.94
0.231-0.430
0.681-0.880 0.821-0.940
80
0.78
0.96 1.00
0.431-0.780
0.881-0.960 0.941-1.000
90
0.93
1.00 1.00
0.781-0.930
0.961-1.000
100
1.00
1.00 1.00
0.931-1.000
:3 2‫ ا‬a ‫ ب ا‬6‫م و‬29 20 ‫ ة‬29 ,` ' 70 ‫آ ة اء‬
T‫و‬- ‫ن‬2/ ‫ف‬2
Random
Numbers for
Type of
Day Newsday
Type of
Random
Revenue Lost Profits
Salvage
Numbers for
from
from Excess
from Sale
Daily
Demand of
Scrap
Profit
Newsday Demand
Demand Sales
1
0.668258
Fair
0.516101
60
12000
-
500
2000
2
0.059141
Good
0.421215
70
14000
-
-
3500
3
0.844465
Poor
0.122752
40
8000
-
1500
-1000
4
0.575663
Fair
0.417585
60
12000
-
500
2000
5
0.777212
Fair
0.873137
70
14000
-
-
3500
6
0.721669
Fair
0.028883
40
8000
-
1500
-1000
7
0.940940
Poor
0.442408
40
8000
-
1500
-1000
8
0.739749
Fair
0.154498
50
10000
-
1000
500
9
0.322162
Good
0.789384
80
16000
2000
-
3500
10
0.933698
Poor
0.948650
70
14000
-
-
3500
29
11
0.682856
Fair
0.462126
60
12000
-
500
2000
12
0.948467
Poor
0.427917
40
8000
-
1500
-1000
13
0.321750
Good
0.436062
70
14000
-
-
3500
14
0.576449
Fair
0.852654
70
14000
-
-
3500
15
0.469982
Fair
0.664128
60
12000
-
500
2000
16
0.325208
Good
0.551011
80
16000
-
3500
17
0.119710
Good
0.149210
60
12000
500
2000
18
0.526681
Fair
0.992919
90
18000
-
3500
19
0.355738
Fair
0.339435
60
12000
-
500
2000
20
0.734686
Fair
0.231963
50
10000
-
1000
500
244000
8000
2000
4000
11000
‫ أ س‬,‫ ه‬1850 2‫ ه‬3 2‫ ا‬a ‫ ا‬w2 ‫ أن‬29 20 ‫آ ة‬
‫ و‬50 ‫ و‬40 ‫ى )اء‬0‫آ ة ا ت ا‬
37000
! ‫ول‬H‫“ ! ا‬6
!9 ‫ آ‬S 7 ‫ك‬9 . 29 ,` ' 70 &?‫ا‬
(‫م‬2‫ ا‬3; ,` ' 100‫ و‬90 ‫ و‬80 ‫ و‬60
:>$‫ ا‬A /BJ# :4 ‫ل‬#
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬R9 !" ] 3 2‫اء ا‬O‫ ا‬SC
Daily Demand
0
1
2
3
4
Probability
0.33
0.25
0.20
0.12
0.10
SC %9 ‫ات‬6‫ و‬6 ‫ وي‬9 ‫ ! او‬MJ‫ ا& ا‬-‫ م ;ذا و‬9‫ ا‬," M‫ا ا ] آ‬.‫ون ! ه‬G ‫` ‹ ا‬9
" : I ‫ )أي‬,f92"I ‫ ت‬C .AIT‫د و‬2-2 ‫ون ا‬G ‫را‬: : I ,C ‫ أي‬.‫ات‬6‫ و‬10
S7‫ ا‬RV‫! و‬6 ! ‫ع‬27: ‫ ! ا‬G‫ ا‬2‫ )وه‬Lead Time ‫م‬:‫ ز ! ا‬.(9- ‫ون‬G ‫ل‬2'‫و‬
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬R9 (&2'‫ و‬6
Lead Time (Days)
1
2
3
Probability
0.3
0.5
0.2
30
‫ا ! اول ا‪20‬ع إذا آ ن ا ‪G‬ون اا?‪ 12 3‬و‪6‬ة و‪ C -2IT‬ت ;‪ R‬ا ‪G‬ون "‬
‫; آ‪9 3‬و‪ 6 9‬أ ‪.U R‬ا ا‪ N‬م ‪6 .‬د ‪ ,‬ا‪ 90‬م ا‪6 3‬ث ;‪ ,C : I 3; ‹: U‬و‪,‬‬
‫ا‪62‬ات ا‪ WC 3‬و‪ : I %‬و ‪ w2‬د ا‪62‬ات ا ‪O , 27‬اء ا‪. 2‬‬
‫ا ‪:M‬‬
‫‬
‫آ ة او‪2/ ,9‬ن ا‪H‬اول ا ‪:,‬‬
‫ول " ‪ ,9‬ا‪ S7‬ا‪:3 2‬‬‫‪Cumulative Probability‬‬
‫‪Random Number‬‬
‫‪Probability‬‬
‫‪Demand‬‬
‫‪0.00 – 0.33‬‬
‫‪0.33‬‬
‫‪0.33‬‬
‫‪0‬‬
‫‪0.34 – 0.58‬‬
‫‪0.58‬‬
‫‪0.25‬‬
‫‪1‬‬
‫‪0.59 – 0.78‬‬
‫‪0.78‬‬
‫‪0.20‬‬
‫‪2‬‬
‫‪0.79 – 0.90‬‬
‫‪0.90‬‬
‫‪0.12‬‬
‫‪3‬‬
‫‪0.91 – 1.00‬‬
‫‪1.00‬‬
‫‪0.10‬‬
‫‪4‬‬
‫ول " ‪ ,9‬ز ! ا‪:‬م‪:‬‬‫‪Random Number‬‬
‫ا‬
‫‪Cumulative Probability‬‬
‫‪Probability‬‬
‫‪Lead Time‬‬
‫‪0.00 – 0.30‬‬
‫‪0.3‬‬
‫‪0.3‬‬
‫‪1‬‬
‫‪0.31 – 0.80‬‬
‫‪0.8‬‬
‫‪0.5‬‬
‫‪2‬‬
‫‪0.81 – 1.00‬‬
‫‪1.0‬‬
‫‪0.2‬‬
‫‪3‬‬
‫آ ة‪:‬‬
‫ا‪6'f‬ع اول‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 12 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.419225 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 11 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.672281 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:P‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 9 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.556692 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫‪31‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.179291 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.066128 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.136442 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.219630 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا‪0‬ول ‪ ! :I‬ا ‪G‬ون ‪ 8‬و‪6‬ات‬
‫‪ ,H‬ا` ‹‪.,C RfIT :‬‬
‫ا'‪6‬ع ا‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.345517 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 7 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.520493 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:P‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.616346 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 4 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.639711 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 2 :‬و‪6‬ات‪.‬‬
‫‪32‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.330888 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 2 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.949622 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫)‪ ‹: , 6‬و‪(!I6‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.640219 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫)‪ ‹: , 6‬و‪(!I6‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا[ ‪ ! :9 % 3‬ا ‪G‬ون † و‪6‬ث ‪ 4 ‹:‬و‪6‬ات‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.315576 3‬ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫ا'‪6‬ع ا ‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.753165 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫)‪ ‹: , 6‬و‪(!I6‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.132686 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪) :P‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.203047 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.592781 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.641142 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫‪33‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.711578 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 4 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.976901 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا[ ‪ ! :9 % P‬ا ‪G‬ون † و‪ 9 %‬ث ‪.‹:‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.612898 3‬ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫ا'‪6‬ع اا !‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.940874 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫)‪ 4 ‹: , 6‬و‪6‬ات(‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.830444 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 3‬و‪6‬ة‪.‬‬
‫)‪ 3 ‹: , 6‬و‪6‬ات(‬
‫ا‪2‬م ا[ ‪) :P‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.761498 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.823155 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 3‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 5 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.996509 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 1 :‬و‪6‬ة‪.‬‬
‫‪34‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.382630 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.018751 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع اا ‪ ! :9 % R‬ا ‪G‬ون † و‪6‬ث ‪ 7 ‹:‬و‪6‬ات‪.‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.015373 3‬ز ! ا‪:‬م ‪29 1‬م‪.‬‬
‫ا'‪6‬ع ا‪:"#$‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.599484 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫)‪ 2 ‹: , 6‬و‪6‬ات(‬
‫ا‪2‬م ا[ ‪) :3‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.583797 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:P‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 9 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.835045 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 3‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.362963 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 5 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.699827 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 3 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.089972 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 3 :‬و‪6‬ات‪.‬‬
‫‪35‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.155004 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا ˆ ‪ ! :I‬ا ‪G‬ون ‪ 3‬و‪6‬ات و‪6‬ث ‪ 2 ‹:‬و‪6‬ة ;‪ 3‬ا‪ ,9‬ا‪20‬ع‪.‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.424699 3‬ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫ا'‪6‬ع ا دس‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 3 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.373323 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 2 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.379252 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪) :P‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 11 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.630487 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 9 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.584059 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.138283 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.615948 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.928577 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا دس ‪ ! :I‬ا ‪G‬ون ‪ 2‬و‪6‬ات و‪ 9 %‬ث ‪.‹:‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.892844 3‬ز ! ا‪:‬م ‪ 3‬ا‪ 9‬م‪.‬‬
‫‪36‬‬
‫)‪ ,9 U‬ا‬
‫آ ة(‬
‫و‪ Rf‬ا ?] ;‪- 3‬ول آ ‪:3‬‬
‫ا‪ 90‬م‬
‫ا ‪G‬ون‬
‫ا‪%J‬‬
‫ا ‪2-2‬د‬
‫ا"‪2O‬ا?‪3‬‬
‫‪:I‬‬
‫ا‪S7‬‬
‫ا ‪G‬ون‬
‫!‬
‫‪,H‬‬
‫ا‪‹:‬‬
‫ا` ‹‬
‫‪S7‬‬
‫ا‪%J‬‬
‫ز!‬
‫ا"‪2O‬ا?‪3‬‬
‫ا‪:‬م‬
‫‪2'2‬ل‬
‫ا‪,7‬‬
‫ا‪20‬ع )‪(1‬‬
‫ا‪2‬م ا‪0‬ول‬
‫‪12‬‬
‫‪0.419225‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪11‬‬
‫‪0.672281‬‬
‫‪2‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪9‬‬
‫‪0.556692‬‬
‫‪1‬‬
‫ا‪2‬م اا ‪R‬‬
‫‪8‬‬
‫‪0.179291‬‬
‫‪0‬‬
‫ا‪2‬م ا ˆ‬
‫‪8‬‬
‫‪0.066128‬‬
‫‪0‬‬
‫ا‪2‬م ا دس‬
‫‪8‬‬
‫‪0.136442‬‬
‫‪0‬‬
‫ا‪2‬م ا ‪R‬‬
‫‪8‬‬
‫‪0.219630‬‬
‫‪0‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪8‬‬
‫‪4‬‬
‫‪8‬‬
‫‪,C RfIT‬‬
‫‪0‬‬
‫ا‪20‬ع)‪(2‬‬
‫ا‪2‬م ا‪0‬ول‬
‫‪8‬‬
‫‪0.345517‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪7‬‬
‫‪0.520493‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪6‬‬
‫‪0.616346‬‬
‫‪2‬‬
‫ا‪2‬م اا ‪R‬‬
‫‪4‬‬
‫‪0.639711‬‬
‫‪2‬‬
‫ا‪2‬م ا ˆ‬
‫‪2‬‬
‫‪0.330888‬‬
‫‪0‬‬
‫ا‪2‬م ا دس‬
‫‪2‬‬
‫‪0.949622‬‬
‫‪4‬‬
‫‪2‬‬
‫ا‪2‬م ا ‪R‬‬
‫‪0‬‬
‫‪0.640219‬‬
‫‪2‬‬
‫‪2‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪0‬‬
‫‪12‬‬
‫‪0‬‬
‫‪10,C RV‬‬
‫‪4‬‬
‫‪0.315576‬‬
‫‪2‬‬
‫ا‪20‬ع)‪(3‬‬
‫ا‪2‬م ا‪0‬ول‬
‫‪0‬‬
‫‪0.753165‬‬
‫‪2‬‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪0‬‬
‫‪0.132686‬‬
‫‪0‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪10‬‬
‫‪0.203047‬‬
‫‪0‬‬
‫ا‪2‬م اا ‪R‬‬
‫‪10‬‬
‫‪0.592781‬‬
‫‪2‬‬
‫ا‪2‬م ا ˆ‬
‫‪8‬‬
‫‪0.641142‬‬
‫‪2‬‬
‫ا‪2‬م ا دس‬
‫‪6‬‬
‫‪0.711578‬‬
‫‪2‬‬
‫ا‪2‬م ا ‪R‬‬
‫‪4‬‬
‫‪0.976901‬‬
‫‪4‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪0‬‬
‫‪2‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪12‬‬
‫‪0‬‬
‫‪10,C RV‬‬
‫‪2‬‬
‫ا‪20‬ع)‪(4‬‬
‫ا‪2‬م ا‪0‬ول‬
‫‪0‬‬
‫‪0.940874‬‬
‫‪4‬‬
‫‪4‬‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪0‬‬
‫‪0.830444‬‬
‫‪3‬‬
‫‪3‬‬
‫‪37‬‬
‫‪0.612898‬‬
‫‪2‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪10‬‬
‫‪0.761498‬‬
‫‪2‬‬
‫ا‪2‬م اا ‪R‬‬
‫‪8‬‬
‫‪0.823155‬‬
‫‪3‬‬
‫ا‪2‬م ا ˆ‬
‫‪5‬‬
‫‪0.996509‬‬
‫‪4‬‬
‫ا‪2‬م ا دس‬
‫‪1‬‬
‫‪0.382630‬‬
‫‪1‬‬
‫ا‪2‬م ا ‪R‬‬
‫‪0‬‬
‫‪0.018751‬‬
‫‪0‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪0‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪17‬‬
‫‪0‬‬
‫‪7‬‬
‫‪10,C RV‬‬
‫‪0.015373‬‬
‫‪1‬‬
‫ا‪20‬ع)‪(5‬‬
‫ا‪2‬م ا‪0‬ول‬
‫‪0‬‬
‫‪0.599484‬‬
‫‪2‬‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪10‬‬
‫‪0.583797‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪9‬‬
‫‪0.835045‬‬
‫‪3‬‬
‫ا‪2‬م اا ‪R‬‬
‫‪6‬‬
‫‪0.362963‬‬
‫‪1‬‬
‫ا‪2‬م ا ˆ‬
‫‪5‬‬
‫‪0.699827‬‬
‫‪2‬‬
‫ا‪2‬م ا دس‬
‫‪3‬‬
‫‪0.089972‬‬
‫‪0‬‬
‫ا‪2‬م ا ‪R‬‬
‫‪3‬‬
‫‪0.155004‬‬
‫‪0‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪3‬‬
‫‪2‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪9‬‬
‫‪3‬‬
‫‪2‬‬
‫‪10,C RV‬‬
‫‪0.424699‬‬
‫‪2‬‬
‫ا‪20‬ع)‪(6‬‬
‫ا‪2‬م ا‪0‬ول‬
‫‪3‬‬
‫‪0.373323‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪2‬‬
‫‪0.379252‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪11‬‬
‫‪0.630487‬‬
‫‪2‬‬
‫ا‪2‬م اا ‪R‬‬
‫‪9‬‬
‫‪0.584059‬‬
‫‪1‬‬
‫ا‪2‬م ا ˆ‬
‫‪8‬‬
‫‪0.138283‬‬
‫‪0‬‬
‫ا‪2‬م ا دس‬
‫‪8‬‬
‫‪0.615948‬‬
‫‪2‬‬
‫ا‪2‬م ا ‪R‬‬
‫‪6‬‬
‫‪0.928577‬‬
‫‪4‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪2‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪11‬‬
‫‪2‬‬
‫‪0‬‬
‫‪10,C RV‬‬
‫‪0.892844‬‬
‫ا‪:g1‬‬
‫ا‪20‬ع‬
‫ا‪S7‬‬
‫د ا‪ 90‬م ا‪6 3‬ث ;‪‹: U‬‬
‫ا‪ ) ‹:‬ا‪ S7‬ا‪(R? f‬‬
‫‪1‬‬
‫‪4‬‬
‫‪0‬‬
‫‪0‬‬
‫‪2‬‬
‫‪12‬‬
‫‪2‬‬
‫‪4‬‬
‫‪3‬‬
‫‪12‬‬
‫‪1‬‬
‫‪2‬‬
‫‪4‬‬
‫‪17‬‬
‫‪2‬‬
‫‪7‬‬
‫‪5‬‬
‫‪9‬‬
‫‪1‬‬
‫‪2‬‬
‫‪6‬‬
‫‪11‬‬
‫‪0‬‬
‫‪0‬‬
‫ا ‪2 H‬ع‬
‫‪65‬‬
‫‪6‬‬
‫‪15‬‬
‫‪38‬‬
‫‪3‬‬
.‫ م‬90‫ ! ا‬14.3% ‫‹ اي‬: U; ‫ث‬6 ‫ م‬9‫ أ‬6 ‫ه ك‬
.R? f‫ ا‬S7‫ ا‬, 23.07% ‫ة أي‬6‫ و‬15 3‫ ه‬: I %‫ و‬WC 3‫ات ا‬62‫د ا‬
3‫ات ا‬62‫ ا ! د ا‬3‫ة وه‬6‫ و‬10.83 2‫اء ا‬O , 27 ‫ات ا‬62‫ د ا‬w2
. UC %9
:-/D‫)) ا‬4 /BJ# 5 ‫ل‬#
‫ "د‬3 [email protected]‫ أ‬R9‫ز‬2‫ ا‬. 29 ‫"ه‬9 3‫ ا‬G‫ أ‬,`^‫ د أر‬w2 9 I !9‫ ا ز‬6‫ أ‬99
:‫ول‬H 7"9 29 !? G‫ا‬
Number of Customers/Day
8
10
12
14
Probability
0.35
0.30
0.25
0.10
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬S6 ,`^‫ر‬0‫ي د ! ا‬O9 ‫ن‬2 ‫ ز‬M‫آ‬
Number of Loafs/Customer
4
8
12
16
Probability
0.4
0.3
0.2
0.1
. 29 ‫"ه ا ز‬9 3‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫د‬6‫ و‬M ‫ م‬9‫ أ‬, 9‫و‬9 3‫ آ‬6
:M ‫ا‬
‫م‬29 M/ !? G‫( "د ا‬1) ‫ول‬- "
Number of Customers
CDF
Random Number
8
0.35
0.01 - 0.35
10
0.65
0.36 - 0.65
12
0.90
0.66 – 0.90
14
1
0.91 - 1
‫ن‬2 ‫ ز‬M/ ,`^‫ر‬0‫( "د ا‬2) ‫ول‬- "
39
Number of Loafs
CDF
Random Number
4
0.40
0.01 - 0.40
8
0.70
0.41 - 0.70
12
0.90
0.71 – 0.90
16
1
0.91 - 1
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.25 :‫ول‬0‫م ا‬2‫ا‬
Customer Number
R
Number of Loafs
1
0.01
04
2
0.93
16
3
0.70
08
4
0.66
08
5
0.74
12
6
0.79
12
7
0.47
08
8
0.68
08
Total = 76
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.18 :3 [‫م ا‬2‫ا‬
Customer Number
R
Number of Loafs
1
0.88
12
2
0.07
04
3
0.99
16
4
0.51
08
5
0.04
04
6
0.01
04
7
0.43
08
8
0.60
08
Total = 64
10 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.59 :P [‫م ا‬2‫ا‬
40
Customer Number
R
Number of Loafs
1
0.55
08
2
0.64
08
3
0.10
04
4
0.61
08
5
0.22
04
6
0.85
12
7
0.42
08
8
0.01
04
9
0.98
16
10
0.05
04
Total = 76
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.20 :R ‫م اا‬2‫ا‬
Customer Number
R
Number of Loafs
1
0.11
04
2
0.23
04
3
0.68
08
4
0.41
08
5
0.96
16
6
0.48
08
7
0.11
04
8
0.59
08
Total = 60
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.11 :ˆ ‫م ا‬2‫ا‬
Customer Number
R
Number of Loafs
1
0.10
04
2
0.25
04
3
0.01
04
4
0.93
16
5
0.70
08
41
6
0.66
08
7
0.74
12
8
0.79
12
Total = 64
‫ د‬w2 ‫ إذا‬. `^‫ ر‬76,64,76,60,64 :3‫ م ه‬9‫ أ‬, 3; , ‫ ا‬,`^‫ر‬0‫ا ;ن د أ‬./‫وه‬
. `^‫ ر‬68 2‫ ه‬,`^‫ر‬0‫ا‬
:( ‫اء‬-‫إ‬
:3 ‫ آ‬,9 " ‫اول‬- ‫ن‬2/ ,9‫آ ة او‬
‫اء ا‬[email protected]
‫م‬29 M/ !? G‫ د ا‬,9 " ‫ول‬Number of Customers/Day
Probability
Cumulative Probability
8
0.35
0.35
10
0.30
0.65
12
0.25
0.90
14
0.10
1.00
‫ن‬2 ‫ ز‬M/ ,`^‫ر‬0‫ د ا‬,9 " ‫ول‬Number of Loafs/Customer
Probability
Cumulative Probability
4
0.4
0.4
8
0.3
0.7
12
0.2
0.9
16
0.1
1.0
:‫ول‬0‫م ا‬2‫ا‬
‫ إذا د‬0.35 ‫ و‬0 ! %J‫ا ا‬.‫أن ه‬
‫ و‬0.125002 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
8 = ‫ول‬0‫م ا‬2 !? G‫ا‬
8 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
Number of Loafs
1
0.747727
12
2
0.165930
04
3
0.807279
12
42
4
0.691822
08
5
0.332073
04
6
0.865662
12
7
0.954414
16
8
0.605033
08
Total
76
`^‫ ر‬76 = ‫ول‬0‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:3 [‫م ا‬2‫ا‬
‫ إذا‬0.65‫ و‬0.35 ! %J‫ا ا‬.‫أن ه‬
‫ و‬0.436581 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
10 = 3 [‫م ا‬2 !? G‫د ا‬
10 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
Number of Loafs
1
0.795704
12
2
0.191331
04
3
0.326339
04
4
0.760580
12
5
0.232169
04
6
0.766908
12
7
0.897992
12
8
0.498371
08
9
0.593898
08
10
0.917927
16
Total
92
`^‫ ر‬92 = 3 [‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:P [‫م ا‬2‫ا‬
‫ إذا‬1.00‫ و‬0.90 ! %J‫ا ا‬.‫أن ه‬
‫ و‬0.975134 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
14 = 3 [‫م ا‬2 !? G‫د ا‬
14 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
43
Number of Loafs
1
0.500345
08
2
0.377338
04
3
0.497917
08
4
0.560237
08
5
0.742156
12
6
0.066540
04
7
0.953874
16
8
0.048342
04
9
0.133688
04
10
0.145730
04
11
0.313932
04
12
0.656628
08
13
0.146369
04
14
0.688054
08
Total
96
`^‫ ر‬96 = P [‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:R ‫م اا‬2‫ا‬
‫ إذا‬0.90 ‫ و‬0.65 ! %J‫ا ا‬.‫أن ه‬
‫ و‬0.852771 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
12 = 3 [‫م ا‬2 !? G‫د ا‬
12 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
Number of Loafs
1
0.102021
04
2
0.352606
04
3
0.739246
12
4
0.278503
08
5
0.495604
08
6
0.471064
08
7
0.214966
04
8
0.784797
12
9
0.922574
16
44
10
0.011573
04
11
0.530562
08
12
0.811989
12
Total
100
`^‫ ر‬100 = R ‫م اا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:ˆ ‫م ا‬2‫ا‬
‫ إذا‬0.90 ‫ و‬0.65 ! %J‫ا ا‬.‫أن ه‬
‫ و‬0.676495 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
12 = 3 [‫م ا‬2 !? G‫د ا‬
12 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
Number of Loafs
1
0.113377
04
2
0.682001
08
3
0.860924
12
4
0.616596
08
5
0.670505
08
6
0.996726
16
7
0.203282
04
8
0.616869
08
9
0.337997
04
10
0.273178
04
11
0.832140
12
12
0.575714
08
Total
96
`^‫ ر‬96 = ˆ ‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
2‫ ه‬29 , ‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫إذا‬
Average Number of Loafs =
76 + 92 + 96 + 100 + 96 460
=
= 92
5
5
. 29 `^‫ ر‬92 ‫ ز إاد‬Mf;0‫ ! ا‬g.‫و‬
45
‫‪#‬ل ‪# :6‬آة ;م ‪: (M,N) >$4‬‬
‫`ض ان ا ‪2‬ى ‪ 11 (M) !9G‬و‪6‬ة و;ة ا ا‪ (N) ,"-‬ه‪ 5 3‬أ‪ 9‬م‪ 9 .‬ان ‪:‬ر‬
‫ام ا‬
‫آ ة ‪ w2‬ا‪62‬ات ا ‪ ,:‬ود ا‪ 90‬م ا‪ 9 3‬ث ;‪ .‹: U‬ا‪2‬ز‪ R9‬ا@‪3 6‬‬
‫"د ا‪62‬ات ا ‪ 3; , 27‬ا‪2‬م ‪H 7"I‬ول ا ‪:3‬‬
‫‪Random Numbers‬‬
‫‪Cumulative Probability‬‬
‫‪Probability‬‬
‫‪Demand‬‬
‫‪0.00 – 0.10‬‬
‫‪0.10‬‬
‫‪0.10‬‬
‫‪0‬‬
‫‪0.11 – 0.35‬‬
‫‪0.35‬‬
‫‪0.25‬‬
‫‪1‬‬
‫‪0.36 – 0.70‬‬
‫‪0.70‬‬
‫‪0.35‬‬
‫‪2‬‬
‫‪0.71 – 0.91‬‬
‫‪0.91‬‬
‫‪0.21‬‬
‫‪3‬‬
‫‪0.92 – 1.00‬‬
‫‪1.00‬‬
‫‪0.09‬‬
‫‪4‬‬
‫ز ! ا‪:‬م ‪ 90‬م & ا‪2‬ز‪ R9‬ا ‪:3‬‬
‫‪Random Numbers‬‬
‫‪Lead Time Probability Cumulative Probability‬‬
‫‪0.00 – 0.60‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪1‬‬
‫‪0.61 – 0.90‬‬
‫‪0.9‬‬
‫‪0.3‬‬
‫‪2‬‬
‫‪0.91 – 1.00‬‬
‫‪1.0‬‬
‫‪0.1‬‬
‫‪3‬‬
‫أ;ض ان و‪ RV‬ا‪ ,9 U 3; RV2I ,7‬ا‪2‬م ا‪ 0‬و‪ M:I‬آ ه‪2‬‬
‫د ‪ ! G‬ا‪:‬م‪ 6 .‬آ‪3‬‬
‫ا‪ N‬م ة ‪ 5‬دورات واو‪ -‬ا ‪27‬ب‪.‬‬
‫ا ‪:M‬‬
‫`ض أ أ ‪2 e‬ى ‪ 11 !9G‬و‪6‬ة و‪ C -2IT‬ت "‪ M9‬ا ‪G‬ون ) ا [ ل‬
‫‪ ! _9‬ا‪ /‬ب ا ‪:‬ر ;‪ 3‬ه‪ 5.‬اا‪( ,9‬‬
‫اورة ا‪0‬و‪:‬‬
‫ا‪2‬م ا‪0‬ول‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 11‬و‪6‬ة‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.664078 S7‬و !‬
‫ا‪H‬ول ا‪0‬ول ‪ H‬ا‪ S7‬ه‪ 2 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪ :3‬ا ‪G‬ون ا ‪2-2‬د ‪ 9‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.607454 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا[ ‪ :P‬ا ‪G‬ون ا ‪2-2‬د ‪ 7‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.607326 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫‪46‬‬
‫ا‪2‬م اا ‪ :R‬ا ‪G‬ون ا ‪2-2‬د ‪ 5‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.906827 S7‬أي‬
‫ا‪ 3 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا ˆ‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 2‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.526820 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫;‪ ,9 U 3‬اورة ا‪0‬و‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 0‬و‪6‬ة‪ 11 ,C RV2I .‬و‪6‬ة‪ .‬ز ! ا‪:‬م ‪ 9‬د‬
‫! ا‪H‬ول ا[ ‪ S 3‬ر‪2O %J‬ا?‪ 0.880703 3‬أي ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫اورة ا[ ‪:,‬‬
‫ا‪2‬م ا‪0‬ول‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 0‬و‪6‬ة‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.017586 S7‬أي ا‪S7‬‬
‫‪ 0‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا[ ‪ :3‬ا ‪G‬ون ا ‪2-2‬د ‪ 0‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.312635 S7‬أي‬
‫ا‪ 1 S7‬و‪6‬ات‪.‬‬
‫) ‪ 1 ‹:‬و‪6‬ة (‬
‫ا‪2‬م ا[ ‪ :P‬ا ‪G‬ون ا ‪2-2‬د ‪ 11‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.656352 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م اا ‪ :R‬ا ‪G‬ون ا ‪2-2‬د ‪ 9‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.037722 S7‬أي‬
‫ا‪ 0 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا ˆ‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 9‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.860003 S7‬أي‬
‫ا‪ 3 S7‬و‪6‬ات‪.‬‬
‫;‪ ,9 U 3‬اورة ا[ ‪ :,‬ا ‪G‬ون ا ‪2-2‬د ‪ 6‬و‪6‬ة‪ 5 ,C RV2I .‬و‪6‬ات‪ .‬ز ! ا‪:‬م ‪ 9‬د‬
‫! ا‪H‬ول ا[ ‪ S 3‬ر‪2O %J‬ا?‪ 0.808951 3‬أي ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫اورة ا[ [‪:,‬‬
‫ا‪2‬م ا‪0‬ول‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 6‬و‪6‬ة‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.921377 S7‬أي ا‪S7‬‬
‫‪ 4‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا[ ‪ :3‬ا ‪G‬ون ا ‪2-2‬د ‪ 2‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.858579 S7‬أي‬
‫ا‪ 3 S7‬و‪6‬ات‪.‬‬
‫) ‪ 1 ‹:‬و‪6‬ة (‬
‫ا‪2‬م ا[ ‪ :P‬ا ‪G‬ون ا ‪2-2‬د ‪ 5‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.989726 S7‬أي‬
‫ا‪ 4 S7‬و‪6‬ات‪.‬‬
‫‪47‬‬
‫ا‪2‬م اا ‪ :R‬ا ‪G‬ون ا ‪2-2‬د ‪ 1‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.528333 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫) ‪ 1 ‹:‬و‪6‬ة (‬
‫ا‪2‬م ا ˆ‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 0‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.784676 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫) ‪ 2 ‹:‬و‪6‬ة (‬
‫;‪ ,9 U 3‬اورة ا[ [‪ :,‬ا ‪G‬ون ا ‪2-2‬د ‪ 0‬و‪6‬ة‪ 11 ,C RV2I .‬و‪6‬ات‪ .‬ز ! ا‪:‬م ‪ 9‬د‬
‫! ا‪H‬ول ا[ ‪ S 3‬ر‪2O %J‬ا?‪ 0.059002 3‬أي ز ! ا‪:‬م ‪29 1‬م‪.‬‬
‫اورة اا "‪:,‬‬
‫ا‪2‬م ا‪0‬ول‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 0‬و‪6‬ة‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.838344 S7‬أي ا‪S7‬‬
‫‪ 3‬و‪6‬ات‪.‬‬
‫) ‪ 3 ‹:‬و‪6‬ة (‬
‫ا‪2‬م ا[ ‪ :3‬ا ‪G‬ون ا ‪2-2‬د ‪ 11‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.643672 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا[ ‪ :P‬ا ‪G‬ون ا ‪2-2‬د ‪ 9‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.425546 S7‬أي‬
‫ا‪ 4 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م اا ‪ :R‬ا ‪G‬ون ا ‪2-2‬د ‪ 5‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.034398 S7‬أي‬
‫ا‪ 0 S7‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا ˆ‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 5‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.441595 S7‬أي‬
‫ا‪ 2 S7‬و‪6‬ات‪.‬‬
‫;‪ ,9 U 3‬اورة اا "‪ :,‬ا ‪G‬ون ا ‪2-2‬د ‪ 3‬و‪6‬ة‪ 8 ,C RV2I .‬و‪6‬ات‪ .‬ز ! ا‪:‬م ‪ 9‬د‬
‫! ا‪H‬ول ا[ ‪ S 3‬ر‪2O %J‬ا?‪ 0.224523 3‬أي ز ! ا‪:‬م ‪29 1‬م‪.‬‬
‫اورة ا ‪:,‬‬
‫ا‪2‬م ا‪0‬ول‪ :‬ا ‪G‬ون ا ‪2-2‬د ‪ 3‬و‪6‬ة‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.696218 S7‬أي ا‪S7‬‬
‫‪ 2‬و‪6‬ات‪.‬‬
‫ا‪2‬م ا[ ‪ :3‬ا ‪G‬ون ا ‪2-2‬د ‪ 9‬و‪6‬ات‪ 2 .‬ر‪2O %J‬ا?‪ 9 3‬ا‪ 0.883172 S7‬أي‬
‫ا‪ 3 S7‬و‪6‬ات‪.‬‬
‫‪48‬‬
‫ أي‬0.785434 S7‫ ا‬9 3?‫ا‬2O %J‫ ر‬2 .‫ات‬6‫ و‬6 ‫د‬2-2 ‫ون ا‬G ‫ ا‬:P [‫م ا‬2‫ا‬
.‫ات‬6‫ و‬3 S7‫ا‬
‫ أي‬0.169593 S7‫ ا‬9 3?‫ا‬2O %J‫ ر‬2 .‫ات‬6‫ و‬3 ‫د‬2-2 ‫ون ا‬G ‫ ا‬:R ‫م اا‬2‫ا‬
.‫ات‬6‫ و‬1 S7‫ا‬
‫ أي‬0.256014 S7‫ ا‬9 3?‫ا‬2O %J‫ ر‬2 .‫ات‬6‫ و‬2 ‫د‬2-2 ‫ون ا‬G ‫ ا‬:ˆ ‫م ا‬2‫ا‬
.‫ات‬6‫ و‬1 S7‫ا‬
‫ د‬9 ‫م‬:‫ ز ! ا‬.‫ات‬6‫ و‬10 ,C RV2I .‫ة‬6‫ و‬1 ‫د‬2-2 ‫ون ا‬G ‫ ا‬:, ‫ اورة ا‬,9 U 3;
.‫م‬29 1 ‫م‬:‫ أي ز ! ا‬0.178084 3?‫ا‬2O %J‫ ر‬S 3 [‫ول ا‬H‫! ا‬
... ‫ا‬./‫وه‬
:3 ‫ول ا‬H‫ ا‬3; ‫و‹ ا‬
Days Until
Beginning
Ending
Cycle Day Inventory Demand Inventory
1
2
3
4
5
Shortage
Order
Quantity Quantity
Order
Arrives
1
11
2
9
0
-
-
2
9
2
7
0
-
-
3
7
2
5
0
-
-
4
5
3
2
0
-
-
5
2
2
0
0
11
2
1
0
0
0
0
-
1
2
0
1
0
1
-
0
3
11
2
9
0
-
-
4
9
0
9
0
-
-
5
9
3
6
0
5
2
1
6
4
2
0
-
1
2
2
3
0
1
-
0
3
5
4
1
0
-
-
4
1
2
0
1
-
-
5
0
2
0
2
11
1
1
0
3
0
3
-
0
2
11
2
9
0
-
-
3
9
4
5
0
-
-
4
5
0
5
0
-
-
5
5
2
3
0
8
1
1
3
2
1
0
-
0
2
9
3
6
0
-
-
3
6
3
3
0
-
-
4
3
1
2
0
-
-
49
5
2
1
1
0
53
85
8
10
1
.‫ة‬6‫ و‬3.4 = 85/25= 29 ,: ‫ات ا‬62‫ ا‬w2
.‫ م‬90‫ ! ا‬%20 ‫ م أي‬9‫ أ‬5 ‹: U; ‫ث‬6 3‫ م ا‬90‫د ا‬
.3/‫ ا‬S7‫ ! ا‬%15.09 ‫ ( اي‬8/53) M/O9 ‹:‫ا‬
:‫ ا ل‬- B ‫ آ‬:7 ‫ل‬#
! ‫ر أن‬:I ,: ‫ ا‬UI ! .‫! ا ل‬
Y ‫ي‬HI ‫ت ا زل‬T2 ‫ ا‬6‫ أ‬I
‫ر أن‬:I U‫ آ ا‬.‫ ل‬-‫ ! ا‬20% ‫ ! ا ء و‬%U 80% M/O9 ‫ ! _ ا ب‬UC 9
‫ ل‬-‫ ! ا‬40% w:; !/‫ ” ! ا ل و‬U? 7 ! :9 UC 9 3I•‫ ! ا ء ا‬70%
R9 ‫& ا ء‬7"9 ‫ي‬.‫ر أن ا ” ا‬:I ,: ‫ ا‬UI ! f9‫ أ‬.g‫ن ذ‬2"`9 U2C 9 !9.‫ا‬
10 ‫ و‬7 ! ‫ وي‬R9‫ز‬2I f9‫ ا‬R9 ‫ ل‬- g‫ ل ذ‬9‫ ر‬22‫ و‬18 ! ‫ وي‬R9‫ز‬2I
w2 ‫ر‬:; ‫ ل‬[email protected]‫ `ˆ ا‬29 TG 15 ‫ إ‬10 ! 37YI ,2 ‫ أن ا‬W ‫ إذا‬. ‫ ل‬9‫ر‬
.‫ل‬2I ‫ م‬9‫ أ‬5 ‫ "د‬3 2‫ ا‬U‫د‬
:M ‫ا‬
:, ‫ ا‬,9 " ‫اول ا‬- ‫ن‬2/
,2 ‫وره ا‬GI 3‫ د ا زل ا‬,9 " ‫ول‬Number of Houses
Probability
CDF
Random Number
10
1/6
0.1666
0.00000-0.16666
11
1/6
0.3332
0.16667-0.33320
12
1/6
0.4998
0.33321-0.49980
13
1/6
0.6664
0.49981-0.66640
14
1/6
0.8330
0.66641-0.83300
15
1/6
1.0000
0.83301-1.00000
SC ‫ ا‬,9 " ‫ول‬Who Answer
Probability
CDF
Random Number
Female
0.8
0.8
0.00 - 0.80
Male
0.2
1.0
0.81 - 1.00
‫ ” ! ا ل‬R;I M‫ ا[ ه‬W ‫ إذا آ‬,9 " ‫ول‬50
Female Donate?
Probability
CDF
Random Number
Yes
0.7
0.7
0.00 - 0.70
No
0.3
1.0
0.71 - 1.00
‫ ” ! ا ل‬R;9 M‫ ه‬M-‫ إذا آ ن ر‬,9 " ‫ول‬Male Donate?
Probability
CDF
Random Number
Yes
0.4
0.4
0.00 - 0.40
No
0.6
1.0
0.41 - 1.00
[0‫;"& ا‬I ‫ي‬.‫ ا ” ا‬,9 " ‫ول‬Female Donation
Probability
CDF
Random Number
18
0.2
0.2
0.00 - 0.20
19
0.2
0.4
0.21 - 0.40
20
0.2
0.6
0.41 - 0.60
21
0.2
0.8
0.61 - 0.80
22
0.2
1.0
0.81 - 1.00
M-‫;"& ا‬9 ‫ي‬.‫ ا ” ا‬,9 " ‫ول‬Male Donation
Probability
CDF
Random Number
7
0.25
0.25
0.000 - 0.250
8
0.25
0.50
0.251 - 0.500
9
0.25
0.75
0.501 - 0.750
10
0.25
1.00
0.751 - 1.000
(‫ول‬H‫ ا‬f9T 6 ,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ون ا‬T ‫ف‬2 :,N6 ) ‫آ ة‬
‫م‬2‫ع ا‬2 H
‫ول ا‬- ‫ن‬2/ ‫اا‬
R;9 %‫آ‬
R;9 M‫ه‬
SC ‫ا‬
‫ل‬G ‫ا‬
‫د ا زل‬
‫م‬2‫ا‬
21
%"
[‫ا‬
1
15
‫ول‬0‫ا‬
8
%"
M-‫ر‬
2
19
%"
[‫ا‬
3
20
%"
[‫ا‬
4
18
%"
[‫ا‬
5
51
‫ا‪2‬م ا[ ‪13 3‬‬
‫ا‪2‬م ا[ ‪11 P‬‬
‫‪6‬‬
‫ا[‬
‫"‪%‬‬
‫‪18‬‬
‫‪7‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪8‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪9‬‬
‫ر‪M-‬‬
‫"‪%‬‬
‫‪7‬‬
‫‪10‬‬
‫ا[‬
‫"‪%‬‬
‫‪22‬‬
‫‪11‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪12‬‬
‫ر‪M-‬‬
‫"‪%‬‬
‫‪7‬‬
‫‪13‬‬
‫ا[‬
‫"‪%‬‬
‫‪18‬‬
‫‪14‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪15‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪1‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪2‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪3‬‬
‫ر‪M-‬‬
‫"‪%‬‬
‫‪10‬‬
‫‪4‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪5‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪6‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪7‬‬
‫ا[‬
‫"‪%‬‬
‫‪22‬‬
‫‪8‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪9‬‬
‫ا[‬
‫"‪%‬‬
‫‪7‬‬
‫‪10‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪11‬‬
‫ا[‬
‫"‪%‬‬
‫‪18‬‬
‫‪12‬‬
‫ا[‬
‫"‪%‬‬
‫‪21‬‬
‫‪13‬‬
‫ا[‬
‫"‪%‬‬
‫‪22‬‬
‫‪1‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪2‬‬
‫ا[‬
‫"‪%‬‬
‫‪18‬‬
‫‪3‬‬
‫ا[‬
‫"‪%‬‬
‫‪18‬‬
‫‪4‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪5‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪52‬‬
‫‪196‬‬
‫‪139‬‬
‫ا‪2‬م اا ‪10 R‬‬
‫ا‪2‬م ا ˆ ‪14‬‬
‫‪6‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪7‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪8‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪9‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪10‬‬
‫ا[‬
‫"‪%‬‬
‫‪22‬‬
‫‪11‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪1‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪2‬‬
‫ر‪M-‬‬
‫"‪%‬‬
‫‪7‬‬
‫‪3‬‬
‫ا[‬
‫"‪%‬‬
‫‪18‬‬
‫‪4‬‬
‫ر‪M-‬‬
‫"‪%‬‬
‫‪7‬‬
‫‪5‬‬
‫ا[‬
‫"‪%‬‬
‫‪21‬‬
‫‪6‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪7‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪8‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪9‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪10‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪1‬‬
‫ا[‬
‫"‪%‬‬
‫‪22‬‬
‫‪2‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪3‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪4‬‬
‫ا[‬
‫"‪%‬‬
‫‪22‬‬
‫‪5‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪6‬‬
‫ر‪M-‬‬
‫‪T‬‬
‫‪0‬‬
‫‪7‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪8‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪9‬‬
‫ر‪M-‬‬
‫"‪%‬‬
‫‪8‬‬
‫‪10‬‬
‫ا[‬
‫"‪%‬‬
‫‪20‬‬
‫‪11‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪12‬‬
‫ا[‬
‫"‪%‬‬
‫‪21‬‬
‫‪53‬‬
‫‪118‬‬
‫‪131‬‬
‫‪13‬‬
‫ا[‬
‫"‪%‬‬
‫‪19‬‬
‫‪14‬‬
‫ا[‬
‫‪T‬‬
‫‪0‬‬
‫‪131‬‬
‫;‪ 5 ,9 U 3‬ا‪ 9‬م ‪ W" -‬ا ‪ 715 ,2‬ر‪ 9‬ل أي د‪ U‬ا‪ 3; 3 2‬ا ‪ 143 w2‬ر‪ 9‬ل‪.‬‬
‫‪ :!9 I‬أ‪ S6‬ا‪ , :‬ا‪) ,9N‬ا@‪ 148.5 , -‬ر‪ 9‬ل(‪.‬‬
‫‪54‬‬
: ‫ا ا‬
:J1‫ت ا‬H ‫)ام‬$'_ ‫اآة‬
: Excel ‫)ام‬$'_ ‫ز! إ‬4 # 1.‫ا‬
:3 ‫ ا‬R9‫ز‬2‫ ا‬U 3‫ل ا‬2'2‫! ا‬
2
3
4
, ‫ أز‬,9 " Excel ‫ف م‬2
Time between arrivals
1
5
6
7
8
Probability
0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125
:, ‫ ا‬, ` ‫ ا‬3; ‫ ا ت آ‬M‫ أد‬%X CDF 3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬,‫ن دا‬2‫آ‬
Y ,/ ‫ ا‬%:‫ول وا‬0‫د ا‬2 "‫ ا‬3; CDF 3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬,‫ دا‬%J ‫ن‬2/I ‫ أن‬SH9 -1
.3 [‫د ا‬2 "‫ ا‬3; 3?‫ا‬2O"‫ا‬
.‫ ( ة‬1.00 ) I 3‫ ا‬, : 3UI‫ ( و‬0 ) ` ‫ ! ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬,‫ دا‬%J ‫أ‬I -2
(C2 [ ) , ‫ ا‬,‫ ا‬3; 3 ‫ ا‬M 3?‫ا‬2O"‫ ا‬Y %J 2I ‫د ا اد‬2 "‫ ا‬3; -3
= VLOOKUP( RAND(), RANGE OF SAMPLING TABLE, 2)
[ 3;‫ و‬,9 " ‫ول ا‬- &; ‫ي أد‬.‫ ل ا‬H ‫ ا‬RANGE OF SAMPLING TABLE P6
. U ( 0,1) 2I 3‫ ا‬RAND() ,‫“ إا ا‬6T .$A$2:$B$9 2‫ ل ه‬H ‫ا ا‬.‫ه‬
.‫ب‬27 , %H ‫ اي د‬2 C2 ,‫( ا‬d) S -4
55
:0l ‫ل‬#
R9‫ز‬2‫ ا‬S6 , , ‫ أز‬2I
Service Times
1
2
3
Probability
0.01
0.020 0.30
4
5
6
0.25
0.10
0.05
:, ‫ ا‬, ` ‫ ا‬3; ‫ ا ت آ‬M‫ أد‬%X 3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬,‫ن دا‬2‫آ‬
. ‫ ا [ ل ا‬3; ‫ات آ‬27‫آرا‬
:; ‫ت‬.‫ز‬4 # 1.‫ا‬
:. 6D‫ از! ا‬# 1.‫ ا‬-1
‫ وإ اف " ري‬% 165 w2
"C ,‫ز‬2 ‫د‬2" g ‫ ا‬," - ‫ب‬C ‫ال‬2C‫`ض ان أ‬
.% ‫ب‬J0 , : ‫ب‬7‫ال ا‬2C‫ ! أ‬, 2I 9 .% 5
:3 ‫ ا‬M O , `' 3;
:‫ دوال‬3 ‫ه ا‬
,J number ‫ب ا"د‬:I ,‫ اا‬5.‫ وه‬.ROUND( number, num_digits) ,‫ اا‬-1
.num_digits
56
‫ هة‬O 37"I ,‫ اا‬5.‫ وه‬.NORMINV(probability,mean,standard_dev) ,‫ اا‬-2
“6T .standard_dev ‫ وإ اف " ري‬mean w2 3"C R9‫ز‬2I & 3?‫ا‬2O Y !
.RAND() ,‫ ! اا‬2I probability ‫ان‬
. U ( 0,1) 37"I 3‫ وا‬RAND( ) ,‫ اا‬-3
.!" ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ هات‬O ‫ ا"د ا اد ! ا‬2I R7 ,‫ ا‬d
:(‫ى‬0‫* ا‬C) . 6D‫ از! ا‬# 1.‫ ا‬-2
Data ‫ و‬Tools ‫ ا ر‬%X ، U 3?‫ا‬2O"‫ ا‬Y , J 2I ‫اد‬9 3‫ ا‬,‫د ا‬6 O , `' 3;
3 ‫ آ‬Analysis
57
‫ة‬.; ‫ ا‬UN;
‫ة‬.; ‫ ا‬UN; .Random Number Generation ‫ ر‬
58
‫‪ R7‬إ ر أي ‪2I‬ز‪ ! R9‬ا‪, ? :‬‬
‫و ‪ S‬ا‪2‬ز‪ R9‬ا ر ‪2 YI‬ا;‪ .‬ا ت ; [ ‪2‬ز‪ R9‬ا‪2/I 3"7‬ن ا ;‪.‬ة‬
‫‪59‬‬
‫‪ P6‬أد ‪" 1‬د ا ‪Y‬ات )أو ا‪ 0‬ة( ا‪9 3‬اد ‪2I‬ه ‪ ،‬و ‪" 20‬د ا ‪ O‬هات ا ‪, 27‬‬
‫و;‪ 3‬ا " ‪ Parameters %‬ا ‪ :‬ا‪ , :‬ا ‪ (Default) ,6:‬وه‪ w2 0 3‬و ‪1‬‬
‫‪ z‬اف ا " ري‪2 b M % .‬اة ا"‪2O‬ا?‪ Random Seed ,‬آ أ ا‪, ,9‬‬
‫ا@د ل ‪ $A$2‬و‪ ]9‬ا ‪:3‬‬
‫‪60‬‬
‫‪ 2‬أي د ! ا ‪ O‬هات ا‪2I RI 3‬ز‪2O Y R9‬ا?‪ 3‬م ا ;‪.‬ة‬
‫وا‪ 7"I 3‬ا@ ر ! ‪2I 7‬ز‪ "9‬ت‪ 3; .‬ا` ‪ M‬ا ˆ ‪2‬ف رس " ا‪7‬ق ‪2‬‬
‫‪ O‬هات ‪0‬ي ‪2O Y‬ا?‪.3‬‬
‫‪61‬‬
Excel ‫)ام‬$'_ ‫آة‬/ /#‫أ‬
:B 4#4‫ ! أو‬1‫آ‬# ‫آة‬# :1 ‫ل‬#
P
,/ ‫ ا‬3; U"fI 3‫ ا‬S"‫ د ا‬9 I ,/I 2I‫و‬T‫ ا‬g"‫ ا‬R !? / ‫ آ ت‬6‫ ا‬9I
80 S2I ,/ ‫ ا‬.
I ‫ زج‬C 2‫ وه‬9‫ دور‬Y9 g"‫ ?! ان ا‬G 362I 3/ , ‫و‬IT
! ‫ ت‬R HI " ., 40 ! W : ‫ آ‬,/ ‫ ا‬,b"I ,‫آ‬O‫ا ;ن ا‬.U‫ و‬g ,
g" 3 2‫ ا‬S7 3 ‫ ا‬R9‫ز‬2‫ن ا‬2‫ آ‬,/ ‫ا‬
Demand
0
1
2
3
4
5
Probability
0.1
0.15
0.20
0.30
0.20
0.05
‫ م‬N‫ا ا‬.‫آ ة ه‬
Excel ‫ف م‬2
:, V2 ‫ ا‬9‫ ا‬3; 3 ‫ ا‬M‫ وأد‬Excel ! , `' a;‫أ‬
1) A1 => Number of Days to sell 40 items
2) A4 => Day
3) B4 => Demand
4) C3 => Cumulative
5) C4 => Demand
6) A5 = 1
7) E4 => CDF
8) F4 => x
9) E5:E10 = 0 , 0.1 , 0.25 , 0.45 , 0.75 , 0.95
10) F5:F10 = 0 , 1 , 2 , 3 , 4 , 5
11) B5 = VLOOKUP(RAND( ),$E$5:$F$10,2)
12) C5 = B5
13) A6 = IF(C5<40,A5+1,” ”)
14) B6 = IF(C5<40,VLOOKUP(RAND(),$E$5:$F$10,2),” ”)
15) C6 = IF(C5<40,B6+C5,” ”)
16) A7:A45 = A6
17) B7:B45 = B6
18) C7:C45 = C6
19) D1= MAX(A5:A45)
62
‫‪ :,N6‬ا‪ %U‬ا ‪ 3"9 M`q A‬إ ر ا‪ ,‬ا‪ S H 3‬ا‪ %U‬و‪( 6 U‬‬
‫ا ‪ H‬ل‪.‬‬
‫;] ا ` ‪ ,‬ا ‪,‬‬
‫ا ر ‪ D1‬وا‪ wYV‬ا ` ح )‪ Y; (F9‬ا‪ 3; %:‬ا‪ 0‬ة ‪ A‬و ‪ B‬و ‪ C‬وآ‪ g.‬ا‪D1 ,‬‬
‫وا‪0‬ة ‪ 37"I‬د ا‪ 90‬م از ‪ MH .g , 40 R ,‬ا‪ %:‬ا ‪ 3; ,HI‬ا‪" D1 ,‬د ‪21‬‬
‫‪ , HI‬وأو‪ -‬ا ‪ w2‬وا ‪ 5.U !9‬ا"‪ ,‬وأو‪6 -‬ود ‪.%95 ,:X‬‬
‫‪=$# /4‬ت اآة _'‪)$‬ام ‪: Excel‬‬
‫‪ wYf‬ا ` ح )‪2:9 (F9‬م ‪ Excel‬دة ‪ 6‬ب '` ‪ ,‬ا" ‪ M‬و‪ ! ]9‬ه‪.‬ا إ‪-‬اء ‪9-‬‬
‫‬
‫آ ة ;‪ 3‬آ‪ M‬ة‪.‬‬
‫" ا‪e‬آ ! ‪2 M‬ذج ا‬
‫آ ة ‪ M/O‬ا ‪27‬ب‪2: ،‬م ‪-‬اء ا ‪2‬ذج د ! ا ات وه‪.‬ا‬
‫ا"د ‪ %H6 "9‬ا"‪ ,‬ا ‪27‬ب ‪ : M/‬س ! ‪ ˆ9 :‬ا@داء‪ ،‬و‪ P6‬أن ا‬
‫آ ة ‪HI‬ى‬
‫ ‪ / @ &; S 6‬ن أ‪ .‬أ‪ H6‬م ت آة ‪ ”I‬ا ‪ b‬ت ‪ M‬ا‪Th‬ف ! ا `دات‪.‬‬
‫ا‪27‬ة ا ‪ , 3; ,‬ا‬
‫آ ة ه‪/I 3‬ار إ‪-‬اء ا ‪2‬ذج ة ‪ b‬ت ! ا ات و‪]? MHI‬‬
‫ا‪ 9‬ا‪2 I 3‬ى ‪ ˆ9 :‬ا@داء ا اد ‪ ، U I‬و`ض ا ‪/I 150 9‬ارا ‪2‬ذج‬
‫‪63‬‬
U ‫ و‬Workbook M "‫ة ! د; ا‬9- Worksheet , `' , 27 ‫! ا ?] ا‬9GI‫و‬
:, ` ‫ ا‬, 3 ‫م‬2: .Simulation
.insert wYf .1
.M "‫ة ; ا‬9- , `' ‫ ف‬V‫ أ‬Excel ‫“ أن‬6 Worksheet ‫ هة ر‬N‫ ا‬, ? :‫ ! ا‬.2
.Format wYf .3
.Worksheet wYf ‫ هة‬N‫ ا‬, ? :‫ ا‬3; .4
.Rename wYf , ? :‫ ا‬3;‫ و‬.5
.3'0‫ ا‬%@‫ ل ا‬Simulation S/; ‫ را‬a'‫ ا‬,J‫ر‬2‫ ا‬%‫“ ان ا‬6 .6
.Enter wYf .7
.3 ‫ة‬27‫ وأ ! ا‬w:; U I " M "‫ د; ا‬3; , , `' ‫د‬2-‫ و‬, 6 3; :,N6
,‫ ?! ! ا‬150 ‫ إ‬1 ! ‫ م‬J‫ر‬0‫ ا‬M Simulation ‫ ه‬3‫ة ا‬9H‫ ا‬, ` ‫ ا‬3;
:3 ‫ ا‬M/O‫ ا‬3; ‫ آ‬A3
:3 ‫ آ‬I‫ ذا‬150 ‫ إ‬1 ! 9‫! † ا‬/ 9‫و‬
.Enter wYV‫ وا‬A3 ,‫ ا‬3; (1) ,‫و‬0‫ ا‬, :‫ ا‬S‫ أآ‬.1
.A3 ,‫ ا ر ا‬.2
.Series , ? :‫ ! ا‬%X Fill , ? :‫ ا‬3; %X Edit wYV‫ ا‬.3
64
.150 , :‫ ا‬Stop value , J M‫ واد‬Series in Columns ‫ ه ا ر‬N‫ ا وق ا‬3; .4
.OK wYV‫ ا‬.5
.150 6 ‫ م‬J‫ر‬0 A3 W I 9‫ ا‬I‫ ذا‬Excel † :1.‫ا‬
‫ د‬,9 " 9 . : ‫ ه‬6 3‫ ا‬,:97 Demand ‫ذج‬2 ‫ي ا‬2 I 3‫ ا‬, ` ‫ ا‬3 M"` ‫ا‬.U Demand ‫ ا ة‬, ` ‫ ا‬3; D1 ,‫ ا‬3; 3‫ ا‬, :‫ أي ا‬,"7J 40 R ‫ م‬90‫ا‬
:3 ‫ا‬
B3 ,‫ ا‬3; , ‫ ا‬,Y ‫ ا‬M .1
=’Demand’!D1
.B152 6‫ و‬A3 ‫ ل‬H ‫ ا ر ا‬.2
.Data wYV‫ ا‬.3
.Table wYV‫ هة ا‬N‫ ا‬, ? :‫ ا‬3; .4
.Column input cell 3; A1 M‫ هة اد‬N‫ة ا‬.; ‫ ا‬3; .5
.OK wYV‫ ا‬.6
., ` ‫ ب ا‬6 ‫ @ دة‬F9 wYV‫ ا‬.7
M"` ‫ ا ت‬M I ‫ض‬Y %:‫ ا‬W[ 3/‫ و‬, ` ‫ ب ا‬6 ‫" د‬9 F9 wYf
M‫“ ا آ‬6
:3 ‫ا‬
.B152 6‫ و‬B3 ‫ ل‬H ‫ ا ر ا‬.1
.Edit wYV‫ ا‬.2
.Copy wYV‫ ا‬.3
.Edit wYV‫ ا‬.4
.Paste Special wYV‫ ا‬.5
.Values wYV‫ ا‬.6
.OK wYV‫ ا‬.7
.Enter wYV‫ ا‬.8
65
., ` ‫ ب ا‬6 ‫ دة‬YIT , X ‫ م‬J‫ ار‬B ‫د‬2 "‫ ا‬3; %:‫ ا‬a I ‫ا‬./‫وه‬
:3 ‫ ا ت آ‬W[ ‫ اى‬,:9C ‫ ه ك‬:,N6
.Tools wYV‫ ا‬.1
.Options wYV‫ هة ا‬N‫ ا‬, ? :‫ ا‬3; .2
.Calculation wYV‫ هة ا‬N‫ة ا‬.; ‫ ا‬3; .3
.Automatic Except Tables ‫ ا ر‬.4
.OK wYV‫ ا‬.5
:, ‫ ا‬, ` ‫] ا‬I‫و‬
66
:3 ‫ ا‬M " Days Y ,?
[email protected]‫ ا ` ت ا‬S 3/
:, ‫ة ا@ رات ا‬.; UN;
‫ة‬.; ‫ ا‬UN; Descriptive Statistics ‫ ر‬
67
‫† ا`ا^ ت آ ه‪ ]; ! 2‬ا ‪:3‬‬
‫ ا‪h‬ن ا`‪ ,V‬أن ‪ w2‬د ا‪ 90‬م ا‪T‬ز ‪ g , 40 R ,‬ه‪ µ = 16 3‬أي‬
‫‪H 0 : µ = 16‬‬
‫‪H1 : µ ≠ 16‬‬
‫‪68‬‬
:3 ‫ آ‬g‫ ذ‬M "‫ و‬t = ( µˆ − µ0 ) se ( µˆ ) ,?
[email protected]‫ ا‬-2 ,V`‫ ا‬5.‫@ ر ه‬
1) C19 => t
2) C20 => p-value
3) D19 = (E3-16)/E4
4) D20 = TDIST(D19,20,2)
:, ‫ة ا‬.; ‫ ا‬3; ‫آ‬
:, ‫ة ا‬.; ‫ ;] ا‬OK wYV‫ا‬
69
‫ان‬
( " ‫ أو‬P ( t ≥ 0.34075 ) = 0.7368 ‫ أي أن‬0.7368 ‫ وي‬I p-value ‫“ ان اـ‬6T
. α = 0.05 ,9` ‫ ا‬,V`‫; ا‬T ; α = 0.05 ! ‫ أآ‬p-value ‫ اـ‬, J
‫)ام‬$'_ Single Channel Queue )‫ اا‬9‫ ر ا‬C ‫آة‬# :2 ‫ل‬#
:Excel
aV2 2‫ ا ت آ ه‬M‫ وأد‬Excel 3; ‫ة‬9- , `' a;‫ا‬
70
‫" إد ل ا ت ا ‪ ,:‬و ‪ ` wYf‬ح ‪ ]I F9‬ا ` ‪ ,‬ا ‪,‬‬
‫‪ wYf‬ا ‪/‬ر ` ح ‪ "I F9‬د ‪ 6‬ب ا ` ‪ ,‬و‪/I‬ر ا‬
‫`‪.,‬‬
‫‪71‬‬
‫آ ة و‪ 3; ]I‬آ‪ M‬ة ?]‬
. ‫ ا [ ل ا‬3; ‫ ت آ‬V; ‫اء وأ‬-‫ إ‬21 ‫ م "د‬N ‫داء‬0‫ˆ ا‬9 : MH
:Excel ‫)ام‬$'_ . ‫ ا‬#)$/ B ‫آة أ) و‬# :3 ‫ل‬#
:M/O‫ ا‬3; aV2 2‫ آ ه‬A1:F6 9‫ ا‬3; ‫ ا ت‬M‫ وأد‬Excel 3; ‫ة‬9- , `' a;‫أ‬
:aV2 2‫ آ ه‬, ‫ ا ت ا‬M‫ اد‬%X 1:104 ‫ م‬J‫ر‬0‫ ا‬G1:G104 9‫ ا‬3; M‫أد‬
H3=> =VLOOKUP(RAND(),$A$3:$B$6,2)
I3=> =H3
I4=> =I3+H4
J3=> =I3
J4=> =IF(L3<=I4,I4,"")
J5=>
=IF(AND(MAX(L$3:L4)<=MAX(O$3:O4),MAX(L$3:L4)>=I5),MAX(L$3:L4),IF(MAX(L$3:L4)<=I
5,I5,""))
K3=> =VLOOKUP(RAND(),$C$3:$D$6,2)
K4=> =IF(J4="","",VLOOKUP(RAND(),$C$3:$D$6,2))
L3=> =J3+K3
L4=> =IF(J4="","",K4+J4)
M4=> =IF(J4="",I4,"")
M5=>
=IF(J5<>"","",IF(AND(MAX(L$3:L4)>MAX(O$3:O4),MAX(O$3:O4)>=I5),MAX(O$3:O4),IF(MAX
(L$3:L4)>I5,I5,"")))
N4=> =IF(M4="","",VLOOKUP(RAND(),$E$3:$F$6,2))
O4=> =IF(M4="","",M4+N4)
P3=> =IF(J3<>"",J3-I3,M3-I3)
E10=> =SUM(K3:K102)
E11=> =SUM(N3:N102)
E12=> =SUM(P3:P102)
E14=> =E10/MAX(L3:L102)
72
E15=> =E11/MAX(O3:O102)
E16=> =E12/MAX(G3:G102)
, ‫ ل ا‬/T‫;] ا‬
:, ‫ ا‬, ` ‫] ا‬I F9 ‫ ` ح‬wYf
73
‫‪ O‬هة اى‪:‬‬
‫‪ :!9 I‬أو‪ ˆ9 : -‬ا‪0‬داء ‪.U‬ا ا ‪2‬ذج وأ ;‪ V‬ت آ ;‪ 3‬ا [ ل ا ‪.‬‬
‫‪74‬‬
‫‪#‬ل ‪ ! /BJ# :4‬ا‪)$'_ 9‬ام ‪:Excel‬‬
‫أد‪ M‬ا ت آ ه‪ 3; aV2 2‬ا‪ /0‬ل ا ‪:,‬‬
‫;‪ UN‬ا ?] ا ‪:,‬‬
‫‪ I‬ر‪:!9‬‬
‫‪ ^ (1‬د ا‬
‫_ ا‪U9O9 3‬‬
‫?‪ R‬ا‬
‫_ ‪ 29 ,` ' 40 ! 29‬و‪100 6‬‬
‫' `‪ 9G ) 29 ,‬دة ‪ _ ' 10‬آ‪ M‬ة ( و‪6‬د ا"د ا‪" M[ 0‬د ا‬
‫‪ R? U9O9‬ا‬
‫_ ‪. 29‬‬
‫‪75‬‬
‫_ ا‪3‬‬
‫‪ 3; (2‬آ‪M‬‬
‫ ‪ a‬ا‬
‫و‪ ! ,‬ا‬
‫و‪T‬ت ا ‪ ,:‬أ‪-‬ي ا‬
‫آ ة ‪ 50‬ة وأو‪ -‬ا‪2‬ز‪ R9‬ا@‪3 6‬‬
‫;‪.Net Profit 3‬‬
‫‪ 3; ^ (3‬ا‪2‬ز‪ "9‬ت ا@‪ , 6‬ا ‪ ،,:‬وأ‪-‬ي ‪ HI‬رب إ‪ 3 ,; O/‬ا ‪2‬ذج‪.‬‬
‫‪#‬ل ‪# :5‬آة ;م ‪)$'_ (M,N) >$4‬ام ‪: Excel‬‬
‫ا‪ /0‬ل ا ‪,:9C aV2I ,‬‬
‫آ ة ‪ N‬م ا‪ !9G‬ا ‪.‬آ‪2‬ر ;‪ [ 3‬ل ‪2 6‬ا‪Excel ,7‬‬
‫‪76‬‬
‫‪#‬ل ‪ :6‬آ ‪ - B‬ا ل‪:‬‬
‫‪ I‬أ‪ 6‬ا ‪T2‬ت ا زل ‪HI‬ي ‪Y‬‬
‫! ا ل‪ UI ! .‬ا ‪:I ,:‬ر أن !‬
‫‪ _ ! UC 9‬ا ب ‪ ! %U 80% M/O9‬ا ء و ‪ ! 20%‬ا‪ -‬ل‪ .‬آ ا‪:I U‬ر أن‬
‫‪ ! 70%‬ا ء ا•‪ ! ” U? 7 ! :9 UC 9 3I‬ا ل و‪ ! 40% w:; !/‬ا‪ -‬ل‬
‫ا‪2"`9 U2C 9 !9.‬ن ذ‪ .g‬أ‪ UI ! f9‬ا ‪:I ,:‬ر أن ا ” ا‪.‬ي ‪ &7"9‬ا ء ‪R9‬‬
‫‪2I‬ز‪ 20 w2 3"C R9‬ر‪ 9‬ل وإ اف " ري ‪ 3‬ر‪ 9‬ل ذ‪ - g‬ل ‪ R9‬ا‪2I f9‬ز‪R9‬‬
‫‪ 10 w2 3"C‬ر‪ 9‬ل وإ اف " ري ‪ 2‬ر‪ 9‬ل‪) .‬إذا ‪ W‬أن ا ‪ 10 ! 37YI ,2‬إ‬
‫‪ ˆ` 29 TG 15‬ا@‪ 6‬ل( ;‪:‬ر ‪ w2‬د‪) U‬ا‪ 3;) (3 2‬ز‪ 9‬رة "د ‪G 200‬ل‪(.‬‬
‫ا ‪:M‬‬
‫أد‪ M‬ا ‪O , `' 3; 3‬‬
‫‪77‬‬
‫‪H‬ي ا ‪ /‬ة ‪ 200‬و‪ MH‬ا ?]‬
‫! ‪ ,H‬ا‬
‫آ ة ‪ H‬أن ا ‪R HI ,2‬‬
‫! ‪ 233‬و ‪ 242‬ر‪ 9‬ل ‪ 29‬و ‪ 6‬ل ‪. 95%‬‬
‫‪78‬‬
‫‪ I‬ر‪:!9‬‬
‫‪ (1‬أ‪-‬ي ا [ ل ا ‪ Y‬آ ‪2 ,‬ى ا ‪G‬ون ا‪Maximum Inventory %N0‬‬
‫‪ Level‬وا‪ , /‬ا " د ‪Reorder Quantity UC‬‬
‫‪ 3; (2‬آ‪ M‬إ‪-‬اء أو‪ w2 -‬ا‪62‬ات ا ‪ ! ,J‬ا ‪G‬ون ود ا‪ 90‬م ا‪6 3‬ث ;‪U‬‬
‫‪ ‹:‬ود ا‪62‬ات ا ‪., J‬‬
‫‪ (3‬أو‪ -‬ا‪2‬ز‪ "9‬ت ا@‪ / , 6‬ت ا ‪ 3; , 27‬ا`‪:‬ة )‪ (2‬ا ‪ ,:‬وأ ا`‪ V‬ت‬
‫ا ‪.,‬‬
‫‪79‬‬
‫ا اا !‪:‬‬
‫‪ ) 4‬أرم ‪J2‬ا ‪:‬‬
‫;‪ 3‬ه‪.‬ا ا` ‪2 M‬ف "ض و ‪ 60 R9 M/O‬ا‪7‬ق ا ‪ 2 ,‬أر‪ J‬م ‪2O‬ا?‪,‬‬
‫وذ‪0 g‬ن ‪ 2I‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬آ رأ‪ 3; 9‬ا` ‪2‬ل ا ‪- %U ,:‬ا ;‪ 3‬إ‪-‬اء ا‬
‫آ ة‪.‬‬
‫‪ V‬ا‪ 2 R9‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ه ه‪ [email protected] w:; 2‬ء ;‪/‬ة ! ا‪7‬ق ا ‪3; ,‬‬
‫ا ت او‪ ,9‬وا ت ا‪ ,h‬وا‪I 3‬م ‪C‬ق ‪27‬رة ‪-‬ا و‪2‬ارز ت "‪:‬ة ‪2‬‬
‫ا‪0‬ر‪ J‬م وا ‪Y‬ات ا"‪2O‬ا?‪ ,‬وا‪ 3‬ا' ‪ , W‬ا‪2H‬دة و‪ 37"I‬أاد و ‪Y‬ات ‪2O‬ا?‪,‬‬
‫ذات ‪ ,J2X2‬آة‪.‬‬
‫‪0‬اص ارم ا‪J.‬ا ‪:‬‬
‫?‪ , U ,‬وه‪3‬‬
‫أي "‪ ! ,‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ SH9 R1 , R2 ,..., ,‬ان ‪ !' : I‬إ‪6‬‬
‫ا‪2‬ز‪ R9‬ا وي وا@‪:‬ار‪ .‬آ‪ M‬ر‪2O %J‬ا?‪ Ri 3‬ه‪ 2‬رة ! ‪! , 2 ,: ,‬‬
‫‪2I‬ز‪ R9‬وي ‪ 0 ! M:‬و ‪ 1‬أي ان دا‪ ,‬ا‪ ,; [/‬ا@‪ RI & , 6‬ا ‪:,Y‬‬
‫‪1, 0 ≤ x ≤ 1‬‬
‫‪f ( x) = ‬‬
‫‪0, otherwise‬‬
‫وا‪ U 3‬ا‪ M/O‬ا ‪:3‬‬
‫‪1.2‬‬
‫‪1‬‬
‫‪0.8‬‬
‫)‪f(x‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.2‬‬
‫‪0‬‬
‫‪1.2‬‬
‫‪1‬‬
‫‪0.8‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.2‬‬
‫‪0‬‬
‫‪x‬‬
‫ا‪ , :‬ا ‪ Ri M/ ,"J2‬ه‪3‬‬
‫‪1‬‬
‫‪x2‬‬
‫‪1‬‬
‫= ‪E ( R ) = ∫ xdx‬‬
‫=‬
‫‪0‬‬
‫‪2 0 2‬‬
‫‪1‬‬
‫‪80‬‬
‫و‪!9 I‬‬
‫‪1‬‬
‫‪2‬‬
‫‪x3‬‬
‫‪1 1 1 1‬‬
‫= ‪−  = −‬‬
‫= ‪V ( R ) = ∫ x dx −  E ( R ) ‬‬
‫‪0‬‬
‫‪3 0  2  3 4 12‬‬
‫‪2‬‬
‫‪2‬‬
‫‪1‬‬
‫! ا‪2‬اص ا ‪2 , U‬ز‪ R9‬ا وي وا@‪:‬ل ه‪:3‬‬
‫‪ (1‬إذا ‪ W J‬ا`ة )‪ (0,1‬إ ‪ ,b; n‬ذات أ‪2C‬ال و‪; ,9‬ن د ا ‪ O‬هات ا ‪3; ,"J2‬‬
‫آ‪ ,b; M‬ه‪ N P6 N n 3‬د ا ‪ O‬هات ا‪.3/‬‬
‫‪ (2‬إ‪ 6‬ل ‪ O‬هة ‪; 3; , J‬ة "‪ , J ! M: ,‬ا‪ %:‬ا ‪.,:‬‬
‫‪ ) 4‬أرم ‪J2 L67‬ا ‪:‬‬
‫ا‪0‬ر‪ J‬م & ا"‪2O‬ا?‪ Pseudo-Random Numbers ,‬ه‪ 3‬أر‪ J‬م ‪2 U‬اص ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪,‬‬
‫و‪2I U/‬‬
‫” ر‪,V 9‬‬
‫دة إذ ‪ ˆ` 2I !/ 9‬ا "‪ ! ,‬ا‪0‬ر‪ J‬م آ_ ‪ O‬ء‪2 3/ .‬‬
‫أر‪ J‬م ‪2O‬ا?‪ ! T ,::6 ,‬إام (‪2O ,‬ا?‪,‬‬
‫‪ M[ ,‬آ ‪ ,‬ا‪0‬ر‪ J‬م ! ‪ 0‬إ ‪ 9‬‬
‫أوراق او آات و‪- U7‬ا و ‪ S‬ور‪ ,J‬او آة ‪ U‬و‪ 2I !/ 9‬أر‪ J‬م ‪2O‬ا?‪,::6 ,‬‬
‫آ ‪:3‬‬
‫‪ S/‬ا‪0‬ر‪ J‬م ! ‪ 0‬إ ‪ 9‬أوراق و‪ 3; RV2I‬و ء و " ا‪ w‬ا‪q H‬وراق ‪ S‬ور‪,J‬‬
‫و‪ U !/‬ا‪ w 9 %J‬ا‪0‬وراق ة اى ‪-‬ا " إ دة ا‪2‬ر‪ ,J‬ا ‪ , 2‬و ‪ S‬ور‪,J‬‬
‫اى و‪ !/‬ا‪ %J‬ا ‪2/‬ب ‪ 4 U‬وه‪./‬ا ‪ ˆ` S‬ا‪ ,XX ,:97‬اوراق اى و‪ 7 !/‬و‬
‫‪ 3‬و ‪ 7‬ا‪2‬ا‪ 3‬ا‪h‬ن ‪2/‬ن ا‪ %J‬ا"‪2O‬ا?‪ 3‬ا‪0‬ول وه‪ 0.94737 2‬وه‪./‬ا ‪2 6‬‬
‫ا"د ا ‪27‬ب ! ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ .,‬وا‪- aV‬ا ان ه‪ 5.‬ا‪ , ^ ,:97‬و‪ I‬ج إ و‪WJ‬‬
‫و‪ U-‬آ ‪ 2‬د ‪ ! w‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪.U ،,‬ا آ ن ! ا ‪- %U‬ا إ‪ H9‬د ‪C‬ق اى‬
‫‪ UH !/ 9 ,"9‬ا ت ‪ 2‬ااد آة ! ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪.,‬‬
‫أ‪ 6‬ه‪ 5.‬ا‪7‬ق ه‪:3‬‬
‫‪ *C‬ا‪ [ D‬ا‪Linear Congruential Method D$‬‬
‫ه‪ 5.‬ا‪ ,:97‬و‪I‬اآ‪ 37"I U‬ا "‪ ,‬ا"د‪ ! X 1 , X 2 ,..., ,9‬ا ` و ‪ S6 m − 1‬ا ‪,Y‬‬
‫ا‪/‬ار‪,9‬‬
‫‪X i +1 = ( aX i + c ) mod m, i = 0,1, 2,...‬‬
‫ا‪ , :‬ا‪0‬و‪ I X 0 ,‬ا‪2‬اة ‪ Seed‬وا[ ‪ W X 9 a W‬ا‪ _ f‬و ا[ ‪ 9 c W‬‬
‫ا‪ 9G‬دة و ‪ 9 m‬ا‪ :‬س ‪ “6T . Modulus‬أن ‪ 3"9 a = b mod m‬ان ) ‪m %:9 ( a − b‬‬
‫‪81‬‬
‫ون ‪ .3J‬إذا آ ‪ I c ≠ 0 W‬ا " د‪ ,‬ا ‪ ,:9C ,:‬ا‪ 7‬ا ‪ w‬و‬
‫‪2/I‬ن ‪c = 0‬‬
‫‪ ,:9C I‬ا‪ 7‬ا‪.3` f‬‬
‫إن إ ر ا‪ X 0 %:‬و ‪ a‬و ‪ c‬و ‪ M/O XA9 m‬آ ا‪2‬اص ا@‪6‬‬
‫?‪q ,‬ر‪ J‬م ا ‪2‬ة‬
‫وآ‪2C g.‬ل اورة ‪ Cycle Length‬وا‪. :6T U6O 3‬‬
‫‪#‬ل‪ [ ) :‬ل ‪((4) R- 8.1‬‬
‫‪2‬ف م ‪ ,:9C‬ا‪ 7‬ا‪ ! ," 2 37‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ .e ,‬ا‪%:‬‬
‫‪X 0 = 27, a = 17, c = 43, m = 100‬‬
‫‪ “6T‬ان ا‪0‬ر‪ J‬م ا‪2/ 2 3‬ن ‪2‬ز‪ ,‬وي ! ‪ 0‬و‪0 99‬ن ) ‪ “6T ( m − 1 = 99‬ا‪f9‬‬
‫ان ا ‪ 2‬أاد ‪2O‬ا?‪ ,‬و‪ W‬أر‪ J‬م و‪ ! 2 3/‬ه‪ 5.‬ا "‪ ,‬أر‪ J‬م ‪2O‬ا?‪2I U ,‬ز‪R9‬‬
‫ وي ! ‪ 0‬و ‪ -2 1‬ا ‪:3‬‬
‫‪Xi‬‬
‫‪, i = 1, 2,...‬‬
‫‪m‬‬
‫= ‪Ri‬‬
‫‪ S I‬ا "‪ ,‬آ ‪:3‬‬
‫‪X 0 = 27‬‬
‫‪X 1 = (17 × 27 + 43) mod 100 = 502 mod 100 = 2‬‬
‫‪2‬‬
‫‪= 0.02‬‬
‫‪100‬‬
‫‪X 2 = (17 × 2 + 43) mod 100 = 77 mod 100 = 77‬‬
‫= ‪R1‬‬
‫‪77‬‬
‫‪= 0.77‬‬
‫‪100‬‬
‫= ‪R2‬‬
‫⋮‬
‫وه‪./‬ا‪...‬‬
‫ ا‪0‬ر‪ J‬م & ا"‪2O‬ا?‪ ,‬ا ‪2‬ة ‪ ,:97‬ا‪ 7‬ا‪ 7‬او ^ه ان ‪ ,; [email protected] : I‬إ‬
‫ '‪ 3‬ا‪2‬ز‪ R9‬ا وي وا@‪:‬ل '‪ ,‬ا‪ ,; [/‬ا"‪Maximum Density N‬‬
‫وا‪3‬‬
‫‪ 3"I‬ان ا‪ %:‬ا‪.eI 3‬ه ‪IT Ri , i = 1, 2,...‬ك ‪YX‬ات آة ;‪ 3‬ا`ة ]‪ . [ 0,1‬و '‪ ,‬اورة‬
‫ا"‪ Maximum Period or Cycle N‬ا‪` 3‬ه‬
‫‪ .eI‬ا‪ %:‬ا‬
‫‪m −1‬‬
‫ودة‬
‫‪m‬‬
‫‪ ,N6‬ان ا‪0‬ر‪ J‬م ا ‪2‬ة ‪ !/ 9‬ان‬
‫‪1 2‬‬
‫‪m m‬‬
‫‪; w:; 0, , ,...,‬ذا ‪/I‬ر اي ر‪; %J‬ن ا "‪/I ,‬ر ! ‪9-‬‬
‫و‪.U‬ا ;ن أ‪ %N‬دورة ‪ ,:97‬ا ‪ ,:‬ه‪ m 3‬و‬
‫‪2‬ل أ‪ %N‬دورة ‪ SH9‬إ ر ‪X 0 %J‬‬
‫و ‪ a‬و ‪ c‬و ‪9 ,9 " m‬ة و‪.U‬ا ‪ m %J .AI‬ا‪ m = 231 − 1 M/O‬و [‪ M‬ه‪ 5.‬ا‪, :‬‬
‫‪I‬م ;‪ 3‬ا ت آ ‪ SH9‬ان ‪2/I‬ن ‪ c‬و ‪) m‬‬
‫‪82‬‬
‫‪ ( c ≠ 0‬او! ‪) Uf" ,‬اي‬
M[ , J .eI a ‫ د ;دي و‬X 0 ‫ن‬2/I ‫ ان‬SH9 g.‫ ( وآ‬U ,‫آ‬O M ‫ا‬2 -2IT
2I ‫ع‬2V2 3; ‫ آ[ا‬R2T ‫ف‬2 . k = 0,1,... %J a = 1 + 4k , a = 3 + 8k , a = 5 + 8k
‫ى‬2 I U‫آ ! ا‬e U ‫ى‬HI 3‫ق " ا@ رات ا‬7‫ و‬,?‫ا‬2O"‫ م & ا‬J‫ر‬0‫ا‬
., ‫ ا‬,?
[email protected]‫اص ا‬2‫ا‬
: ‫ا‬J.‫رم ا‬o ‫رات‬60‫إ‬
,?
[email protected]‫ ا‬U'‫ا‬2 ! ‫آ‬e ,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ى ا‬HI 3‫ه ك د آ ! ا@ رات ا‬
‫ و& ;ن‬Independence ‫ل‬:@‫ وا‬Uniformity ‫ ا وي‬R9‫ز‬2‫ ا‬3‫ ه‬3‫وا‬
:! J ‫ إ‬%:I UV" ‫ف‬2 3‫ا@ رات ا‬
Frequency Test ‫ار‬/‫ إ ر ا‬2‫ ا وي وه‬R9‫ز‬2‫ول @ ر ا‬0‫ ا‬%:‫ا‬
3I‫ا‬.‫ ا‬w ‫ وإ ر اا‬Runs Test ‫ي‬H‫ن ! إ ر ا‬2/9‫ل و‬:@‫ @ ر ا‬3 [‫ ا‬%:‫ا‬
. Autocorrelation Test
:‫ر از! ا وي‬60‫إ‬
,V`‫ف ا‬2
H 0 : Ri
H1 : Ri
distributed as U [ 0,1]
is not distributed as U [ 0,1]
Kolmogrov- ‫ف‬2 – ‫روف‬2-2 2‫إ ر آ‬
‫ م إ‬,V`‫ ا‬5.‫@ ر ه‬
Chi-square Test ‫ آ ي‬R ‫ أو إ ر‬Smirnov Test
Kolmogrov-Smirnov Test ‫ر آ=روف – ' ف‬60‫ إ‬-1
,‫ ا وي ودا‬R9‫ز‬2 F ( x ) ‫ ا ة‬3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ رن ! دا‬:9 ‫ا ا@ ر‬.‫ه‬
. N U H6 ," S N ( x ) ," Empirical CDF 39H‫ ا‬3 ‫ ااآ‬R9‫ز‬2‫ا‬
H _9"‫; ! ا‬
F ( x ) = x, 0 ≤ x ≤ 1
39H‫ ا‬3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ ;ن دا‬R1 , R2 ,..., RN ‫ة‬2 ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ! ا‬,"‫و‬
3 ‫"ف آ‬I S N ( x ) ,"
SN ( x ) =
number of R1 , R2 ,..., RN which are ≤ x
N
83
P
R(1) , R( 2 ) ,..., R( N ) M/O‫ ا‬R1 , R2 ,..., RN ‫ة‬2 ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬WI‫وإذا ر‬
‫ ;ن‬R(1) ≤ R( 2) ≤ ... ≤ R( N )

 0,

k
SN ( x ) =  ,
N

 1,

x < R(1)
R( k ) ≤ x < R( k +1) , k = 1, 2,..., N
x ≥ R( N )
, ' ‫ أ س‬F ( x ) ,‫ ا‬9:I [‫ اآ‬a I S N ( x ) ‫ ;ن‬N , J /I ‫“ ا& آ‬6T
Step Function ,-‫ در‬,‫ دا‬3‫ ه‬," 39H‫ ا‬3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ دا‬.,9` ‫ ا‬,V`‫ا‬
(‫ ا ت‬M I M ; 3; M ` M/O U6O ‫ف‬2) ‫ هة‬O , J M‫ات آ‬G`J ‫ذات‬
,?
[email protected]‫ أي ا‬S N ( x ) ‫ و‬F ( x ) ! ‫آ إ اف‬0 ,:7 ‫ ا‬, :‫` ‹ ا‬9 ‫ا ;ن ا@ ر‬.U‫و‬
D = max F ( x ) − S N ( x )
, ‫ ر‬:‫ ا‬,Y ‫ف م ا‬2 /‫ول و‬H ‫"وف و‬
‫ م‬J‫ر‬T‫ ! ا‬, 2I ‫ن‬0 N ≥ 35 ‫ن‬2/I D ,?
D ,?
6z 3"‫ ا‬R9‫ز‬2‫ا‬
6z Asymptotic Formula
.& ,` ^ 2 ‫ي‬0 35 ! MJ‫ ا‬,?‫ا‬2O"‫ا‬
D ,?
N
D0.10
1.22
N
≥ 35
D0.05
6z , ‫ ا‬%:‫ف م ا‬2
D0.01
1.36
N
1.63
N
:3 ‫ارزم ا‬2‫ ا وي م ا‬R9‫ز‬2‫ ا‬,V; W I ‫اء ا@ ر‬[email protected]
‫ ;ن‬Y ‫ ا‬3; i UI‫ ر‬3‫ هة ا‬O ‫ ا‬3‫ ه‬R(i ) W ‫ ;ذا آ‬. 9
I ‫ م‬J‫ر‬0‫ ا‬SI‫ ر‬: (1) ‫ة‬27
R(1) ≤ R( 2) ≤ ⋯ ≤ R( N ) ‫ن‬2/9 ]I ‫ا‬
‫ ت‬/‫ ا‬S6‫ أ‬: (2) ‫ة‬27
i

D + = max  − R(i ) 
1≤ i ≤ N
N

i − 1

D − = max  R( i ) −

1≤i ≤ N
N 

D = max ( D + , D − ) , /‫ ا‬S6‫ أ‬: (3) ‫ة‬27
84
‫‪27‬ة )‪6 : (4‬د ا‪ , :‬ا ‪ ! Dα ,-‬ا‪H‬ول ا ‪2 ," %:‬ى ا "‪ α ,92‬و ‪%H‬‬
‫ا"‪N ≥ 35 ,‬‬
‫‪27‬ة )‪ : (5‬إذا آ ‪ W‬ا‪ , :‬ا ‪6z , 2‬‬
‫?‪ D ,‬اآ ! ا‪ , :‬ا ‪H‬و‪; ; Dα ,‬‬
‫ا`‪ ,V‬ا `‪e ,9‬ن ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا ‪2‬ة ‪ RI‬ا‪2‬ز‪ R9‬ا وي وإ‪ ] ; T‬ا ‪%‬‬
‫‪; _O/‬ق ! ا‪2‬ز‪ R9‬ا ‪q 3::‬ر‪ J‬م } ‪ { R1 , R2 ,..., RN‬وا‪2‬ز‪ R9‬ا وي‪.‬‬
‫إ‪60‬ر آ=روف – ' ف ‪)$'_ Kolmogrov-Smirnov Test‬ام‬
‫‪: Excel‬‬
‫‪2‬ف "ض ه‪.‬ا ا@ ر ! ‪ 3;) Excel‬ا ‪ ,::‬ه‪.‬ا إ ر ‪ 2‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪,‬‬
‫;‪9- , `' 3; ( Excel 3‬ة ! ‪ Excel‬أد‪ M‬ا ‪:3‬‬
‫‪85‬‬
‫;] ا‪0‬ر‪ J‬م & ا"‪2O‬ا?‪ ,‬آ ‪:3‬‬
‫‪ SI‬ا‪0‬ر‪ J‬م ا ‪ ,HI‬آ ‪:3‬‬
‫‪86‬‬
:3 ‫ ا‬M/O‫ ا‬3; aV2 2‫ ا ” آ ه‬M‫أد‬
:, ‫ ا ?] ا‬M
‫و‬
‫ م‬J‫ر‬q 3:: ‫ ا‬R9‫ز‬2‫_ ;ق ! ا‬O/ % ‫ أي ا‬,-2 ‫ ا@ ر‬,H ‫“ ان‬6T
.‫ ا وي‬R9‫ز‬2‫ { وا‬R1 , R2 ,..., R1000 }
” ‫ ام ا‬K-S ‫ @ ر‬,"`‫ ل ا‬[email protected]‫ ا‬%J ‫ ب‬6 !/ 9

0.11  
P ( D > Dobs ) = Q   N + 0.12 +
 D , N ≥ 2
N 

∞
Q ( λ ) = 2∑ ( −1) e −2 j λ
j −1
2 2
j =1
:3 ‫ آ‬Excel ‫ ام‬U 3‫وا‬
87
M
D4 ,‫ ا‬3; Dobs , 2 ‫ ا‬, :‫ وا‬D3 ,‫ ا‬3; N ,9 ‫ ت ا‬-‫ ر‬%J RV2
:3 ‫ آ‬D6 ,‫ ا‬3; p-value ,"`‫ ل ا‬[email protected]‫ ا‬%J Chi-square Test ‫ ! آي‬# ‫ر‬60‫ إ‬-2
,?
n
χ 02 = ∑
i =1
( Oi − Ei )
[email protected]‫م ا‬9 ‫ آ ي‬R ‫إ ر‬
2
Ei
‫ و‬i ,b`‫ ا‬3; ,"J2 ‫ د ا ت ا‬2‫ ه‬Ei ‫ و‬i ,b`‫ ا‬3; ‫ هة‬O ‫ د ا ت ا‬2‫ ه‬Oi
2‫ ه‬i ,b`‫ ا‬3; R:I 3‫ ! ا ت ا‬RJ2 ‫ ا وي ا"د ا‬R9‫ز‬2 .‫—ت‬b`‫ د ا‬n
‫ آ ي‬R R9‫ز‬2‫ آ‬9:I ‫زع‬2I χ 02 ,?
[email protected]‫ ا‬.,"‫ ا‬%H6 N P6 Ei = N n
. n − 1 ,96 ‫ ت‬-‫ر‬
88
:Excel ‫)ام‬$'_ ‫ ! آي‬# ‫ر‬60‫ إ‬:‫ل‬#
Excel ! , `' 3; , ‫ هات ا‬O ‫ ا‬M‫أد‬
R
0.34
0.9
0.25
0.89
0.87
0.44
0.12
0.21
0.46
0.67
0.83
0.76
0.79
0.64
0.7
0.81
0.94
0.74
0.22
0.74
0.96
0.99
0.77
0.67
0.56
0.41
0.52
0.73
0.99
0.02
0.47
0.3
0.17
0.82
0.56
0.05
0.45
0.31
0.78
0.05
0.79
0.71
0.23
0.19
0.82
0.93
0.65
0.37
0.39
0.42
0.99
0.17
0.99
0.46
0.05
0.66
0.1
0.42
0.18
0.49
0.37
0.51
0.54
0.01
0.81
0.28
0.69
0.34
0.75
0.49
0.72
0.43
0.56
0.97
0.3
0.94
0.96
0.58
0.73
0.05
0.06
0.39
0.84
0.24
0.4
0.64
0.4
0.19
0.79
0.62
0.18
0.26
0.97
0.88
0.64
0.47
0.6
0.11
0.29
0.78
:3 ‫ † ا ت آ‬%X
[0,0.1), [0.1,0.2), …, [0.9,1.0) 3 ‫ ;ات آ‬10 ‫[ إ‬0,1) ‫ ا`ة‬%:I ! C e"I
C2:C11 ‫ ل‬H ‫ ا‬3; 0.1, 0.2, ,…, 1.0 ‫ ت‬b` "‫ ا‬%:‫ ا‬MI‫و‬
:3 ‫ و† ا`ا^ ت آ‬Tools => Data Analysis => Histogram ‫أ ر‬
89
‫;‪ 3‬ا ‪ H‬ل ‪ F2:F11‬أد‪ M‬ا‪ %X Ei = N n = 100 10 = 10 , :‬أد‪ M‬ا ” آ ;‪G1:G4 3‬‬
‫)ا ت ;‪ 3‬ا" ‪2‬د ‪ I‬ب ‪ ,Y' ! CHITEST‬ا"‪ _9‬ا ‪.(,:‬‬
‫ا‪:g1‬‬
‫‪ “6‬ان ا‪ , :‬ا ‪ R , 2‬آ ي ‪ 3.4‬ر‪ -‬ت ‪ 9 ,96‬ا‪ ! MJ‬ا‪ , :‬ا‪H‬و‪16.92 ,‬‬
‫ ‪2‬ى "‪ α = 0.05 ,92‬و ‪.U‬ا ;ن ‪ ,H‬ا@ ر ‪ ,-2‬أي ا ‪; _O/ %‬ق !‬
‫ا‪2‬ز‪ R9‬ا ‪q 3::‬ر‪ J‬م } ‪ { R1 , R2 ,..., R100‬وا‪2‬ز‪ R9‬ا وي‪.‬‬
‫‪90‬‬
:‫ل‬r*'^‫رات ا‬60‫إ‬
,V`‫ف ا‬2
H 0 : Ri
distributed independently
H1 : Ri
is not distributed independently
: ‫ه‬6‫ أ‬Runs Tests ‫ي‬H‫ رات ا‬I ‫ ه ك ة إ رات‬,V`‫ ا‬5.‫@ ر ه‬
:Runs Up and Runs Down ' ‫ي‬T‫ وا‬U/2 ‫ي‬T‫ا‬
:3 ‫& [ ل ا‬6O ‫ف‬2‫ و‬Nonparametric Test 3 " T ‫ إ ر‬2‫وه‬
: Excel ‫)ام‬$'_ ' ‫ي‬T‫ وا‬U/2 ‫ي‬T‫ا‬
Excel , `' 3; , ‫ ا ت ا‬M‫أد‬
R
0.41
0.19
0.18
0.31
0.68
0.72
0.01
0.42
0.89
0.75
0.95
0.73
0.94
0.08
0.69
0.04
0.74
0.54
0.18
0.83
0.91
0.02
0.47
0.45
0.55
0.01
0.23
0.13
0.62
0.36
0.32
0.57
0.36
0.16
0.82
0.63
0.27
0.28
0.53
0.29
:3Ih ‫ آ‬9‫ ا‬,: %X A2:A41 9‫ ا‬3; MI ‫ م‬J‫ر‬0‫“ ان ا‬6T
B2=IF(A2<A3,"+",IF(A3="","","-"))
‫ ل‬H ‫ ا‬,9 U 6 dI %X
C2 = 1
%X
C3=IF(B3="","",IF(B3=B2,C2,C2+1))
‫ ل‬H ‫ ا‬,: 6 dI‫و‬
D2 =MAX(C:C)
E2 =COUNT(A:A)
F2 =(2*E2-1)/3
G2 =SQRT((16*E2-29)/90)
G4 =(D2-F2)/G2
G6 =NORMSDIST(G4)
91
‫;‬
‫‪ M‬ا‪,H‬‬
‫ا‪J‬ح‪:‬‬
‫‪"9‬ف ا‪H‬ي ا& "‪ ! ,‬ا@ رات ا ‪ 3`; &U O‬ا [ ل ا ‪- 26 -29‬ي‬
‫آ ‪:3‬‬
‫‪92‬‬
Run Mark
1
+++
2
−
3
+
4
−
5
+
6
−−−
7
++
8
−
9
+
10
−−
11
+
12
−
13
+
14
−−
15
+
16
−−
17
+
18
−
19
++
20
−−
21
++
22
−
23
+
24
−−
25
++
26
−
w2 ‫ ;ن‬,:: ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ! ا‬," 3; ‫ي‬H 3/‫ ا"د ا‬2‫ ه‬a ‫ أن‬V; ‫;ذا‬
‫ ت‬J" 7"I a !9 I‫و‬
2N −1
3
16
N − 29
σ a2 =
90
µa =
‫ و‬N ( µ a , σ a2 ) R9‫ز‬2I 9:I U ‫ن‬2/9 a ‫ ;ن‬N > 20 W ‫ ;ذا آ‬.,"‫ ا‬%H6 N P6
U 3‫ ا‬Z 0 =
a − µa
σa
,?
[email protected]‫ ب ا‬
‫ي‬H‫ ر ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ل ا‬:‫ إ‬,V;
93
‫‪2I 9:I‬ز‪ W I 3 J 3"C R9‬ا`‪ ,V‬ا `‪ 6 " .,9‬ب ‪ Z 0‬و ‪2‬ى "‪α ,92‬‬
‫‪ :‬ر‪ %: U‬ا‪H‬و‪; ,‬ذا آ ‪ ;T ; − zα 2 ≤ Z 0 ≤ zα 2 W‬ا`‪ ,V‬ا `‪.,9‬‬
‫ا‪:‬ار ‪9 :‬ك آ ‪. S 7 !9‬‬
‫ا‪T‬ي ‪A‬ق و‪ t4‬ا'‪: Runs above and below the mean 8‬‬
‫إذا ‪q !" N‬ر‪ J‬م ا"‪2O‬ا?‪ 3; ,‬ا [ ل ا و‪ J‬ر آ‪ O M‬هة ‪ w2‬ا ‪ O‬هات ‪H‬‬
‫ان _ ا ‪ O‬هات ا‪0‬ول )اـ ‪ O 20‬هة ا‪0‬و ( آ‪ U‬أ ! ا ‪ w2‬و‪ R -‬ا ‪ O‬هات‬
‫^‬
‫;‪ 3‬ا _ ا‪ h‬أ‪ ! MJ‬ا ‪ w2‬و‪6‬وث [‪ M‬ه‪.‬ا ا ‪ O 3; w‬هات ‪2O‬ا?‪I ,‬‬
‫ ‪.U M‬ا ‪:9‬ح إ‪-‬اء إ ر ‪H‬ي ;‪2‬ق و‪ W I‬ا ‪e w2‬آ ! إ‪ ,:‬ا‪0‬ر‪ J‬م‬
‫ا"‪2O‬ا?‪ ,‬ا ‪2‬ة‪.‬‬
‫إ ر ا‪H‬ي ;‪2‬ق و‪ W I‬ا ‪H9 w2‬ى `ˆ ‪ ,:9C‬ا@ ر ا وذ‪g‬‬
‫‪ :‬ر‪ ,‬آ‪M‬‬
‫‪ O‬هة ‪ w2‬ا ‪ O‬هات ;ذا آ ‪2; W‬ق ا ‪ + Rf w2‬أ إذا آ ‪ W I W‬ا ‪Rf; w2‬‬
‫ ‪ S %X‬د ا‪H‬ي ا‪ .3/‬و‪H‬ي ا@ ر آ ‪:3‬‬‫إذا آ ‪ n1 W‬د ا ‪ O‬هات ا‪ 3‬ه‪2; 3‬ق ا ‪ w2‬و ‪ n2‬د ا ‪ O‬هات ا‪ 3‬ه‪W I 3‬‬
‫ا ‪ w2‬و ‪ b‬د ا‪H‬ي ا‪ “6T) 3/‬أن ‪; (1 ≤ b ≤ n1 + n2 = N‬ن ‪ w2‬و‪7"I b !9 I‬‬
‫"‪ J‬ت‪:‬‬
‫‪2n1n2 1‬‬
‫‪+‬‬
‫‪N‬‬
‫‪2‬‬
‫) ‪2n n ( 2 n n − N‬‬
‫‪σ b2 = 1 2 2 1 2‬‬
‫)‪N ( N − 1‬‬
‫= ‪µb‬‬
‫;ذا آ ‪ W‬اي ! ‪ n1‬و ‪ n2‬أآ ! ‪; 20‬ن ‪ W I b‬ا`‪ ,V‬ا `‪2/9 ,9‬ن ‪2I 9:I U‬ز‪R9‬‬
‫‪ 3"C‬و@‪-‬اء ا@ ر ‪2/‬ن ا@‪6‬‬
‫?‪,‬‬
‫‪b − µb‬‬
‫‪σb‬‬
‫= ‪ Z 0‬و ‪2‬ى "‪ : α ,92‬ر‪U‬‬
‫‪%:‬‬
‫ا‪H‬و‪; ,‬ذا آ ‪ ;T ; − zα 2 ≤ Z 0 ≤ zα 2 W‬ا`‪ ,V‬ا `‪.,9‬‬
‫‪#‬ل‪ :‬ا‪T‬ي ‪A‬ق و‪ t4‬ا'‪Runs above and below the mean 8‬‬
‫_'‪)$‬ام ‪:Excel‬‬
‫‪2‬ف ‪ -2‬إ ر ا‪H‬ي ;‪2‬ق و‪ W I‬ا ‪q w2‬ر‪ J‬م ا"‪2O‬ا?‪ 3; ,‬ا [ ل ا ‪ .‬أد‪M‬‬
‫ا ‪ O‬هات ا ‪9- , `' 3; ,:‬ة ! ‪ Excel‬آ ‪:3‬‬
‫‪94‬‬
‫;‬
‫‪ M‬ا ?] ا ‪,‬‬
‫‪95‬‬
‫ا‪:‬ار ‪9 :‬ك آ ‪. S 7 !9‬‬
‫إ‪60‬ر اا ‪ 8‬ا‪3‬ا‪:4‬‬
‫وه‪.‬ا إ ر ( @‪ ,:‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬و‪ 9‬ا@ د أو ا@ر‪ I‬ط ! "‪! ,‬‬
‫ا‪0‬اد‪2 .‬ف ‪7‬ق إ ‪ ,:9C‬ا@ ر ;‪0 w:‬ن ا‪ _ ,9N‬ه‪.‬ا ا@ ر ‪,` S7I‬‬
‫ا ! ‪2‬ى ه‪.‬ا ا‪ /‬ب و‪2‬ف ‪I‬رس ;‪ 3‬دة ‪221‬‬
‫آ ب ‪C‬ق ا‪ A‬ا@‪6‬‬
‫‪C) P‬ق ا‪ A‬ا@‪6‬‬
‫?‪ .(3‬أ‪N‬‬
‫?‪ 3‬ا‪GH‬ء ا‪0‬ول ‪ _eI‬د‪ .‬ن ‪ -‬ي‪(3) .‬‬
‫‪#‬ل‪:‬‬
‫) ‪ 3; :,N6‬ه‪.‬ا ا [ ل ‪2‬ف م '‪ ,Y‬ب اا ‪ w‬ا‪.‬ا‪ 3I‬أ‪ ! %‬ا ” ا ‪2-2‬دة‬
‫ء(‬
‫;‪ 3‬ا‪ /‬ب ا ‪:‬ر وه‪ 5.‬ا ‪ ,Y‬أآ[ إ‪ O‬را وإا ;‪ 3‬آ‪ S‬ا@‪6‬‬
‫;‪ 3‬ا [ ل ا ‪2‬ف ;‪ ,V‬ا@‪:‬ل وذ‪ g‬ر ‪ %J‬اا ‪ w‬ا‪.‬ا‪," 3I‬‬
‫ا ‪ O‬هات‪; .‬ذا ;‪ V‬أن ‪ ρi‬ه‪ 2‬اا ‪ w‬ا‪.‬ا‪ ! 3I‬ار‪ i ,-‬وا‪.‬ي ‪,J" 7"9‬‬
‫‪, i = 0,1, 2,...‬‬
‫)‪− R‬‬
‫‪∑ ( R − R )( R‬‬
‫=‬
‫)‪∑ (R − R‬‬
‫‪N −i‬‬
‫‪t +i‬‬
‫‪2‬‬
‫‪t‬‬
‫‪N‬‬
‫‪t‬‬
‫ا@‪6‬‬
‫?‪ ! ," ρi ,‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا ‪ U ,::‬ا‪2‬اص ا@‪6‬‬
‫‪t =1‬‬
‫‪ρi‬‬
‫‪t =1‬‬
‫?‪ ,‬ا ‪:,‬‬
‫‪E ( ρi ) = 0, i = 1, 2,...‬‬
‫‪1‬‬
‫‪, i = 1, 2,...‬‬
‫‪N‬‬
‫= ) ‪V ( ρi‬‬
‫‪Approx‬‬
‫) ‪ρi ∼ N ( 0,1 N‬‬
‫@ ر ا@‪:‬ل ;ن ا`‪ ,V‬ه‪:3‬‬
‫‪H 0 : ρi = 0‬‬
‫‪H1 : ρ i ≠ 0‬‬
‫إ‪60‬ر اا ‪ 8‬ا‪3‬ا‪)$'_ 4‬ام ‪:Excel‬‬
‫@ ر ه‪ 5.‬ا`‪ ,V‬ام ‪ Excel‬أد‪ M‬ا ‪Excel ! , `' 3; 3‬‬
‫‪96‬‬
‫;‪ UN‬ا ?] ا ‪,‬‬
‫‪ “6‬أن ‪ ρi , i = 1, 2,...,5 %J‬آ‪ R:I U‬دا‪ M‬ا`ة ) ‪ ( −0.3099, 0.3099‬وه‪.‬ا ‪ 9A9‬ا`‪,V‬‬
‫ا `‪.,9‬‬
‫‪97‬‬
‫ا ا‪:"#$‬‬
‫‪ u# ) 4‬ات ‪J2‬ا ‪:‬‬
‫إن ‪Y 2I‬ات ‪2O‬ا?‪2I RI ,‬ز‪ " "9‬ه‪ 3‬أ س ا‬
‫آ ة إذ ‪ 2I / 9‬أ‪6‬اث ‪2O‬ا?‪,‬‬
‫‪ I‬آ‪ 3‬أي ‪ N‬م ‪ 3::6‬وذ‪2I ,9 " g‬ز‪ "9‬ت إ‪ 7I , 6‬أ‪6‬اث و ‪2‬اص ه‪.‬ا ا‪ N‬م‪.‬‬
‫; [ أز ‪,‬‬
‫! ا‪2'2‬ل ;‪ 3‬أ‪ , N‬ا‪27‬ا وه‪ 3‬أ‪6‬اث ‪2O‬ا?‪. I ,‬ج ^ ‬
‫‪2‬ز‪R9‬‬
‫ا‪.30‬‬
‫ه ك ة ‪C‬ق و‪2‬ارز ت ‪Y 2‬ات ‪2O‬ا?‪2I ! ,‬ز‪ !" R9‬و‪2‬ف "ض اه ‪U‬‬
‫وأآ[ه إ‪ O‬را وذ‪Y g‬ض ا@ م ‪ 5.U‬ا‪7‬ق ;‪ w:‬وˆ @ا ‪U‬‬
‫إذ ;‪ 3‬ا ‪ ,::‬أن‬
‫ا‪2‬ارز ت ا ‪ 3; ,‬ا ] ا ‪ S‬اآ[ ‪27I‬را و‪ , ]? 37"I‬ا ‪ ,J2X2‬و‪%I J‬‬
‫;‬
‫‪ U‬وإ ره ! ‪ MJ‬ا‪ ! [/‬ا ‪ 3; ![6‬أ ث ‪H 3; ,:X2‬ت ا ‪ P‬ا" ‪.3‬‬
‫‪ O 2 3/‬هات ‪2OY x1 , x2 ,...‬ا?‪X 3‬‬
‫‪ R9‬ا‪2‬ز‪R9‬‬
‫∞ < ‪FX ( x ) = P ( X ≤ x ) , − ∞ < x‬‬
‫; م "‪ ! ,‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ P6 R1 , R2 ,... ,‬آ‪ U Ri M‬دا‪ ,‬آ[ ;‪ ,‬إ‪, 6‬‬
‫‪1, 0 ≤ x ≤ 1‬‬
‫‪fR ( x) = ‬‬
‫‪0, otherwise‬‬
‫ودا‪2I ,‬ز‪I R9‬اآ ‪3‬‬
‫‪x<0‬‬
‫‪0,‬‬
‫‪‬‬
‫‪FR ( x ) =  x, 0 ≤ x ≤ 1‬‬
‫‪1,‬‬
‫‪x >1‬‬
‫‪‬‬
‫و‪ :9‬ل أن )‪. i %J R H Ri ∼ U ( 0,1‬‬
‫‪ *C‬ا ا‪Inverse Transform Technique B.‬‬
‫وه‪ 3‬ا‪ ,:97‬ا‪0‬آ[ إا و '‪2 ,‬ز‪ "9‬ت ا@‪ , 6‬ا‪ !/ 9 3‬إ‪ H9‬د ) ‪U FX−1 ( x‬‬
‫وآ‪2 g.‬ز‪ "9‬ت ا‪ Empirical Distributions ,9H‬و‪2:I‬م ا‪ 7‬‬
‫‪FX ( X ) = R‬‬
‫و‪2‬ف ‪2 M ` U6O‬ز‪ R9‬ا‪.30‬‬
‫‪ :,N6‬ا‪2‬ز‪ "9‬ت ا@‪ , 6‬ا ‪.‬آ‪2‬رة ;‪ 3‬ه‪.‬ا ا` ‪ M‬وا‪ O U 2 3‬هات ‪O‬و‪,6‬‬
‫` ‪ 3; M‬ا` ‪ M‬ا دس ! ‪ ,-.‬ا ت‪.‬‬
‫‪98‬‬
:'‫! از! ا‬6 ‫ا‬J2 u# # ‫ه)ات‬J# ) 4
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬30‫ ا‬R9‫ز‬2‫ ا‬R9 X 3?‫ا‬2O"‫ ا‬Y ‫ا‬
λ e − λ x , x ≥ 0
f X ( x) = 
x<0
 0,
3 ‫اآ‬I R9‫ز‬2I ,‫ودا‬
F ( x) = ∫
x
−∞
1 − e − λ x , x ≥ 0
f ( t ) dt = 
x<0
 0,
, ‫ز‬0 ‫ آ ن‬2 [ ; ., ‫ة ز‬6‫ و‬3; ‫ د ا وث‬w2 ,‫` أ‬9 λ %" ‫ا‬
!
‫ة‬62 ‫ل‬2'2‫ د ا‬w2 U‫` ا‬I λ ‫ ;ن‬λ ‫ "ل‬3‫ أ‬R9‫ز‬2I X 1 , X 2 ,... ‫ل‬2'2‫ا‬
‫ ;ن‬i , J ‫ي‬0 &‫“ ا‬6T .‫ل‬2'2‫ أو "ل ا‬, ‫ز‬
E ( Xi ) =
1
λ
.‫ل‬2'2‫! ا‬
! ‫ ز‬w2 2‫ ه‬1 λ ‫ا ;ن‬./‫وه‬
‫ ام‬3‫ أ‬R9‫ز‬2I U 3‫ وا‬X 1 , X 2 ,... ,?‫ا‬2O"‫ات ا‬Y ‫ هات ! ا‬O 2 ‫ف‬2
:3 ‫ارزم ا‬2 3/"‫ ا‬M92 ‫ ا‬,:9C
. X 3?‫ا‬2O"‫ ا‬Y 3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ دا‬-‫ أو‬:(1) ‫ة‬27
F ( x ) = 1 − e − λ x , x ≥ 0 3‫ ه‬3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ دا‬30‫ ا‬R9‫ز‬2
F ( X ) = R RV X ‫ ل‬H :(2) ‫ة‬27
. x ≥ 0 ‫ ل‬H ‫ ا‬1 − e − λ X = R 30‫ ا‬R9‫ز‬2
. R ,T X Y , F ( X ) = R ,‫ ا " د‬M6 :(3) ‫ة‬27
:3 ‫ آ‬R ,T X Y 1 − e− λ X = R ,‫ ا " د‬M 30‫ ا‬R9‫ز‬2
1 − e−λ X = R
e−λ X = 1 − R
−λ X = ℓn (1 − R )
X=
−1
λ
ℓn (1 − R )
99
M/O‫ ا‬3‫ وه‬30‫ ا‬R9‫ز‬2 3?‫ا‬2O Y 2 I X =
−1
λ
ℓn (1 − R ) ,‫ا " د‬
. X = F −1 ( R )
! ‫ هات‬O ‫ ا‬S6‫ ا‬%X ! ‫ و‬R1 , R2 ,... ,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ب ! ا‬27 ‫ و ا"د ا‬:(4) ‫ة‬27
. X i = F −1 ( Ri ) ,Y ‫ ا‬S6 X 3?‫ا‬2O"‫ ا‬Y ‫ا‬
3 ‫ آ‬X 1 , X 2 ,... S R1 , R2 ,... ,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬7" 30‫ ا‬R9‫ز‬2
Xi =
−1
λ
ℓn (1 − Ri ) , i = 1, 2, 3,...
(‫ ) ذا؟‬X i =
−1
λ
ℓn Ri , i = 1, 2, 3,... ‫ إ‬,Y ‫ ا‬5.‫ ه‬wI !/ 9 :,N6
:Excel ‫)ام‬$'_ '‫ از! ا‬# ‫ه)ات‬J# ) 4 (1) ‫ل‬#
. λ = 1 30‫ ا‬R9‫ز‬2‫ ا‬R9 ‫ي‬.‫ ا‬X 3?‫ا‬2O"‫ ا‬Y ‫ هة ! ا‬O 1000 ‫و‬
aV2 2‫ ا ت آ ه‬M‫ وأد‬Excel 3; ‫ة‬9- , `' a;‫أ‬
100
, ‫ ا ?] ا‬S ; F9 ‫ ا ` ح‬wYV‫" إد ل ا ت ا‬
‫اري‬/I Rf ! 90‫ ا‬M/O‫ا‬
,?‫ا‬2O"‫ م ا‬J‫ر‬q ‫اري‬/I Rf ‫ ا ر‬M/O‫ا‬
39:I ‫ر‬: 2‫ ه‬Histogram ‫اري‬/‫ ا‬Rf ‫“ أن ا‬6T ، 30‫ ا‬R9‫ز‬2 ‫ة‬2 ‫ هات ا‬O ., [email protected]‫ ا‬,; [/‫ ا‬,‫ا‬
: (a,b) ‫ از! ا وي‬# ‫ه)ات‬J# ) 4 (2) ‫ل‬#
,J" 7"I U , [email protected]‫ ا‬,; [/‫ ا‬,‫ ;ن دا‬X ~ U ( a, b ) ‫إذا آ ن‬
 1
, a≤ x≤b

f ( x) = b − a
 0,
otherwise
:3 ‫ارزم ا‬2‫ات ا‬27 R X ~ U ( a, b ) 3?‫ا‬2O"‫ ا‬Y 2 O 3/
3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ دا‬-2 :(1) ‫ة‬27‫ا‬

x<a
 0,

x−a
F ( x) = 
, a≤ x≤b
b − a

x>b
 1,

. a ≤ x ≤ b ‫ ل‬H ‫ ا‬F ( X ) = ( X − a ) ( b − a ) = R Rf :(2) ‫ة‬27‫ا‬
101
]; R ,T X Y , F ( X ) = ( X − a ) ( b − a ) = R ,J"‫ ا‬M :(3) ‫ة‬27‫ا‬
. X = a + (b − a) R
. X ~ U ( 0,10 ) 3?‫ا‬2O"‫ ا‬Y ‫ هة ! ا‬O 1000 ‫ و‬:!9 I
: Weibull 6‫ز! و‬4 # ‫ه)ات‬J# ) 4 (3) ‫ل‬#
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬M9‫ و‬R9‫ز‬2I R9 X 3?‫ا‬2O"‫ ا‬Y ‫ا‬
β
 β  x  β −1 − x 

e α  ,
x≥0
f ( x ) =  α  α 

0,
otherwise

.(,Y ‫ ا‬5.‫ ه‬3; ν = 0 RJ2 ‫ ا‬%" ) R9‫ز‬2 M/O‫ وا‬%H ‫ ا‬% " 3‫ ه‬β > 0 ‫ و‬α > 0 P6
:, ‫ات ا‬27‫ ا‬R M9‫ و‬R9‫ز‬2I ! ‫ هات‬O 2
3‫ ه‬3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ ان دا‬H , [email protected]‫ ا‬,; [/‫ ا‬,‫ ! دا‬:(1) ‫ة‬27‫ا‬
F ( x) = 1− e
 x
− 
α 
β
, x≥0
F ( x) = 1− e
X = α  −ℓn (1 − R ) 
1
β
x
− 
α 
β
= R RV :(2) ‫ة‬27‫ا‬
]; R ,T X -‫ أو‬:(3) ‫ة‬27‫ا‬
: Excel ‫)ام‬$'_ Weibull 6‫ز! و‬4 # ‫ه)ات‬J# ) 4
:3 ‫ آ‬Excel ‫ ام‬β = 2 ‫ و‬α =
1
%: M9‫ و‬R9‫ز‬2I ! ‫ هة‬O 1000 2 ‫ف‬2
2
102
‫اري‬/I Rf ! 90‫ ا‬M/O‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬q ‫اري‬/I Rf ‫ ا ر‬M/O‫ا‬
.M9‫ و‬R9‫ز‬2 ‫ة‬2 ‫ هات ا‬O : Triangular Distribution /‫ از! ا‬# ‫ه)ات‬J# ) 4 (4) ‫ل‬#
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬Tri [ a, b, c ] 3[[ R9‫ز‬2I & ‫ن‬2/9 X 3?‫ا‬2O"‫ ا‬Y ‫ا‬
 2( x − a)
, a≤ x≤b

 ( b − a )( c − a )
 2 (c − x)

f ( x) = 
, b< x≤c
 ( c − b )( c − a )

 0,
elsewhere

:3 ‫اآ‬I R9‫ز‬2I ,‫ ودا‬a ≤ b ≤ c P6

x≤a
 0,


2
 ( x − a)
,
a< x≤b
 ( b − a )( c − a )

F ( x) = 
2
c − x)
(

1 − c − b c − a , b < x ≤ c
)(
)
 (

 1,
x>c

103
,‫ ا‬Tri [ 0,1, 2] 3[[ R9‫ز‬2I & ‫ي‬.‫ ا‬X 3?‫ا‬2O"‫ ا‬Y ,?‫ا‬2O ‫ هات‬O 2 ‫ف‬2
:, 6‫ إ‬,; [‫آ‬
0 ≤ x ≤1
 x,

f ( x ) = 2 − x, 1 < x ≤ 2
 0,
elsewhere

:3 ‫اآ‬I R9‫ز‬2I‫و‬

 0,

 x2

,

F ( x) =  2
2
(2 − x) ,

1
−

2


 1,

x≤0
0 < x ≤1
1< x ≤ 2
x>2
:“6 3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫! دا‬
X = 2 R ‫ن‬2/9 ‫ وه‬0 ≤ R ≤
1
X2
2‫ ه‬R ‫ ل‬H ‫ن‬2/9‫ و‬R =
‫ ;ن‬0 ≤ X ≤ 1
2
2
( 2 − X ) ‫ ;ن‬1 ≤ X ≤ 2
1
‫ن‬2/9 ‫ ≤ وه‬R ≤ 1 2‫ ه‬R ‫ ل‬H ‫ن‬2/9‫ و‬R = 1 −
2
2
2
‫و‬
,J" 7"9 X 3?‫ا‬2O"‫ ا‬Y ,?‫ا‬2O ‫ هات‬O 2 ‫ا ;ن‬./‫ وه‬X = 2 − 2 (1 − R )
1

2R ,
0≤ R≤

2
X =
1
2 − 2 (1 − R ) ,
< R ≤1

2
‫)ام‬$'_ Triangular Distribution /‫ از! ا‬# ‫ه)ات‬J# ) 4
Excel
:3 ‫ آ‬Excel ‫ ام‬X 3?‫ا‬2O"‫ ا‬Y ‫ هة ! ا‬O 1000 2 ‫ف‬2
104
‫ا‪ M/O‬ا ر ‪/I Rf‬اري ‪q‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا‪ M/O‬ا‪/I Rf ! 90‬اري‬
‫ ‪ O‬هات ا ‪2‬ة ‪2‬ز‪ R9‬ا [[‪.3‬‬
‫‪105‬‬
‫ت‬.‫ز‬4 ‫ أو‬Empirical Distributions 6T‫ت ا‬.‫از‬
Sampling Distributions 1.‫ا‬
79 3 " R9‫ز‬2I ‫د‬2-‫ م و‬, 6 3; ,9 " ‫" ت ا‬9‫ز‬2I ‫ أو‬,9H‫" ت ا‬9‫ز‬2‫م ا‬I
! ," H ‫ ا ت ا‬%N" 79 ‫ا‬.‫ وه‬.&I ‫آ‬
‫& و‬-. ‫اد‬9 ‫ م‬N ! ," H ‫ا ت ا‬
‫ هات‬O ‫ ! ا‬, 9 W ‫ ;ذا آ‬.3 " R9‫ز‬2I ‫ ا ت‬7I
‫ر‬9‫ و‬,::6 , N‫ا‬
:3 ‫ آ‬S I ," R9‫ز‬2‫ ا‬,‫ أو دا‬39H‫ ا‬R9‫ز‬2‫ ا‬,‫ ;ن دا‬x1 , x2 ,..., xn
S6‫ أ‬x(1) ≤ x( 2) ≤ ... ≤ x( n) P
x(1) , x( 2) ,..., x( n ) M/O‫ ا‬x1 , x2 ,..., xn ‫ هات‬O ‫ ا‬SI‫ر‬
:,J"‫ ! ا‬39H‫ ا‬R9‫ز‬2‫ ا‬,‫دا‬

 0,

k
Sn ( x ) =  ,
n

 1,

x < x(1)
x( k ) ≤ x < x( k +1) , k = 1, 2,..., n
x ≥ x( n )
‫ف‬2‫ ( و‬, ` ) ,"7: ‫ ة او‬
‫ن إ‬2/I ,9H‫" ت ا‬9‫ز‬2‫ ا ت ;ن ا‬S6 .‫[ ل‬
‫"ض آه‬
:Excel ‫)ام‬$'_ 1‫ ا‬6T‫ از! ا‬U/2 ‫ل‬#
, X ‫ إ‬6‫اوح ! ‹ وا‬I ‫ ت‬2 H 3; ‫اء‬.Y‫ ا‬WJ‫ و‬% 7 ‫ ا‬6‫ ?! إ أ‬G‫ ا‬M 9
‫ ا ت‬W /; .,2 H 300 ‫ل‬2'‫ ل و‬/‫ إ‬6 ‫ م‬N‫ا ا‬.‫ ت ! ه‬W" - .‫أ ص‬
:3 ‫آ‬
4
5
1
2
2
3
2
4
3
2
3
3
2
3
2
6
8
3
6
4
2
2
4
4
4
1
1
4
7
3
2
3
6
2
1
2
3
2
3
4
2
2
2
3
4
8
4
5
2
4
1
2
4
2
3
1
7
8
4
2
3
1
8
2
2
3
2
7
1
2
2
4
2
6
2
4
2
8
2
3
4
4
2
2
4
4
3
4
1
2
2
1
1
6
2
1
3
4
1
1
7
7
1
6
4
2
2
7
3
2
2
5
1
4
3
2
2
4
3
2
2
1
2
2
4
2
3
5
8
2
3
3
2
2
2
3
2
4
4
4
6
2
6
4
5
2
1
5
2
4
5
1
2
1
3
4
1
2
2
2
1
3
5
3
1
2
2
8
6
3
3
2
2
2
2
2
106
4
2
4
5
5
1
2
4
2
3
2
1
2
4
1
1
2
8
2
4
8
8
6
4
2
6
4
4
2
4
4
1
4
4
5
3
4
4
2
4
7
4
2
2
4
2
2
4
3
2
3
2
1
2
6
4
2
3
2
4
5
2
3
2
3
2
3
1
1
1
4
4
2
4
2
4
2
2
5
2
4
8
6
4
3
1
1
7
3
2
8
4
4
2
3
4
2
3
8
4
4
4
2
4
2
2
2
1
3
1
1
3
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪6‬‬
‫‪2‬‬
‫‪2‬‬
‫‪7‬‬
‫‪4‬‬
‫‪4‬‬
‫‪3‬‬
‫‪1‬‬
‫‪2‬‬
‫ا ‪27‬ب إ‪ H9‬د دا‪ ,‬ا‪2‬ز‪ R9‬ااآ ‪ 3‬ا‪39H‬‬
‫ا‪ M/O‬ا‪ 37"9 90‬ا ‪ Rf‬ا‪/‬اري ا‪ 3‬وه‪: 2‬ر ا‪ ,‬ا‪ ,/‬ا@‪., 6‬‬
‫ا‪ M/O‬ا‪ 37"9 ! 90‬ا رج ا‪/‬اري ا‪ 3‬وه‪ 2‬دا‪ ,‬ا‪2‬ز‪ R9‬ا‪.39H‬‬
‫‪#‬ل ‪ U/2‬از! ا‪ 6T‬ا _'‪)$‬ام ‪: Excel‬‬
‫ا ت ا ‪q ,‬ز ‪ ,‬ا‪ 3; S C 500 UJY9 3‬إ ن دة‬
‫‪0.6‬‬
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‫‪1.0‬‬
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‫‪0.6‬‬
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‫‪0.4‬‬
‫‪0.5‬‬
‫‪107‬‬
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‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.2‬‬
‫‪0.6‬‬
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‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.2‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.7‬‬
‫‪0.4‬‬
‫‪1.0‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.7‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.8‬‬
‫‪0.9‬‬
‫‪0.4‬‬
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‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫آ‪GH‬ء ! و‪ WJ‬ا@ ن‬
‫‪0.6‬‬
‫‪0.5‬‬
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‫‪0.5‬‬
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‫‪0.4‬‬
‫‪0.7‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.7‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.7‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.7‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.7‬‬
‫‪0.4‬‬
‫‪0.1‬‬
‫‪0.5‬‬
‫‪0.9‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.2‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.9‬‬
‫‪0.3‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.1‬‬
‫‪0.5‬‬
‫‪0.8‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.8‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.8‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.3‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.3‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.2‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.8‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪1.0‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.8‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫‪0.8‬‬
‫‪0.9‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.9‬‬
‫‪0.5‬‬
‫‪0.3‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.5‬‬
‫‪0.3‬‬
‫‪0.7‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫‪0.4‬‬
‫‪0.6‬‬
‫‪0.6‬‬
‫‪0.8‬‬
‫‪0.5‬‬
‫‪0.6‬‬
‫‪0.4‬‬
‫‪0.4‬‬
‫‪0.7‬‬
‫‪0.3‬‬
‫‪0.6‬‬
‫‪0.3‬‬
‫‪0.7‬‬
‫‪0.5‬‬
‫ا ‪27‬ب إ‪ H9‬د دا‪ ,‬ا‪2‬ز‪ R9‬ااآ ‪ 3‬ا‪39H‬‬
‫آ [ ل ا ‬
‫ا‪ M/O‬ا‪ 37"9 90‬ا ‪ Rf‬ا‪/‬اري ا‪ 3‬وه‪: 2‬ر ا‪ ,‬ا‪ ,/‬ا@‪., 6‬‬
‫ا‪ M/O‬ا‪ 37"9 ! 90‬ا رج ا‪/‬اري ا‪ 3‬وه‪ 2‬دا‪ ,‬ا‪2‬ز‪ R9‬ا‪.39H‬‬
‫‪#‬ل )‪J# ) 4 (5‬ه)ات ‪ #‬از! ا‪ 6T‬ا‪:1‬‬
‫‪ :‬وأن ‪ J7I‬إ " ‪ ,9‬ا‪2‬ز‪ R9‬ا‪ 39H‬ا ` ‪ 3; M‬أول ا` ‪ M‬ا[ ‪2 W I P‬ان‬
‫ا " ‪2I ! ,9‬ز‪ R9‬إ‪ 3 6‬ام ‪.Excel‬‬
‫‪#‬ل )‪J# ) 4 (6‬ه)ات ‪ #‬از! ا‪ 6T‬ا _'‪)$‬ام ‪:Excel‬‬
‫‪2‬ف " ‪ ! !9‬ا‪2‬ز‪ R9‬ا ‪ M‬ا ‪:3‬‬
‫‪CDF‬‬
‫‪108‬‬
‫‪Interval‬‬
0.25 ≤ x ≤ 0.50 0.31
0.50 < x ≤ 1.00
0.41
1.00 < x ≤ 1.50
0.66
1.50 < x ≤ 2.00 1.00
:aV2 2‫ ا ت آ ه‬M‫ وأد‬Excel 3; , `' a;‫أ‬
:, ‫ ا ?] ا‬M
109
;
:‫ ا‬6T‫ از! ا‬# ‫ه)ات‬J# ) 4 (7) ‫ل‬#
:3 ‫ ا‬M ‫ ا‬R9‫ز‬2‫! ! ا‬9 " ‫ف‬2
Interval
CDF
0.00 < x ≤ 0.80
0.2
0.80 < x ≤ 1.24
1.24 < x ≤ 1.45
0.4
0.6
1.45.0 < x ≤ 1.83 0.8
1.83 < x ≤ 2.76
1.0
:aV2 2‫ ا ت آ ه‬M‫ وأد‬Excel 3; , `' a;‫أ‬
:3 ‫ ا‬M‫ أد‬F1 ‫د‬2 "‫ ا‬3; Observations W I
=IF(A2<=$C$3,$D$2+$E$2*(A2- C$2),IF(A2<=$C$4,$D$3+$E$3*(A2-$3),IF(A2<=$C$5,
110
$D$4+$E$4*(A2-C$4),IF(A2<=$C$6,$D$5+$E$5*(A2-$C$5),IF(A2<=$C$7,$D$6+$E$6*(A2$C$6),2)))))
, ‫ ا ?] ا‬UN;
:3 ‫! آ‬: ‫ ا [ ! ا‬3; ‫ ة‬7" ‫! ا‬H ‫ ا‬M ,`‫ح آ‬O ‫ف‬2‫و‬
.M 3?‫ا‬2O Y 39HI 3 ‫اآ‬I R9‫ز‬2I ,‫ ا‬3 ‫ ا‬M/O‫ا‬
1.2
1
(2.76,1.0)
0.8
(1.83,0.80)
0.6
(1.45,0.60)
0.4
(1.24,0.40)
0.2
(0.80,0.20)
(0,0)
0
0
0.5
1
1.5
2
111
2.5
3
Linear 37‫ ل ا‬/@‫ م ا‬3?‫ا‬2O"‫ ا‬Y ‫ا ا‬.‫ ! ه‬, ‫ هات‬O 2 3/
‫ ( و‬x1 , y1 ) = ( 0, 0 ) !7:‫ ! ا‬R:I y ,T x Y , J -2 3/; Interpolation
,J"‫ ا‬3; ‫ض‬2" ( x, y ) [ UI X‫ا‬6‫! إ‬/‫ ( و‬x2 , y2 ) = ( 0.8,0.2 )
 x −x 
x = x1 + ( y − y1 )  2 1 
 y2 − y1 
‫ ;ن‬y = 0.18 W ‫; [ إذا آ‬
 0.8 − 0 
x = 0 + ( 0.18 − 0 ) 
 == 0.72
 0.2 − 0 
‫ ;ن‬yi < R ≤ yi +1 W ‫ ;ذا آ‬R , J -2 3 ‫ ااآ‬R9‫ز‬2‫ هات ! ا‬O 2 3/;
 x −x 
X = xi + ( R − yi )  i +1 i 
 yi +1 − yi 
‫ ;ن‬0.6 < R < 0.8 ‫ أي‬R = 0.71 W ‫ آ‬2 [ ;
 1.83 − 1.45 
X = 1.45 + ( 0.71 − 0.6 ) 
 = 1.659
 0.8 − 0.6 
‫ ط‬:‫ا‬
!
,;" ‫و‬
R ~ U ( 0,1)
!
‫ب‬27 ‫ ا"د ا‬2I R7
%:
,‫ا " د‬
5.‫ه‬
3;
( xi , yi ) , i = 1, 2,..., Number of
92"
‫ا‬./‫وه‬
Classes of CDF
.‫ هات‬O ‫ا‬
. ‫ ا‬R9‫ز‬2‫ هات ! ا‬O 10 9‫و‬9 ‫ و‬:!9 I
: Direct Transformation . 6D‫ز! ا‬/ 76‫* ا ا‬C
,` ‫ق‬7 ‫ ون ان‬3 :‫ ا‬3"7‫ ا‬R9‫ز‬2‫ هات ! ا‬O 2 ‫ارزم‬2 ‫ف "ض‬2
.& ,V 9‫ا‬
! !I‫ ه‬O 37"I , ‫ ا ” ا‬R2 ~ U ( 0,1) ‫ و‬R1 ~ U ( 0,1) !?‫ا‬2O ! J‫ ر‬7"
Z ~ N ( 0,1) 3?‫ا‬2O Y
Z1 = ( −2ℓn R1 ) cos ( 2π R2 )
12
Z1 = ( −2ℓn R1 ) sin ( 2π R2 )
12
. X = µ + σ Z M92 ‫ي ا‬H X ~ N ( µ , σ 2 ) 2
112
:‫ى‬0‫ق ا‬C
&‫ ه آ ا‬U7YI !/ 9T 7" 3?‫ا‬2O Y ! ‫ هات‬O 2 ‫ق‬7‫[ ! ا‬/‫ه ك ا‬
‫م‬G6 %N" 3; ,H 3?‫ا‬2O Y ! ‫ هات‬O ‫ات‬2 ‫[ ! ا‬/‫ن ا‬0 U7YI ‫م‬G9T
%I J‫ و‬,J2X2 ‫دة وا‬2H‫ ا‬, 3‫ وه‬O‫ث ا" ت و ا ] '` ت ا‬2 ‫ء و‬
,//‫ ا‬S/‫ ا‬3; ‫رة‬2‫آ‬. ‫ق ا‬7‫ان " ا‬
‫ آ‬.![6 ‫[ ! ا‬/‫ ا‬MJ !
;‫ل وا‬2:‫ ا‬,:9C‫ و‬Convolution Method ‫ ا@` ف‬,:9C M[
[email protected]‫ا ] ا‬
‫إ ره‬
‫آة‬
,6 ‫ ! ا‬Unefficient , ; ^ ‫ق‬C 3‫ ه‬Acceptance-Rejection Method
. U ‫ق‬7 % ‫ا‬.U‫ و‬, ‫ارز‬2‫ا‬
:!9 I
. Excel ‫ ام‬X ~ N (160,9 ) ! ‫ هة‬O 1000 ‫و‬
113
‫ا ا دس‪:‬‬
‫‪ =3‬ا)‪r0‬ت ‪: Input Modeling‬‬
‫;‪ 3‬ه‪.‬ا ا` ‪2 M‬ف ‪2:‬م را‪ ,-. ,‬و‪ M I‬ا ت‪ ،‬وه‪ ! 3‬اه‪ %‬ا‪27‬ات ا" ‪ ,‬ا‪3‬‬
‫‪ .I‬ء ا ‪2‬ذج ا‪.‬ي ‪2‬ف ‪H‬ي & ا‪ H‬رب أ‪ X‬ء ا‬
‫ ‪ ,-.‬و‪ M I‬ا ت ‪I M OI‬‬
‫آ ة‪.‬‬
‫‪ %‬وأ‪ .‬ت ! ا‪ N‬م ا اد ‪ 9:I %X ,-.‬ا‪2‬ز‪ "9‬ت‬
‫ا@‪ , 6‬ا‪ I 3; %/ I 3‬ف ا‪ N‬م و‪2I 7I‬ز‪ "9‬ت ‪ ,9N‬ا ت ا ‪ O‬هة إذا‬
‫أ ‪ !/‬ذ‪? ; ،g‬ة ا‪2‬ز‪ "9‬ت ا‪ ,9N‬ه‪ 2‬إ ‪ , /‬إ‪-‬اء ‪Sensitivity Analysis , 6 M I‬‬
‫‪ N‬م و‪ !/‬إذا ‪."I‬ر ‪9:I‬ه أي ‪ ! !/ %‬إ‪ H9‬د ‪2I‬ز‪N R9‬ي ‪ 79‬ا ‪ O‬هات‬
‫و‪ H9‬ز إ رات ‪ !6‬ا‪ 3; !/ 9 &; Goodness of Fit Tests 7‬ه‪ 5.‬ا ‪ ,‬إام‬
‫ا‪2‬ز‪ "9‬ت ا‪ " ،,9H‬ا ‪ Mf`9 ![6‬إام ا‪2‬ز‪ "9‬ت ا‪ ,9H‬أ' ‪ M[ I U0‬ا‪ N‬م‬
‫ا ‪ 3::‬أ;‪ Mf‬و '‪ ,‬إذا ‪ W" -‬ا" ت " ‪.,9‬‬
‫‪2‬ف ‪7T‬ق إ ‪I‬‬
‫‪ %‬وأ‪ .‬ا" ت ‪0‬ن ه‪.‬ا ‪2V2‬ع ‪ M O9‬درا‪C ,‬ق ا " ‪ ,9‬وه‪2‬‬
‫ء‪2 ،‬ف `ض ;‪ 3‬ه‪.‬ا ا ‪:‬ر أ& ‪9 -29‬‬
‫‪2V2‬ع دة آ ‪I ,‬رس ‪ % ! V‬ا@‪6‬‬
‫‪ O‬هات ‪ -‬ه‪G‬ة و‪ ) U9 " W I J‬أي ‪O‬وع ;‪3‬‬
‫‬
‫! ;‪T H 3‬ت‬
‫‪2‬ث ا" ت وا@‪6‬‬
‫‪ N‬م ا ‪; 3::‬ذا آ ن ا‪ N‬م إ‪J‬‬
‫ا@‪J‬‬
‫‪2‬ث ا" ت ‪ T‬ان ‪2:9‬م & ;‪M O9 9‬‬
‫ء وا ‪ S‬وأي ‪V ‹ I‬وري & ‪,J‬‬
‫دي [ ;‪ SH‬ان ‪2/9‬ن ;‪ 3‬ا`‪ 9‬أ‪ 6‬ا ‬
‫! ;‪3‬‬
‫د (‪.‬‬
‫ا‪.‬ف ‪ U/2‬از! ‪ #‬ا‪J‬ه)ات‪:‬‬
‫إذا آ ‪ O 9 W‬هات ;ن اول ‪27‬ة ‪2:‬م ‪ U‬ه‪ 3‬إ‪ H9‬د ‪2I‬ز‪ U 79 S R9‬وذ‪g‬‬
‫‪ % " 9:‬ا‪2‬ز‪ ،R9‬و‪ MJ !/‬أن ‪2:‬م ‪ g.‬ا"ف ‪ M/‬ا‪2‬ز‪ R9‬وذ‪ H9 g‬د‬
‫ا‪2‬ز‪ R9‬ا‪/‬اري أو ا ‪ Rf‬ا‪/‬اري ‪ Histogram‬وا‪.‬ي ‪: "9‬را او‪ 3‬ا‪ ,‬ا‪,/‬‬
‫ا@‪ O , 6‬هات ! ‪ M ` Y‬او دا‪ ,‬ا‪ ,; [/‬ا@‪ O , 6‬هات ! ‪.M Y‬‬
‫و‪2:‬م ‪ O‬ء ا‪2‬ز‪ R9‬ا‪/‬اري آ ‪:3‬‬
‫‪ H %J (1‬ل ا ‪ O‬هات إ ;ات و‪ ,9‬ذات د ‪.S‬‬
‫‪ M[ (2‬ه‪ 5.‬ا`ات ا ‪2‬ر ا‪.3:;0‬‬
‫‪ ! (3‬ا‪/‬ارا‪ 3; 3‬آ‪; M‬ة‪.‬‬
‫‪ %J (4‬إ‪6‬ا‪ X‬ت ا ‪2‬ر اأ‪ M[ 9 M/O 3‬ا‪/‬ارات ا‪.,‬‬
‫‪114‬‬
‫‪ (5‬أر‪ %‬ا‪/‬ارات ا‪; M/ ,‬ة‪.‬‬
‫د ا`ات ‪ %H6 "9‬ا"‪ ,‬و إ‪ O‬ر ا ‪ O‬هات‪; ،‬ذا آ ‪ W‬ا`ات ‪,f9‬‬
‫و‪; ,J‬ن ا‪2‬ز‪ R9‬ا‪/‬اري و ^ ` ‪ M‬و ‪2 M/‬آ ت و ‪.U‬ا ;ن ‪&/‬‬
‫و‪2/I ! &' `I‬ن وا‪ ،, V‬أ إذا آ ‪ W‬ا`ات ‪- ,:V‬ا وآ[ة ;ن ا‪2‬ز‪ R9‬ا‪/‬اري‬
‫و ‪ !O‬آ[ ا` '‪ M‬و! ‪ U 9‬ا ‪ O‬هات‪ .‬ه ك ‪ J‬ة ‪ H60 ,9:I‬م ا"‪! ,‬‬
‫ا ‪ ,72‬وا‪/‬ة وه‪ 2‬أ‪ .‬د ا`ات ‪ 9‬وي ا‪.H‬ر ا "‪ %H 3‬ا ‪ O‬هات‪ .‬ا [ ل‬
‫ا ‪ !9 3‬أ‪ X‬د ا`ات ‪ M/‬ا‪2‬ز‪ R9‬ا‪/‬اري‪.‬‬
‫‪#‬ل‪)2 `v4 :‬د ا‪K‬ت ‪ B7 U/2‬از! ا‪B‬اري‪:‬‬
‫ا‪ /0‬ل ا ‪ !I ,‬أ‪ X‬د ا`‪ b‬ت ‪ M/‬ا‪2‬ز‪ R9‬ا‪/‬اري ‪ O‬هات ا ‪:,‬‬
‫‪115‬‬
‫ا‪ M/O‬ا ‪ !9 3‬أ‪ X‬د ا`ات ‪ M/‬ا‪2‬ز‪ R9‬ا‪/‬اري ‪ O‬هات ا ` ‪:,‬‬
‫‪116‬‬
‫ا ‪ O‬هات ا ` ‪ O ! 3 "IT ,‬آ‪ M‬د ا`ات '‪ ,‬إذا آ ‪ W‬ا‪ %:‬ا ‪Y ,/‬‬
‫ا"‪2O‬ا?‪ 3‬ا ` ‪.,J M‬‬
‫ا‪.‬ف ‪ U/2‬وإ‪ 0‬ر از! ‪ #‬ا‪J‬ه)ات‪:‬‬
‫‪ : !/ 9‬ر‪ M/ ,‬ا‪2‬ز‪ R9‬ا‪/‬اري ا ‪" ]I‬ف ا ?‪ M/ 3‬ا‪2‬ز‪ R9‬ا‪N‬ي ا ‪:‬ح‬
‫و ! ‪ 7I %X‬ا‪2‬ز‪ R9‬ا ‪:‬ح ا ‪ O‬هات او ا‪2‬ز‪ R9‬ا‪/‬اري وإ ر ‪ !6‬ا‪ 7‬‬
‫‪2‬ا‪ ,7‬أ‪ 6‬ا@ رات [‪ M‬إ ر آ‪2-2 2‬روف – ‪2‬ف أو إ ر ‪ R‬آ ي‪.‬‬
‫ه ك ا‪ ! [/‬ا‪2‬ز‪ "9‬ت ا@‪ , 6‬ا‪ ,9N‬ا‪ 7I 3‬دة ا ت ا ‪ O‬هة و ! أه‪%‬‬
‫ه‪ 5.‬ا‪2‬ز‪ "9‬ت وأآ[ه إا ا ‪:,‬‬
‫‪4 (1‬ز! ذات ا) ‪ : Binomial‬و‪. 9‬ج د ات ا‪ H‬ح ;‪n 3‬‬
‫ان ‪2/I‬ن ا‬
‫و‪ ,‬ط‬
‫و‪T‬ت ‪ ,:‬و‪ ˆ` U‬ا@‪ 6‬ل‪ .‬و‪2:‬ل ان ا ‪ Y‬ا"‪2O‬ا?‪ 3‬ا ` ‪M‬‬
‫‪2I & X‬ز‪ R9‬ذات ا ‪ !9‬إذا آ ‪ W‬دا‪ ,‬ا‪ ,/‬ا@‪ & , 6‬ه‪:3‬‬
‫‪ n  x‬‬
‫‪n− x‬‬
‫‪  p (1 − p ) , x = 0,1, 2,..., n ; 0 ≤ p ≤ 1, n = 1, 2,...‬‬
‫‪P ( X = x ) = p ( x ) =  x ‬‬
‫‪‬‬
‫‪0,‬‬
‫‪otherwise‬‬
‫‪‬‬
‫" ‪ %‬ا‪2‬ز‪ R9‬ه‪ n, p 3‬و& ‪ (w2 ) ,"J2 , J‬و‪!9 I‬‬
‫) ‪E ( X ) = np, V ( X ) = np (1 − p‬‬
‫‪117‬‬
3‫ & ه‬,/‫ ا‬,‫ دا‬M/‫و‬
Binomial pmf
0.3
0.25
0.2
0.15
0.1
0.05
0
3U‫ ا‬R9‫ز‬2‫ ا‬M OI‫ و‬: Negative Binomial - ‫ز! ذات ا) ا‬4 (2
‫ل‬2
,‫و‬. ‫ت ا‬T‫و‬
‫ج د ا‬. I‫ و‬,' , ‫ آ‬Geometric Distribution
M ` ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ل ان ا‬2:‫ و‬.( k = 1 3U‫ ا‬R9‫ز‬2 ) ‫ ح‬H k ‫ د‬3
:3‫ & ه‬, [email protected]‫ ا‬,/‫ ا‬,‫ دا‬W ‫ إذا آ‬, ‫! ا‬9 ‫ ذات ا‬R9‫ز‬2I & X
 x + k − 1 k
x
p (1 − p ) , x = 0,1,...; 0 ≤ p ≤ 1, k = 1, 2,...


p ( x ) =  x

 0,
otherwise

‫! ه‬9 ‫ وا‬RJ2‫ ا‬k , p 3‫ ه‬R9‫ز‬2‫ ا‬% "
E(X ) =
k (1 − p )
p
, V (X ) =
k (1 − p )
p2
Negative B ino mial pmf with k=5
0.3
0.25
0.2
0.15
0.1
0.05
0
k =1
3U‫ ا‬R9‫ز‬2‫ ا‬3‫ ه‬R9‫ز‬2‫ا ا‬.‫ ! ه‬,' , ‫آ‬
118
x −1
 p (1 − p ) , x = 0,1,...; 0 ≤ p ≤ 1
p ( x) = 
otherwise
0,
Geometric pmf
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
, ‫ ;ة ز‬3; ‫ ث‬I 3‫ ا‬,: ‫اث ا‬60‫ج د ا‬. 9‫ و‬: Poisson ‫ز! ا'ن‬4 (3
‫ن‬2‫ا‬2 R9‫ز‬2I & X M ` ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ل ان ا‬2:‫ و‬., X , / , ; ‫ أو‬, X
:3‫ & ه‬, [email protected]‫ ا‬,/‫ ا‬,‫ دا‬W ‫إذا آ‬
α x −α
 e , x = 0,1,...; α > 0
p ( x ) =  x!
 0,
otherwise

‫! ه‬9 ‫ وا‬RJ2‫ ا‬، α > 0 2‫ ه‬R9‫ز‬2‫ ا‬%"
E(X ) =V (X ) =α
3 ‫ ا‬M/O‫ ا‬U & , [email protected]‫ ا‬,/‫ ا‬,‫ودا‬
P o isso n pmf
0.3
0.25
0.2
0.15
0.1
0.05
0
‫ع " ت‬2 H ‫! إ ره آ‬/ 9 , R9‫ز‬2I ‫ج‬. 9‫ و‬: Normal . 6D‫( از! ا‬4
R I UJY9 3‫ ا‬, ‫ز‬0‫ع ا‬2 H 2‫ رة ه‬R ‫ق‬Y ‫ ! ا‬G‫ ; [ ا‬.,?G-
119
! G , 3‫ ه‬3‫ وا‬, %J 37"9 J 3"7‫ ا‬R9‫ز‬2‫“ ان ا‬6T . U; ,"7J M‫آ‬
‫ إذا‬3"C R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ل ان ا‬2: .‫ رة‬R ‫ق‬Y ‫ا‬
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫آ‬
f ( x) =
1
2πσ
2
e
−
1
2σ 2
( x − µ )2
, − ∞ < x < ∞ ; − ∞ < µ < ∞, σ 2 > 0
E ( X ) = µ , V ( X ) = σ 2 !9 I‫ و‬RJ2I &‫ و‬، − ∞ < µ < ∞, σ 2 > 0
‫ذج ه‬2 ‫ ا‬% "
. µ = 0, σ 2 = 1 ‫ن‬2/I 3 :‫ ا‬3"7‫ ا‬R9‫ز‬2‫ ا‬3‫ ه‬,' , 6
:M/O‫ ا‬U & , [email protected]‫ ا‬,; [/‫ ا‬,‫ودا‬
N (0,1)
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
‫! إ ره‬/ 9 , R9‫ز‬2I ‫ج‬. 9‫ و‬: Lognormal `‫ر‬w/‫ ا‬. 6D‫( از! ا‬5
M' 6 2‫ ه‬a ‫ ا‬S‫آ‬9 ‫ ! إ[ ر‬M‫ ; [ "ل ا‬.,?G- ‫ _ " ت‬f‫آ‬
R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ل ان ا‬2: .‫ د ! ا`ات‬3 ‫ل‬2‫ب ا‬V
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬3 X‫^ ر‬2 3"C
f ( x) =
1
x 2πσ
2
e
−
1
2σ 2
( log x − µ )2
, x > 0 ; µ > 0, σ 2 > 0
!9 I‫ و‬RJ2I &‫ و‬، µ > 0, σ 2 > 0
E(X ) = e
1
2
µ+ σ 2
, V (X) =e
(
2 µ +σ 2
)
−e
‫ذج ه‬2 ‫ ا‬% "
( 2 µ +σ )
2
:M/O‫ ا‬U & , [email protected]‫ ا‬,; [/‫ ا‬,‫ودا‬
120
Lognormal
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Y ‫ل ان ا‬2: .,: ‫اث‬6‫ ! أ‬, ‫ج أز‬. 9‫ و‬: Exponential '‫( از! ا‬6
& R9‫ز‬2‫ ا‬,‫ ودا‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬3‫ ا‬R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ا‬
: ‫ه‬
λ e − λ x , x ≥ 0; λ > 0
f ( x) = 
otherwise
 0,
x<0
 0,
F ( x) = 
−λ x
1 − e , x ≥ 0
!9 I‫ و‬RJ2I &‫ و‬، λ > 0 2‫ ه‬R9‫ز‬2‫ ا‬%"
E(X ) =
1
λ
, V (X ) =
1
λ2
:M/O‫ ا‬U & , [email protected]‫ ا‬,; [/‫ ا‬,‫ودا‬
Exponential
2.5
2
1.5
1
0.5
0
.S ^ 3?‫ا‬2O Y ‫ج اي‬. 9 ‫ا‬- ‫ ن‬R9‫ز‬2I 2‫ وه‬: Gamma #= !‫ز‬4 (7
,‫ ودا‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫إذا آ‬
- R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ا‬
: ‫ & ه‬R9‫ز‬2‫ا‬
121
β −1 − βθ x
 βθ
, x > 0; β > 0, θ > 0
 Γ β ( βθ x ) e
f ( x) =  ( )
 0,
otherwise

∞ βθ
β −1 − βθ t

x>0
1 − ∫x Γ β ( βθ t ) e dt ,
( )
F ( x) = 
 0,
otherwise

‫ ;ن‬a ' ‫ د‬β ‫ن‬2/I , ‫ ا‬3;‫و‬
∞
- ,‫ دا‬I Γ ( β ) = ∫0 x β −1e − x dx ,‫اا‬
!9 I‫ و‬RJ2I &‫ و‬، β > 0, θ > 0 3‫ ه‬R9‫ز‬2‫ ا‬% " ، Γ ( β ) = ( β − 1)!
E(X ) =
1
θ
, V (X ) =
1
βθ 2
:M/O‫ ا‬U & , [email protected]‫ ا‬,; [/‫ ا‬,‫ ودا‬.W X ,; V ` ‫ ! ا‬R9‫ز‬2‫ ا‬,6‫! إزا‬/ 9
Gamma
& ‫ود ) أي‬
3?‫ا‬2O Y ‫ج اي‬. 9 ‫ا‬- ‫ ن‬R9‫ز‬2I 2‫ وه‬: Beta !‫ز‬4 (8
,‫ دا‬W ‫ إذا آ‬R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ ا‬.( , X ‫ود ود‬6
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ا‬
β −1
 1
α −1
 Β α , β x (1 − x ) , 0 < x < 1; α , β = 1, 2,...
)
f ( x) =  (
 0,
otherwise

‫ و‬α 3‫ ه‬R9‫ز‬2‫ ا‬% " ،, '‫ و‬,-2 β ‫ و‬α %: Β (α , β ) =
Γ (α ) Γ ( β )
,‫اا‬
Γ (α + β )
‫! ه‬9 ‫ وا‬RJ2‫ ا‬، β
E(X ) =
α
αβ
, V (X)=
2
α +β
(α + β ) (α + β + 1)
122
‫ب‬f [ 0,1] ! U H R2I !/ 9 ‫ آ‬W X ,; V ` ‫ ! ا‬R9‫ز‬2‫ ا‬,6‫! إزا‬/ 9
:M/O‫ ا‬U & , [email protected]‫ ا‬,; [/‫ ا‬,‫ ودا‬.W [
Beta
0.06
0.05
0.04
0.03
0.02
0.01
0
U M‫ع "ة ت آ‬2 H ‫! إ ره آ‬/ 9 , ‫ج‬. 9‫ و‬: Erlang gf‫ز! إر‬4 (9
P6 k ,-‫] ! ار‬T‫ إر‬R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ ا‬.3‫ ا‬R9‫ز‬2I &
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬k = 1, 2,...
k −1 − kθ x
 kθ
 k − 1 ! ( kθ x ) e , x > 0 ; k = 1, 2,..., θ > 0
)
f ( x) = (
 0,
otherwise

]T‫ إر‬R9‫ز‬2I ‫ أن‬3"9 ‫ا‬.‫وه‬
1
θ
w2 3‫ ا‬a 9 R9‫ز‬2‫ا ا‬.‫ ;ن ه‬k = 1 ‫“ ان‬6T
,?‫ا‬2O"‫ات ا‬Y ‫ ! ا‬k ‫ع‬2 H ! ‫ رة‬2‫ ه‬3?‫ا‬2O Y "9‫ز‬2I ‫! إ رة‬/ 9
!9 ‫ وا‬RJ2‫ وا‬θ ‫ و‬k
‫] ه‬T‫ إر‬R9‫ز‬2I % " .3‫ ا‬R9‫ز‬2I U 6‫ وا‬M/ 3‫ ا‬,: ‫ا‬
1
1
θ
kθ 2
:M/O‫ ا‬U & , [email protected]‫ ا‬,; [/‫ ا‬,‫ ودا‬. E ( X ) = , V ( X ) =
‫ه‬
Erlang
0.6
0.5
0.4
0.3
0.2
0.1
0
,‫ آ‬MO; ‫ ث‬9 6 ‫ق‬Y ‫ ! ا‬G‫ج ا‬. 9‫ و‬:Weibull 6‫ز! و‬4
(10
Y ‫ ا‬._/‫ ز ا‬U- M7"9 36 ‫ق‬Y ‫ ! ا‬G‫ ; [ ا‬.Time-to-failure
123
& R9‫ز‬2‫ ا‬,‫ ودا‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ إذا آ‬M9‫ و‬R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ا‬
: ‫ه‬
β
 β  x −ν  β −1 − x −ν 

e  α  , x ≥ ν ; −∞ < ν < ∞, α > 0, β > 0
f ( x ) =  α  α 

otherwise
 0,
x <ν
 0,

β
F ( x) = 
 x −ν 
−

1 − e  α  , x ≥ ν
‫ س‬:‫ ا‬%" α > 0 ‫ و‬Location Parameter ‫ ن‬/ ‫ ا‬%" −∞ < ν < ∞ ,X[‫ ا‬% " ‫ا‬
‫! ه‬9 ‫ وا‬RJ2‫ ا‬. Shape Parameter M/O‫ ا‬%" β > 0 ‫ و‬Scale Parameter
2
 2   1
1 
 
2
E ( X ) = ν + α Γ  + 1 , V ( X ) = α  Γ  + 1  −  Γ  + 1   
  β
β

  β
  
:3‫ & ه‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ودا‬
Weibull
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Discrete or Continuous 1‫از! ا وي ا أو ا‬
(11
.‫ ل‬[email protected]‫ `ˆ ا‬U ,/ ‫ ا‬%:‫ ا‬R - ‫آ ا م إذ ان‬e‫ج م ا‬. 9‫ و‬: Uniform
,‫ ودا‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ وي إذا آ‬R9‫ز‬2I & X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ا‬
: ‫ & ه‬R9‫ز‬2‫ا‬
 1
, a ≤ x ≤ b ; −∞ < a < b < ∞

f ( x) = b − a
 0,
otherwise
124

 0,

x−a
F ( x) = 
,
b − a

 1,

x<a
a≤ x≤b
x≥b
(b − a )
a+b
.E(X ) =
, V (X ) =
2
12
2
‫! ه‬9 ‫ وا‬RJ2‫ ا‬، b ‫ و‬a 3‫ ه‬R9‫ز‬2‫ ا‬% "
M ` ‫ وا‬M ‫ ا وي ا‬R9‫ز‬2 , [email protected]‫ ا‬,; [/‫ ا‬,‫دا‬
Unif or m
1.2
1
0.8
0.6
0.4
0.2
0
M ` ‫ ا وي ا‬R9‫ز‬2 , [email protected]‫ ا‬,/‫ ا‬,‫دا‬
Uniform
1.2
1
0.8
0.6
0.4
0.2
0
%:‫ ^ ا‬U ‫"ف‬T ‫ج ت‬. 9‫ و‬: Triangular /‫از! ا‬
(12
& X M ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ ا‬.(‫ال‬2 ‫ )ا‬X‫و‬6 [‫آ‬0‫ ا‬, :‫ى وا‬/‫ى وا‬Y ‫ا‬
: ‫ & ه‬R9‫ز‬2‫ ا‬,‫ ودا‬, [email protected]‫ ا‬,; [/‫ ا‬,‫ دا‬W ‫ وي إذا آ‬R9‫ز‬2I
 2( x − a)
, a≤ x≤b

 ( b − a )( c − a )
 2(c − x)

f ( x) = 
, b<x≤c
 ( c − b )( c − a )

 0,
otherwise

125

x≤a
 0,


2
 ( x − a)
,
a< x≤b
 ( b − a )( c − a )

F ( x) = 
2
c − x)
(

1 − c − b c − a , b < x ≤ c
)(
)
 (

 1,
x>c

%" ‫ و ا‬X 3?‫ا‬2O"‫ ا‬Y , J MJ‫ ا‬M[ 9 −∞ < a < ∞ R9‫ز‬2‫ ا‬% "
M[ 9 −∞ < c < ∞ %" ‫ و ا‬X 3?‫ا‬2O"‫ ا‬Y , J‫ اآ‬M[ 9 −∞ < b < ∞
‫! ه‬9 ‫ ا‬RJ2‫ ا‬a ≤ b ≤ c P6 X 3?‫ا‬2O"‫ ا‬Y X‫و‬6 [‫آ‬0‫ ا‬, :‫ا‬
E(X ) =
a+b+c
19
7
, V ( X ) = ( a 2 + b 2 + c 2 ) + ( ab + ac + bc )
3
18
9
:3‫ & ه‬,; [/‫ ا‬,‫ دا‬M/‫و‬
Triangular
0.6
0.5
0.4
0.3
0.2
0.1
0
," H ‫ ! `ˆ ا ت ا‬,9 " ‫ إ دة ا‬: Empirical 6T‫از! ا‬
(13
,[ ‫ "ة أ‬J7I J‫ و‬.‫ هات‬O ‫ ا‬79 ‫ي‬N R9‫ز‬2I HT ‫م دة‬9‫و‬
.,: ‫ل ا‬2 `‫ ا‬3; &
: Parameters Estimation .‫*) ا‬4
.,;‫ ا "و‬,?
[email protected]‫ق ا‬7 R9‫ز‬2‫ا ا‬.‫ ه‬% " 9: ‫م‬2: ،‫ح‬: R9‫ز‬2I ‫" ا"ف‬
،& " 9: ‫م‬2: ,: ‫ق ا‬7 R9‫ز‬2‫ ا‬M/ ‫ ة و " ا"ف‬7" ‫ هات ا‬O ‫; ! ا‬
:‫ ت‬J" 7"I 3‫ وا‬,"‫! ا‬9 I‫ و‬w2 % " ‫ ا‬5.‫ ه‬%‫و ! أه‬
126
2‫ ه‬,"‫ ا‬w2 { x1 , x2 ,..., xn } U G 3‫ وا‬X 3?‫ا‬2O Y ! n U H6 ,"
x=
1 n
∑ xi
n i =1
2‫ ه‬,"‫! ا‬9 I‫و‬
s2 =
1  n 2

xi − nx 2 
∑

n − 1  i =1

2‫ ه‬w2 ‫ ;ن ا‬,9‫ار‬/I ‫ ت‬b; 3; ," H ‫ هات‬O ‫و‬
∑
x=
∑
k
i =1
k
f i xi
i =1
fi
∑
=
n
i =1
f i xi
n
!9 I‫ و‬،‫ ت‬b`‫ د ا‬k ‫ و‬i %J‫ ر‬,b`‫ار ا‬/I fi P6
s2 =
1  k

fi xi2 − nx 2 
∑

n − 1  i =1

:‫ت‬.‫ از‬a.6 *‫ ا*)رات ا‬a.
:% " ‫ ا‬g ,6: ‫رات ا‬: ‫ وا‬U " ‫ و‬, U ‫" ت ا‬9‫ز‬2‫! " ا‬9 3 ‫ول ا‬H‫ا‬
Distribution
Parameters
Suggested Estimators
Poisson
α
αˆ = x
Exponential
λ
λˆ =
Gamma
Uniform




1
βˆ = 0.105 + 0.504 

n
1
 ℓn x − ∑ ℓn xi 
n i =1


1
θˆ =
x
β ,θ
n +1
bˆ =
Max ( x )
n
b
on ( 0, b )
Normal
1
x
µ ,σ 2
µˆ = x , σˆ 2 = s 2
127
1β
1 n β 
∑ xi 
 n i =1 
α, β
Weibull
αˆ = 
with ν = 0
βˆ'0 =
(
(
f βˆ" j −1
x ˆ
, β j = βˆ j −1 −
s
f ′ βˆ" j −1
f (β ) =
+ ∑ ℓnxi −
β
n ∑ i =1 xiβ ℓnxi
n
n
n
∑
i =1
f ′( β ) = −
β2
−
n
xβ
i =1 i
n∑ i =1 xiβ ( ℓnxi )
n
n
)
)
∑
n
xβ
2
+
i =1 i
n
( ∑ x ℓnx )
(∑ x )
β
n
i =1 i
n
2
i
β
2
i =1 i
: Goodness of Fit Tests [ D‫رات أو =دة ا‬60‫إ‬
: Quantile-Quantile Plots ‫ت‬. ‫ا‬-‫ت‬. ‫ت ا‬#'‫ ر‬:f‫او‬
R ‫ ;ن ا‬F ( x ) = P ( X ≤ x ) , − ∞ < x < ∞ 3 ‫اآ‬I R9‫ز‬2I ,‫ & دا‬3?‫ا‬2O Y X ‫إذا آ ن‬
‫ إذا آ ن‬F (γ ) = P ( X ≤ γ ) = q, 0 < q < 1 P
γ , :‫ ا‬2‫ ه‬X 3?‫ا‬2O"‫ ا‬Y q
: X ! , { x1 , x2 ,..., xn } !/ . γ = F −1 ( q ) ‫ب ;ن‬2: 3 ‫ ااآ‬R9‫ز‬2
P6 { y(1) , y( 2) ,..., y( n) } SI‫! " ا‬/‫آ و‬q Y'0‫ هات ! ا‬O ‫ ا‬SI‫ ر‬:(1) ‫ة‬27‫ا‬
.‫آ‬q G I j = n ‫ و‬Y'q G 9 j = 1 ‫ أي ان‬SI‫ ا‬%J‫ ر‬j !/ y(1) ≤ y( 2) ≤ ... ≤ y( n)
j − 0.5 
 S6‫ أ‬:(2) ‫ة‬27‫ا‬
 n 
. F −1 
j − 0.5 
 V y j %‫ أر‬:(3) ‫ة‬27‫ا‬
 n 
. F −1 
X ‫ ; ] ان‬9:I a ' 1 M & %: w 9:I ]I ‫ ا‬%‫ إذا آ ن ا‬:(4) ‫ة‬27‫ا‬
. F ( x ) R9‫ز‬2‫ & ا‬79
Excel ‫)ام‬$'_ Quantile-Quantile Plots ‫ت‬. ‫ا‬-‫ت‬. ‫ت ا‬#'‫ر‬
: 2 w2 3‫ ا‬R9‫ز‬2I ! 3IeI , ‫ هات ا‬O ‫ ان ا‬:"9
0.20692
0.58793
1.21450
0.41281
1.31682
0.29661
3.21539
5.33858
2.09976
1.18708
2.97769
1.41334
0.67564
0.39297
1.49500
2.44013
1.92938
0.15600
5.91988
2.58200
1.09586
4.20245
1.09669
5.00697
0.39858
2.92840
1.05554
0.44567
2.55631
1.59807
0.33593
6.20755
0.59653
0.13079
2.76867
1.99443
0.99720
1.01247
4.08498
4.30203
2.49832
5.17293
3.51228
0.22544
6.50522
1.90866
0.45222
0.06469
0.50055
2.48196
2.09068
0.33031
1.19646
2.00545
2.47376
1.14820
0.55138
4.09509
5.18077
0.58391
0.53511
5.33081
0.23273
0.33408
1.09374
1.97417
0.16207
0.67742
6.34901
3.61865
5.66158
0.37610
0.67374
0.59829
0.01717
1.41298
4.37080
1.28729
2.91489
1.34904
5.42604
5.78524
3.23956
6.51468
2.25422
1.35675
1.95070
0.42152
0.89192
0.75789
1.37260
0.94249
2.39745
3.28936
0.83093
0.73263
1.53591
1.38920
1.45426
0.76330
.‫ د‬:@‫ا ا‬.‫ ه‬V ‫ او‬f" q-q %‫أم ر‬
128
‫ا ‪ :M‬أد‪ M‬ا ‪: Excel ! , `' 3; 3‬‬
‫;] ا‪ %‬ا ‪:3‬‬
‫وا‪ ! aV‬ر‪ q-q %‬أن ا ‪ O‬هات ‪2/9T J‬ن ‪2I U‬ز‪ R9‬ا‪.3‬‬
‫‪ :,N6‬ه‪.‬ا ا@ ر ‪ "9‬اأي ا‪ 3 O‬و‪` & .A9T‬دا ‪ 7I SH9 M‬أ‪6‬‬
‫ا@ رات ا ‪.,‬‬
‫‪129‬‬
Chi-square Goodness of Fit [ D‫دة ا‬T ‫ ! آي‬# ‫ر‬60‫ إ‬: `
: Test
Y ! 3IeI ‫ هات‬O ‫ ! ا‬,2 H ‫ أن‬,V`‫ ا‬9 7‫دة ا‬2H ‫ آ ي‬R ‫إ ر‬
‫ "! أي‬R9‫ز‬2I R9 3?‫ا‬2O
H 0 : X is distributed with F ( x )
H1 : X is not distributed with F ( x )
,?
k
χ 02 = ∑
( Oi − Ei )
[email protected]‫ ;ن ا‬,9` ‫ ا‬,V`‫ ا‬, ' ‫و أ س‬
2
Ei
i =1
i ,b`‫ ا‬3; R:I 3‫ هات ا‬O ‫ د ا‬Oi P6 k − 1 ,96 ‫ ت‬-‫ آ ي ر‬R R9‫ز‬2I U ‫ن‬2/9
.‫ ا `وض‬R9‫ز‬2‫ب ! ا‬2
,b`‫ `ˆ ا‬3; R:9 ‫ي‬.‫ هات ا‬O ‫ ! ا‬RJ2 ‫ ا"د ا‬Ei ‫و‬
Chi-square Goodness of Fit Test [ D‫دة ا‬T ‫ ! آي‬# ‫ر‬60‫إ‬
: Excel ‫)ام‬$'_
3 w2 ‫ن‬2‫ا‬2 R9‫ز‬2I U ‫ ان‬:"9 , ‫ هات ا‬O ‫ا‬
3
3
1
3
4
2
3
3
9
2
3
4
3
3
7
2
2
5
1
6
2
4
3
1
6
4
2
2
4
6
6
2
1
3
1
2
4
2
1
5
3
3
2
3
1
1
3
2
3
2
6
3
6
4
1
2
1
2
5
2
1
4
5
4
6
3
4
1
8
3
1
0
1
2
2
3
1
2
3
5
2
5
5
3
6
0
1
2
5
6
3
3
3
2
3
2
4
3
2
5
3 w2 ‫ن‬2‫ا‬2 R9‫ز‬2I R ‫ هات‬O ‫ ا‬7I ‫دة‬2- ‫أ‬
:M ‫ا‬
,J"‫ ! ا‬,"J2 ‫ ا‬%:‫ ا‬S I
Ei = n × P ( X = xi ) , xi = 0,1, 2,...
‫ ;ن‬x1 = 0 , : [ ;
E1 = 100 × P ( X = 0 ) = 100 ×
30 −3
e
0!
Excel , `' 3; 3 ‫ ا‬M‫ا أد‬.‫ ب ه‬
130
‫;] ا‪ %:‬ا ‪:,‬‬
‫ا‪:‬ار‪9 :‬ك ‪ S 7‬آ ‪.!9‬‬
‫إ ر ‪ R‬آ ي ! ا@ رات ا‪ ,`"f‬و‪ 3/‬‬
‫‪2X2 ]? M‬ق ‪ T U‬ان ‪2/I‬ن‬
‫‪ %H6‬ا"‪ ,‬آ و‪2/I‬ن ‪ R -‬ا‪ %:‬ا ‪ ,"J2‬أآ ! ‪ , 6 3`; 5‬و‪2-‬د ‪ ,"J2 %J‬أ‪5 ! MJ‬‬
‫‪ ] I‬ه‪ 5.‬ا‪ %J R %:‬ا`‪ b‬ت ا ‪ H‬ورة ‪ . U‬إ ر آ‪2-2 2‬روف‪2 -‬ف أ‪2J‬ى ! إ ر‬
‫ ‪ R‬آ ى وأآ[ ‪ ,:X2‬آ ا& ‪ H60 a 9‬م ‪Y' ,‬ة‪.‬‬
‫` ‪ :‬إ‪60‬ر آ=روف‪ ' -‬ف ‪T‬دة ا‪K-S Goodness of [ D‬‬
‫‪: Fit Test‬‬
‫إذا آ ن ‪2O Y X‬ا?‪ & 3‬دا‪2I ,‬ز‪I R9‬اآ ‪ F ( x ) = P ( X ≤ x ) , − ∞ < x < ∞ 3‬وآ ‪W‬‬
‫‪ ! , 9‬ه‪.‬ا ا‪2‬ز‪; { x1 , x2 ,..., xn } R9‬ن دا‪ ,‬ا‪2‬ز‪ R9‬ااآ ‪ 3‬ا‪:,J" 7"I 39H‬‬
‫‪131‬‬
Sn ( x ) =
number of x1 , x2 ,..., xn ≤ x
n
x(1) ≤ x( 2) ≤ ... ≤ x( n ) P
x(1) , x( 2) ,..., x( n ) M/O‫ ا‬x1 , x2 ,..., xn ‫ هات‬O ‫ ا‬WI‫وإذا ر‬
‫;ن‬

 0,

k
Sn ( x ) =  ,
n

 1,

,?
x < x(1)
x( k ) ≤ x < x( k +1) , k = 1, 2,..., n
x ≥ x( n )
[email protected]‫ ا‬S F ( x ) 3 ‫ ااآ‬R9‫ز‬2‫ ! ا‬3IeI ,"‫ أن ا‬,V`‫ ا‬3/;
D = max F ( x ) − S n ( x )
. α = 0.05 ,92" ‫ى‬2 g‫ وذ‬1.36 n R ,?
[email protected]‫ رن ا‬:I n ≥ 35 %:‫و‬
K-S Goodness of Fit [ D‫دة ا‬T ‫ ' ف‬-‫ر آ=روف‬60‫إ‬
: Excel ‫)ام‬$'_ Test
. α = 0.05 ,V`‫ ا‬5.‫ أ ه‬.3 J 3"C R9‫ز‬2I ! , ‫ هات ا‬O ‫ أن ا‬:"9
:, V2 ‫ ا ” ا‬R 3 ‫ ا‬M/O‫ ا‬3; aV2 2‫ هات آ ه‬O ‫ ا‬M
:, ‫ ا‬,H‫ " ا ب ا‬,: ‫ ا‬, ` ‫] ! ا‬9
132
‫ا‪:‬ار‪9 :‬ك ‪ S 7‬آ ‪.!9‬‬
‫‪133‬‬
:! ‫ا ا‬
SIMAN (SIMulation ANalysis) ‫ اآة‬u ‫)ام‬$'_ ‫اآة‬
, HI ‫ ر‬C‫ وإ‬MODEL FRAME ‫ذج‬2 ‫ ر‬C‫ ! إ‬SIMAN ! M /‫ذج ا‬2 ‫ن ا‬2/9
EXPERIMENT FRAME
‫ذج‬2 ‫ ر ا‬C‫ إ‬3; ‫ وا" رات‬.‫ م‬N‫ ! ا‬V ‫اث‬6q 3:7 ‫ _ ا@ ب ا‬9 :‫ذج‬2 ‫ ر ا‬C‫إ‬
SM.MOD ‫ آ [ ل‬MOD ,; [email protected]‫ ا _ ا‬7"9‫ و‬BLOCKS S‫ا‬2J 3 I
' I , H‫ ر ا‬C‫ إ‬3; ‫ ا" رات‬.‫ذج‬2 ‫اء ا‬[email protected] , H‫"! وط ا‬9 :, H‫ ر ا‬C‫إ‬
SM.EXP ‫ آ [ ل‬EXP ,; [email protected]‫ ا _ ا‬7"9‫ و‬ELEMENTS
SIMAN ‫ات إ=اء‬D0
1- C:\SIMAN5\MODEL.EXE EXAMPLE.MOD ====> EXAMPLE.M
2- C:\SIMAN5\EXPMT.EXE EXAMPLE.EXP ====> EXAMPLE.E
3- C:\SIMAN5\LINKER.EXE EXAMPLE.M EXAMPLE.E ====> EXAMPLE.P
4- C:\SIMAN5\SIMAN.EXE EXAMPLE.P ====> EXAMPLE.OUT
Text File
*.MOD
Text File
*.EXP
MODEL
EXPMT
*.M
*.E
LINKER
*.P
SIMAN
*.OUT
134
SIMAN A =31‫أ'' ت ا‬
‫ " ت‬،‫د‬2: ،‫ ت‬6 ،R7J ،!? G‫ ا‬M[ ‫ م‬N‫ ب ل ا‬I ‫ أ ء‬: ENTITIES ‫ ? ت‬/‫ ا‬.d‫ا‬
. JA ‫ ? ت‬/‫ ا‬,‫آ‬6 _J2I P6 ‫ ر‬N‫ إ‬C : QUEUES ‫ا‬2C ،‫ 'اف‬،‫ ل‬،‫ت‬Th‫ ا‬M[ ‫ ? ت‬/‫ ا‬U 9 3‫ م ا‬N‫اء ا‬G-‫ أ‬: RESOURCES ‫ارد‬2 .d‫ " ت ا‬C
! ‫ ز‬،‫ل‬2'2‫ ا‬WJ‫ و‬،,`ƒ2‫ع ا‬2 M[ !? ‫ آ‬M/ ,' %J M[ I‫ و‬: ATTRIBUTES ‫ '` ت‬.d‫ ا‬, ‫ا‬
_? ƒ2‫ د ا‬M[ ‫ م‬N‫ ا‬, 6 _ I %J M[ I‫ و‬: GLOBAL VARIABLES , ‫ات‬Y .d‫ ا‬,6 ‫ت ا‬Th‫ د ا‬،‫ م‬N‫ ا‬3;
: SIMAN u )2‫ا‬
: MODEL BLOCKS ‫ذج‬1‫ ا‬-‫ا‬
BEGIN,
Model Listing, Model Name;
CREATE, Batch Size, Offset Time: Interval, Maximum
Batches; ( CREATE: EXPONENTIAL(4.4) )
ASSIGN: Variable or Attribute = Value: repeats;
QUEUE,
Queue ID, Capacity, Balk Label;
SEIZE,
Priority: Resource ID, Number of Units:repeats;
(SEIZE,3:
DELAY:
/
SEIZE:
Machine:Worker)
Duration, Storage ID;
RELEASE:
COUNT:
Worker, 2;
Resource ID, Quantity to Release: repeats;
Counter ID, Counter Increment;
(COUNT:
JobsDone; /
COUNT:
7, BatchSize)
DISPOSE;
MARK
(Attribute ID);
* A modifier that can be added to any block in the
model.
* It stores the time at which an entity
arrives at the block in an attribute of the
activating entity
135
TALLY: Tally ID, Value;
* Tally ID: specifies the tally register to which
the observations are added (Tally’s name or
number defined in TALLIES)
* Value: specifies the value recorded at each
entity’s arrival at the block.
It can be any
SIMAN defined or user defined variable or an
expression involving one or more variables
* Interval( Attribute ID): To record the elapsed
time (TNOW – Attribute Value)
* Between: To Record the time between successive
arrivals to the block.
(TNOW – Time of
Previous Arrival)
BRANCH, Max Number of Branches:
WITH, Probability, Label:
IF, Condition, Label:
ELSE, Label:
ALWAYS, Label;
(BRANCH,
2:
ALWAYS, Repeat:
IF, TNOW < 4, Go;)
: EXPERIMENT ELEMENTS T‫ ا‬H12
PROJECT,
Title, Analyst Name,Date,Summary Report;
ATTRIBUTES: Number, Name(Index), Initial Values,
…:repeats;
QUEUES: Number, Name, Ranking Criterion: repeats;
{FIFO,
LIFO, LVF(A ID), HVF(A ID)}
RESOURCES: Number, Name, Capacity: repeats;
COUNTERS: Number, Name, Limit, Initialize Option, Output
File: repeats;
REPLICATE: Number of Replications, Beginning Time,
Replication Length, Initialize System,
Initialize Statistics, Warm-Up Period;
136
DSTATS: Number, Expression, Name, Output File: repeats;
* To record statistics about time-dependent
variables
* For sequences of values persisting over a
period of time
* The statistics for the sequences of values are
weighed by the length of the period the value
persist
TALLIES: Number, Name, Output File: repeats;
* To record statistics about observational data
* For sequences of values that are one-shot
(non-persistent)
* The statistics for the sequences are based on
equally weighed
observations
VARIABLES: Number, Name(Index), Initial Values, …:
repeats;
STORAGES: Number, Name: repeats; (Associated with DELAY
block)
137
The Single Machine Problem ‫ اا)ة‬1 B‫ ا‬/BJ# :1‫ل‬#
M‫"& آ‬7J M I ‫ول‬0‫ع ا‬2‫ ا‬.‫ ت‬H ‫! ` ! ! ا‬2 ‫ة @ ج‬6‫ وا‬,‫" آ‬I ,‫ور‬
, " M 9 R7:‫ ! ا‬3 [‫ع ا‬2‫ ا‬.,‫ & آ‬M " ? J‫ د‬4 ‫ ج إ‬9‫ ? و‬J‫ د‬10
,"7:‫ ج ا‬I‫ ? و‬J‫ د‬6 M‫ آ‬," ,"7J M I %X ‫ول‬0‫ع ا‬2‫ ! ا‬,"7J ‫ل أول‬2'‫ ? ! و‬J‫د‬
.,‫ ا آ‬M ? J‫ د‬3 ,
.‫ ت‬8 3; U- ‫! إ‬/ 9 3‫ع وا‬2 M‫ ! آ‬R7:‫د د ا‬6
Type 1 Arrivals
Out
Buffer
Machine
Type 2 Arrivals
:‫ أن‬xf
.‫ ? ت‬/‫ ا‬3‫ ه‬R7:‫ ا‬.‫ '` ت‬3‫ ه‬ProcessTime ,"7:‫ ا‬M "‫ و ز ! ا‬JobTybe ,`ƒ2‫ع ا‬2 . Buffer , G ‫ر ه‬2 7‫ ا‬.‫رد‬2 3‫ ه‬,‫ ا آ‬:[D1‫إ ب ا‬
- CREATE arriving jobs.
-ASSIGN values to ProcessTime and JobType.
- QUEUE the jobs for machine in the Buffer
- SEIZE the machine.
- DELAY by ProcessTime.
- RELEASE the machine.
- COUNT the JobType completed.
- DISPOSE of the finished jobs.
138
SM.EXP : T‫ ا‬9/#
BEGIN;
;Single Machine job Shop
PROJECT, Single Machine, OR241;
ATTRIBUTES:
1, JobType:
2, ProcessTime;
RESOURCES:
1, Machine, capacity(1);
QUEUES:
1, Buffer;
COUNTERS: 1, Type 1 Job Count:
2, Type 2 Job Count;
REPLICATE, 1, 0, 480;
END;
SM.MOD :‫ذج‬1‫ ا‬9/#
BEGIN;
;Single machine job shop
;Attributes: JobType, ProcwssTime
;Resources: Machine
;Queue: Buffer
CREATE: 10; Create type 1 jobs
ASSIGN: JobType=1:
ProcessTime=4:
NEXT(process);
CREATE, 1, 5: 6;
Create type 2 jobs
ASSIGN: JobType=2:
ProcessTime=3;
processQUEUE,
Buffer;
SEIZE, 1: machine, 1;
DELAY:
ProcessTime;
139
RELEASE: machine;
COUNT: JobType;
DISPOSE;
END;
:3 ‫م‬2: , H‫ذج وا‬2 ‫ ` ت ا‬, ‫" آ‬
1- C:\SIMAN5\MODEL.EXE SM.MOD ====> SM.M
2- C:\SIMAN5\EXPMT.EXE SM.EXP ====> SM.E
3- C:\SIMAN5\LINKER.EXE SM.M SM.E ====> SM.P
4- C:\SIMAN5\SIMAN.EXE SM.P ====> SM.OUT
:];
SM.OUT :‫=ت‬$‫ ا‬9/#
SIMAN V - License #6666666
Systems Modeling Corporation
Summary for Replication 1 of 1
Project: Single Machine
Run execution date : 7/28/2002
Analyst: OR241
Model revision date: 7/28/2002
Replication ended at time
: 480.0
COUNTERS
Identifier
Count Limit
_________________________________________
Type 1 Job Count
48 Infinite
Type 2 Job Count
79 Infinite
Execution time: 0.00 minutes.
Simulation run complete.
140
: 2 ‫ل‬#
3‫ن أ‬2/9 ‫ول‬0‫ع ا‬2‫ ! ا‬R7: ‫ل‬2'2‫! ا‬
, ‫ أن از‬P
‫ذج ا‬2 ‫ر ا‬27 ‫ف‬2
M "‫ )ا‬, ‫ ز ! ا‬،? J‫ د‬6 w2 3‫ أ‬3 [‫ع ا‬2‫ ! ا‬R7:‫ ? و‬J‫ د‬10 w2
.,:J‫ د‬4.5 ‫ و‬1.5 ! ‫ وي‬3 [‫ع ا‬2‫ ? و‬J‫ د‬6 ‫ و‬2 ! ‫ول وي‬0‫ع ا‬2 (,"7:‫ا‬
:, ‫? ت ا‬
[email protected]‫ ا‬R -‫ا‬
. Machine Utilization ,‫ ا آ‬, "; -1
.‫ر‬2 7‫ ا‬3; ‫ة‬N ‫ ا‬R7:‫ د ا‬-2
.R7: ‫ م‬N‫ ا‬3; ‫ق‬Y ‫ ! ا‬G‫ ا‬-3
.‫! اوج‬
, ‫ از‬-4
Type 1 Arrivals
EXP(10)
Out
Buffer
Machine
Type 1 PT
U(2,6)
Type 2 PT
U(1.5,4.5)
Type 2 Arrivals
EXP(6)
SM2.EXP : T‫ ا‬9/#
BEGIN;
;Modified Single Machine job Shop
PROJECT, Single Machine, OR241;
ATTRIBUTES:
JobType: ProcessTime: ArrTime;
RESOURCES:
Machine;
QUEUES:
Buffer;
COUNTERS: Type 1 Job Count:
Type 2 Job Count;
TALLIES:
Flowtime:
ExitPeriod;
141
DSTATS:
NQ(Buffer), Queue Length:
NR(Machine), Machine Utilization:
REPLICATE,
1, 0, 480;
END;
SM2.MOD :‫ذج‬1‫ ا‬9/#
BEGIN;
;Modified Single machine job shop
CREATE: EXPO(10): MARK(ArrTime);
ASSIGN: JobType=1:
ProcessTime=UNIF(2,6):
NEXT(process);
CREATE, 1, 5: EXPO(6): MARK(ArrTime);
ASSIGN: JobType=2:
ProcessTime=UNIF(1.5,4.5);
process
QUEUE,
SEIZE:
DELAY:
Buffer;
machine;
ProcessTime;
RELEASE: machine;
TALLY:
1, INTERVAL(ArrTime);
TALLY:
2, BETWEEN;
COUNT: JobType;
DISPOSE;
END;
:3 ‫م‬2: , H‫ذج وا‬2 ‫ ` ت ا‬, ‫" آ‬
1- C:\SIMAN5\MODEL.EXE SM2.MOD ====> SM2.M
2- C:\SIMAN5\EXPMT.EXE SM2.EXP ====> SM2.E
3- C:\SIMAN5\LINKER.EXE SM2.M SM2.E ====> SM2.P
4- C:\SIMAN5\SIMAN.EXE SM2.P ====> SM2.OUT
:];
142
SM2.OUT :‫=ت‬$‫ ا‬9/#
SIMAN V - License #6666666
Systems Modeling Corporation
Summary for Replication 1 of 1
Project:
Single Machine
Run execution date :
7/29/2002
Analyst:
OR241
Model revision date:
7/29/2002
Replication ended at time
: 480.0
TALLY VARIABLES
Identifier
Average
Variation
Minimum
Maximum
Observations
____________________________________________________________________________
___
Flowtime
7.6548
.56697
1.5939
18.865
116
ExitPeriod
4.1137
.61447
1.5089
18.021
115
DISCRETE-CHANGE VARIABLES
Identifier
Average
Variation
Minimum
Maximum
Final
Value
____________________________________________________________________________
___
Queue Length
1.0582
1.1846
.00000
5.0000
1.0000
Machine Utilization
.80701
.48902
.00000
1.0000
1.0000
COUNTERS
Identifier
Count
Limit
_________________________________________
Type 1 Job Count
43
Infinite
Type 2 Job Count
73
Infinite
Execution time: 0.00 minutes.
Simulation run complete.
143
‫‪#‬ل ‪: 3‬‬
‫‪ # 2‬ا‪ 9y‬و‪: Two Job Types and Two Workstation 2 D#‬‬
‫‪Repair‬‬
‫‪Reject‬‬
‫‪Depart‬‬
‫‪Good‬‬
‫‪Buffer‬‬
‫‪Inspector‬‬
‫‪Buffer‬‬
‫‪Machine‬‬
‫ا‪ R7:‬ا اد ‪ MI U" I‬و‪ NI‬دوره ‪ %9 3/‬ا" ‪2 U M‬ا‪ ,7‬آ‪ ,‬وا‪6‬ة‪ " .‬إ‪ U‬ء‬
‫ ‪ ,‬ا ‪ R‬ا آ‪; ,‬ن ا‪ I R7:‬إ‬
‫ا` ‹ ‪ _ I‬ا‪ R7:‬ا‬
‫آ‪; %9 P6 , X ,‬‬
‫‪ . U‬‬
‫‪,7‬‬
‫"‪ ,‬آ‪H‬ة او ;‪ ,V2‬او ‪ "9‬د ‪ ، U" I‬ا‪ R7:‬ا‪H‬ة وا‪R7:‬‬
‫ا ;‪ YI ,V2‬در ا‪ N‬م وا‪ R7:‬ا‪ "9 3‬د ‪ R-I U" I‬ة اى إ‪ 3‬ا آ‪ ,‬ا‪0‬و ‪P6‬‬
‫‪ "9‬د ا" ‪ ، U M‬ا‪ N‬ا ‪ w7‬ا‪.5‬‬
‫ز!‬
‫! ا‪2'2‬ل ‪2 R7:‬زع ا‬
‫‪ 9 w2‬د‪ ! !2 -29 .? J‬ا‪ _? ƒ2‬ا‪M I 3‬‬
‫‪2O M/O‬ا?‪ ! U 30% ،3‬ا‪2‬ع ا‪0‬ول و ‪U 70%‬‬
‫! ا‪2‬ع ا[ ‪ ،3‬ا‪ R7:‬ا ‪N‬ة‬
‫" ‪ SII U M‬آ‪ ! M‬ا آ‪ ,‬و ‪ ,7‬ا` ‹‪ ،‬وƒ ?_ ا‪2‬ع ا‪0‬ول ‪ U‬ا;‪ ,f‬‬
‫وƒ ?_ ا‪2‬ع ا[ ‪ ! V 3‬ا‪2 7‬ر ا‪2‬ا‪ ،6‬ا‪GH‬ء ا‪0‬ول ! ا‪2 7‬ر ‪2 9‬ي ا‪2‬ع ا‪0‬ول !‬
‫ا‪ S6 ,I _? ƒ2‬ز ! و'‪ ; U2‬ا‪2 7‬ر‪ ،‬وا‪2‬ع ا[ ‪ ! 3‬ا‪ R9 _? ƒ2‬ا‪2‬ع ا‪0‬ول‬
‫! ا‪ _? ƒ2‬و‪2/9‬ن ‪ S6 SI‬ا‪2'2‬ل ا‪ N . f9‬م ا‪` ^ ,f;0‬غ‬
‫" إذا آ ‪W‬‬
‫وƒ`‪ ! ,‬ا‪2‬ع ا[ ‪ U M "9 3‬أ‪ X‬ء و'‪2‬ل وƒ`‪ ! ,‬ا‪2‬ع ا‪0‬ول ;ن ا" ‪ 9 M‬‬
‫ا‪ ,"7:‬ا[ ‪ ,‬و‪ ،R7:9T‬ا‪ R7:‬ا‪ "9 3‬د ‪2"I U" I‬د إ ‪2 C‬ر ا آ‪ MJe ,‬ا;‪ ,f‬وآ‪U g.‬‬
‫أ‪ MJ‬أ;‪ , 3; ,f‬إ دة ا` ‹‪ ،‬وه‪./‬ا ‪X -29‬ث إ' ف ! ا‪I ,f;0‬م ‬
‫ا آ‪ ,‬و‬
‫‪ ,7‬ا` ‹ ‪2 :‬ع أول و‪2‬ع ‪ 3 X‬و‪2‬ع " د ‪.&" I‬‬
‫ز ! ا` ‹ ‪ Y ،,"7J M/‬ا‪ U2 !N‬أو ‪2‬ع ا" ‪2I & ، U M‬ز‪( 5,8,10) 3[[ R9‬‬
‫! ا‪ _? ƒ2‬ا‪ ‹ `I 3‬‬
‫‪ ,7‬ا` ‹ ‪- _ I U 80%‬ة و‪ YI‬در ا‪ N‬م‪10% ،‬‬
‫‪ ,V2; _ I U‬و‪ YI‬در ا‪ N‬م ا‪ "9 _ I U 10% ، f9‬د ‪ U" I‬و‪2"I‬د إ ‪2 C‬ر‬
‫ا آ‪ ˆ` ،,‬ا‪ S‬ا ‪ 7I ,:‬آ‪ ! M‬ا‪ ! !2‬ا‪ Y _? ƒ2‬ا‪, 6 ! N‬‬
‫إ دة ا ‪ “6T ،R‬ان اي وƒ`‪ !/ 9 ,‬إ دة ا" ‪ U M‬ة ات‪.‬‬
‫‪144‬‬
3"C R9‫ز‬2I & U" I ‫ وا " د‬3 [‫ول وا‬0‫ع ا‬2‫ ! ا‬R7:‫ ا‬M "‫ وا‬f ‫ز ! ا‬
:3 ‫ول ا‬H‫ ا‬3; ‫ ? آ‬J ,9‫ ت وإ ا; ت " ر‬72
Regular
Rework
Mean
Std
Mean
Std
Type 1
5
2
4
1
Type 2
3
1
2
1
,`ƒ2‫ع ا‬2 S6 ,U ‫ ا‬R7:‫ د ا‬MHI‫ و‬,:J‫ د‬480 ‫ م ة‬N‫ا ا‬.‫آ ة ه‬
, ";‫ر و‬2 C M‫ل آ‬2C ! ‫? ت‬
2‫ه; ه‬
6‫ إ‬R H ‫ ان‬f9‫ ا‬9 .,V2; ‫ ا‬R7: 3/‫ ا"د ا‬g.‫وآ‬
3; R7:‫& ا‬JYI ‫ي‬.‫ ! ا‬G‫ƒ ?_ ( وا‬2‫اع ا‬2‫ع ! ا‬2 M/ ‹ `‫ ا‬, "; M OI‫ارد ) و‬2 ‫ا‬
.‫ م‬N‫ا‬
SM3.EXP : T‫ ا‬9/#
145
SM3.MOD :‫ذج‬1‫ ا‬9/#
:3 ‫م‬2: , H‫ذج وا‬2 ‫ ` ت ا‬, ‫" آ‬
1- C:\SIMAN5\MODEL.EXE SM3.MOD ====> SM3.M
2- C:\SIMAN5\EXPMT.EXE SM3.EXP ====> SM3.E
3- C:\SIMAN5\LINKER.EXE SM3.M SM3.E ====> SM3.P
4- C:\SIMAN5\SIMAN.EXE SM3.P ====> SM3.OUT
:];
146
SM3.OUT :‫=ت‬$‫ ا‬9/#
147
:, ‫ اا ] ا‬M ;‫ أدرس و‬:!9‫ ر‬I
1) MODEL FILE: SIMPLE QUEUEING EXAMPLE
BEGIN;
CREATE:
EXPO(4.4);
QUEUE,
BUFFER;
SEIZE:
MACHINE;
DELAY:
RELEASE:
TRIA(3.2,4.2,5.2);
MACHINE;
COUNT:
JOBSDONE;
DISPOSE;
END;
EXPERMINT FILE: SIMPLE QUEUEING EXAMPLE
BEGIN;
PROJECT,
SAMPLE PROBLEM;
DISCRETE, 100;
QUEUES:
BUFFER;
RESOURCES:
MACHINE;
COUNTERS: JOBSDONE;
REPLICATE, 1, 0, 480;
END;
148
2) MODEL FILE: Simple Processing System
;
;
;
Model statements for module: Arrive 1
;
42$
CREATE,
1:EXPO( 5.0):MARK(Time of Arrival);
3$
STATION,
In Door;
51$
TRACE,
-1,"-Arrived to system at station In Door\n":;
6$
ASSIGN:
Picture=Default;
27$
DELAY:
0.;
55$
TRACE,
-1,"-Transferred to next module\n"::NEXT(0$);
;
;
;
Model statements for module: Server 1
;
0$
STATION,
Machine;
158$
TRACE,
-1,"-Arrived to station Machine\n":;
121$
DELAY:
0.;
165$
TRACE,
-1,"-Waiting for resource Machine_R\n":;
82$
QUEUE,
Machine_R_Q:MARK(QueueTime);
83$
SEIZE,
1:
Machine_R,1;
192$
BRANCH,
1:
If,RTYP(Machine_R).eq.2,193$,Yes:
If,RTYP(Machine_R).eq.1,95$,Yes;
193$
MOVE:
Machine_R,Machine;
95$
TALLY:
Machine_R_Q Queue Time,INT(QueueTime),1;
202$
DELAY:
TRACE,
0.0;
-1,"-Delay for processing time TRIA( 1, 4, 8)\n":;
149
84$
DELAY:
TRIA( 1, 4, 8);
166$
TRACE,
-1,"-Releasing resource\n":;
85$
RELEASE:
Machine_R,1;
149$
DELAY:
0.;
172$
TRACE,
-1,"-Transferred to next module\n"::NEXT(2$);
;
;
;
Model statements for module: Depart 1
;
2$
STATION,
Out Door;
233$
TRACE,
-1,"-Arrived to station Out Door\n":;
203$
DELAY:
0.;
225$
COUNT:
Production,1;
230$
TALLY:
Flowtime,Interval(Time of Arrival),1;
240$
TRACE,
-1,"-Disposing entity\n":;
232$
DISPOSE;
EXPERMINT FILE: Simple Processing System
PROJECT,
Simple Processing System,Desdemona Rocketship;
ATTRIBUTES: QueueTime:
Time of Arrival;
QUEUES:
Machine_R_Q,FIFO;
PICTURES:
Default;
RESOURCES:
Machine_R,Capacity(1,),-,Stationary;
150
STATIONS:
In Door:
Out Door:
Machine;
COUNTERS:
TALLIES:
Production;
Machine_R_Q Queue Time:
Flowtime;
DSTATS:
NR(Machine_R),Machine_R Busy:
NQ(Machine_R_Q),# in Machine_R_Q:
MR(Machine_R),Machine_R Available;
REPLICATE,
1,0.0,15,Yes,Yes;
151
3) MODEL FILE: Electronic Assembly and Test
;
;
;
Model statements for module: Arrive 1
;
50$
CREATE,
1:EXPO( 5 ):MARK(Arrival Time);
51$
ASSIGN:
Sealer Time=TRIA( 1 , 3 , 4 );
11$
STATION,
59$
TRACE,
-1,"-Arrived to system at station Part A Arrive\n":;
14$
ASSIGN:
Picture=Default;
35$
DELAY:
0.;
64$
TRACE,
-1,"-Transferred to station Part A Prep\n":;
37$
ROUTE:
2,Part A Prep;
Part A Arrive;
;
;
;
Model statements for module: Arrive 2
;
129$
CREATE,
4:EXPO( 30 ):MARK(Arrival Time);
130$
ASSIGN:
Sealer Time=NORM( 2.4 , 0.5 );
90$
STATION,
Part B Arrive;
138$
TRACE,
-1,"-Arrived to system at station Part B Arrive\n":;
93$
ASSIGN:
Picture=Default;
114$
DELAY:
0.;
143$
TRACE,
-1,"-Transferred to station Part B Prep\n":;
116$
ROUTE:
2,Part B Prep;
;
152
;
;
Model statements for module: Server 1
;
0$
STATION,
Part A Prep;
245$
TRACE,
-1,"-Arrived to station Part A Prep\n":;
208$
DELAY:
0.;
252$
TRACE,
-1,"-Waiting for resource Part A Prep_R\n":;
169$
QUEUE,
Part A Prep_R_Q:MARK(QueueTime);
170$
SEIZE,
1:
Part A Prep_R,1;
279$
BRANCH,
1:
If,RTYP(Part A Prep_R).eq.2,280$,Yes:
If,RTYP(Part A Prep_R).eq.1,182$,Yes;
280$
MOVE:
Part A Prep_R,Part A Prep;
182$
TALLY:
Part A Prep_R_Q Queue Time,INT(QueueTime),1;
289$
DELAY:
0.0;
TRACE,
-1,"-Delay for processing time TRIA( 1 , 4 , 8 )\n":;
171$
DELAY:
TRIA( 1 , 4 , 8 );
253$
TRACE,
-1,"-Releasing resource\n":;
172$
RELEASE:
236$
DELAY:
0.;
258$
TRACE,
-1,"-Transferred to station Sealer\n":;
176$
ROUTE:
2,Sealer;
Part A Prep_R,1;
;
;
;
Model statements for module: Server 2
;
2$
STATION,
Part B Prep;
366$
TRACE,
-1,"-Arrived to station Part B Prep\n":;
329$
DELAY:
0.;
153
373$
TRACE,
-1,"-Waiting for resource Part B Prep_R\n":;
290$
QUEUE,
Part B Prep_R_Q:MARK(QueueTime);
291$
SEIZE,
1:
Part B Prep_R,1;
400$
BRANCH,
1:
If,RTYP(Part B Prep_R).eq.2,401$,Yes:
If,RTYP(Part B Prep_R).eq.1,303$,Yes;
401$
MOVE:
Part B Prep_R,Part B Prep;
303$
TALLY:
Part B Prep_R_Q Queue Time,INT(QueueTime),1;
410$
DELAY:
0.0;
TRACE,
-1,"-Delay for processing time TRIA( 3 , 5 , 10 )\n":;
292$
DELAY:
TRIA( 3 , 5 , 10 );
374$
TRACE,
-1,"-Releasing resource\n":;
293$
RELEASE:
357$
DELAY:
0.;
379$
TRACE,
-1,"-Transferred to station Sealer\n":;
297$
ROUTE:
2,Sealer;
Part B Prep_R,1;
;
;
;
Model statements for module: Inspect 1
;
4$
STATION,
Sealer;
523$
TRACE,
-1,"-Arrived to Inspect station Sealer\n":;
464$
DELAY:
0.;
411$
QUEUE,
Sealer_R_Q:MARK(QueueTime);
412$
SEIZE,
1:
Sealer_R,1;
576$
BRANCH,
1:
If,RTYP(Sealer_R)==2,577$,Yes:
If,RTYP(Sealer_R)==1,425$,Yes;
577$
MOVE:
Sealer_R,Sealer;
154
425$
TALLY:
Sealer_R_Q Queue Time,INT(QueueTime),1;
594$
DELAY:
0.0;
TRACE,
-1,"-Delay for processing time Sealer Time with failure
probability 0.09\n
":;
413$
DELAY:
420$
BRANCH,
Sealer Time;
1:
With,0.09,531$,Yes:
Else,530$,Yes;
531$
TRACE,
-1,"-Entity failed inspection\n":;
516$
DELAY:
0.0;
475$
RELEASE:
500$
DELAY:
0.;
535$
TRACE,
-1,"-Transferred to station Rework\n":;
419$
ROUTE:
2,Rework;
530$
TRACE,
-1,"-Entity passed inspection\n":;
515$
DELAY:
0.0;
414$
RELEASE:
499$
DELAY:
0.;
541$
TRACE,
-1,"-Transferring to station Shipping\n":;
418$
ROUTE:
2,Shipping;
Sealer_R,1;
Sealer_R,1;
;
;
;
Model statements for module: Inspect 2
;
6$
STATION,
Rework;
707$
TRACE,
-1,"-Arrived to Inspect station Rework\n":;
648$
DELAY:
0.;
595$
QUEUE,
Rework_R_Q:MARK(QueueTime);
155
596$
SEIZE,
1:
Rework_R,1;
760$
BRANCH,
1:
If,RTYP(Rework_R)==2,761$,Yes:
If,RTYP(Rework_R)==1,609$,Yes;
761$
MOVE:
Rework_R,Rework;
609$
TALLY:
Rework_R_Q Queue Time,INT(QueueTime),1;
778$
DELAY:
0.0;
TRACE,
-1,"-Delay for processing time EXPO( 45 ) with failure
probability .2\n":;
597$
DELAY:
604$
BRANCH,
EXPO( 45 );
1:
With,.2,715$,Yes:
Else,714$,Yes;
715$
TRACE,
-1,"-Entity failed inspection\n":;
700$
DELAY:
0.0;
659$
RELEASE:
684$
DELAY:
0.;
719$
TRACE,
-1,"-Transferred to station Scrap\n":;
603$
ROUTE:
2,Scrap;
714$
TRACE,
-1,"-Entity passed inspection\n":;
699$
DELAY:
0.0;
598$
RELEASE:
683$
DELAY:
0.;
725$
TRACE,
-1,"-Transferring to station Salvaged Parts\n":;
602$
ROUTE:
2,Salvaged Parts;
Rework_R,1;
Rework_R,1;
;
;
;
Model statements for module: Depart 1
;
156
8$
STATION,
Shipping;
809$
TRACE,
-1,"-Arrived to station Shipping\n":;
779$
DELAY:
0.;
801$
COUNT:
Shipping_C,1;
806$
TALLY:
Shipping_Ta,Interval(Arrival Time),1;
816$
TRACE,
-1,"-Disposing entity\n":;
808$
DISPOSE;
;
;
;
Model statements for module: Depart 2
;
9$
STATION,
Salvaged Parts;
848$
TRACE,
-1,"-Arrived to station Salvaged Parts\n":;
818$
DELAY:
0.;
840$
COUNT:
Salvaged Parts_C,1;
845$
TALLY:
Salvaged Parts_Ta,Interval(Arrival Time),1;
855$
TRACE,
-1,"-Disposing entity\n":;
847$
DISPOSE;
;
;
;
Model statements for module: Depart 3
;
10$
STATION,
Scrap;
887$
TRACE,
-1,"-Arrived to station Scrap\n":;
857$
DELAY:
0.;
879$
COUNT:
Scrap_C,1;
884$
TALLY:
Scrap_Ta,Interval(Arrival Time),1;
894$
TRACE,
-1,"-Disposing entity\n":;
157
886$
DISPOSE;
EXPERMINT FILE: Electronic Assembly and Test
PROJECT,
Electronic Assembly and Test,Mr. Munchkin;
ATTRIBUTES: Sealer Time:
Arrival Time:
QueueTime;
QUEUES:
Part B Prep_R_Q,FIFO:
Rework_R_Q,FIFO:
Part A Prep_R_Q,FIFO:
Sealer_R_Q,FIFO;
PICTURES:
Default;
RESOURCES:
Sealer_R,Capacity(1,),-,Stationary:
Part A Prep_R,Capacity(1,),-,Stationary:
Rework_R,Capacity(1,),-,Stationary:
Part B Prep_R,Capacity(1,),-,Stationary;
STATIONS:
Part B Arrive:
Shipping:
Rework:
Part B Prep:
Sealer:
Part A Prep:
Scrap:
Part A Arrive:
Salvaged Parts;
COUNTERS:
Salvaged Parts_C:
158
Scrap_C:
Shipping_C;
TALLIES:
Salvaged Parts_Ta:
Rework_R_Q Queue Time:
Sealer_R_Q Queue Time:
Scrap_Ta:
Part B Prep_R_Q Queue Time:
Shipping_Ta:
Part A Prep_R_Q Queue Time;
DSTATS:
NQ(Rework_R_Q),# in Rework_R_Q:
NR(Part A Prep_R),Part A Prep_R Busy:
NQ(Sealer_R_Q),# in Sealer_R_Q:
MR(Part B Prep_R),Part B Prep_R Available:
NQ(Part A Prep_R_Q),# in Part A Prep_R_Q:
MR(Sealer_R),Sealer_R Available:
MR(Part A Prep_R),Part A Prep_R Available:
MR(Rework_R),Rework_R Available:
NR(Sealer_R),Sealer_R Busy:
NR(Rework_R),Rework_R Busy:
NR(Part B Prep_R),Part B Prep_R Busy:
NQ(Part B Prep_R_Q),# in Part B Prep_R_Q;
REPLICATE,
1,0.0,2000,Yes,Yes;
159
:#‫ا ا‬
: ARENA ‫ اآة‬#> ‫)ام‬$'_ ‫= واآة‬31‫ا‬
:#)*#
Process Analysis, Modeling and ‫آ ة ا" ت‬
‫ و‬,-. ‫ و‬M I 3; Arena ‹I
.Business Decision Support ‫ ل‬0‫ارات ا‬J % Simulation
! Resource ‫رد‬2 ,7‫ا‬2 ‫ م‬N‫ ا‬3; !? ‫ آ‬%9 M ‫اء أو‬-‫ أي إ‬3‫ ه‬Process , "‫وا‬
.‫ م‬N‫ارد ا‬2
‫م ام‬2:I‫ ا" و‬Uf" R ‫ م و‬N‫ ت ا‬2/ R M `I ,‫آ‬6 ‫ أ ء‬3‫ ? ت ه‬/‫وا‬
.6‫ا‬2‫ م ا‬N‫ ا‬3; ‫ ? ت‬/‫ ! ا‬6‫ع وا‬2 ! [‫ن ه ك أآ‬2/9 J‫ و‬.‫ م‬N‫ارد ا‬2
. ‫ م‬N‫ ا‬3; ‫ ! ا" ت‬M6‫ ا‬I ‫ آ ? ت‬," g‫ ا" ت وذ‬,-. Arena ‫م‬2:I
:Arena ‫ت‬B#
‫ذج‬2 ‫ ;& إد ل ا‬%9 3‫ ا@ ب وا‬w7 N ,-. ‫ة ا‬.; UN; Arena ] MY
‫ ت‬2/ ‫اص‬2 &; UN9‫ و‬O‫ ا‬, `' N ,-. ‫ة ا‬.; ‫ إ ب و‬w7 M/ ‫ ا" ت‬,62 ‫ي‬2 9‫ و‬Project Bar ‫وع‬O ‫د ا‬2 ‫ و‬O , `' M/ ‫ذج‬2 ‫ا‬
Navigate ‫ال‬2H‫ة ا‬.; ‫ و‬Reports Panel 9‫ ر‬:‫ ا‬,62‫ و‬Basic Process Panel , 0‫ا‬
UN; ‫وع‬O ‫د ا‬2 M‫ ! دا‬90‫ر ا` رة ا‬G wYf ‫ ت اى‬62 ,; V‫! إ‬/ 9 ‫ آ‬Panel
‫ ا" ت‬M[ ‫رة‬27 ‫ ت‬62 ‫ي‬2 I ‫ ! ا ` ت‬, ? J UN; Attach... U ‫ار أ ر‬26 ‫ة‬.; ' "‫ ا‬,62‫ و‬Blocks Panel S‫ا‬2:‫ ا‬,62‫ و‬Advanced Process Panel ‫رة‬27 ‫ا‬
. ‫ و^ه‬Elements Panel
160
161
SIMAN ( SIMulation ANalysis) ‫ اآة‬u
, HI ‫ ر‬C‫ وإ‬MODEL FRAME ‫ذج‬2 ‫ ر‬C‫ ! إ‬SIMAN ! M /‫ذج ا‬2 ‫ن ا‬2/9
EXPERIMENT FRAME
‫ذج‬2 ‫ ر ا‬C‫ إ‬3; ‫ وا" رات‬.‫ م‬N‫ ! ا‬V ‫اث‬6q 3:7 ‫ _ ا@ ب ا‬9 :‫ذج‬1‫ر ا‬C‫إ‬
SM.MOD ‫ آ [ ل‬MOD ,; [email protected]‫ ا _ ا‬7"9‫ و‬BLOCKS S‫ا‬2J 3 I
' I , H‫ ر ا‬C‫ إ‬3; ‫ ا" رات‬.‫ذج‬2 ‫اء ا‬[email protected] , H‫"! وط ا‬9 : T‫ر ا‬C‫إ‬
SM.EXP ‫ آ [ ل‬EXP ,; [email protected]‫ ا _ ا‬7"9‫ و‬ELEMENTS
3b ‫ ا‬5 [email protected]‫ ا‬RI‫ و‬U J‫آ ة وأ‬
‫ ت ا‬Y ‫ى‬2J‫ ! أ‬3‫ ه‬SIMAN ‫آ ة‬
‫ ا‬,Y‫و‬
M " ‫م‬2:I 3‫ ا‬,`‫ ا‬M "‫ ا‬,—‫ آ‬Arena ] ‫ري‬27 U ‫ أ‬J‫ و‬Object-Orientation
‫ري‬27 U"- J‫ و‬.Arena ] GUI ,9‫ر‬2 ‫ ا م ا‬,-‫ وا‬W I 3`I 3‫ وا‬3"`‫ا‬
, ‫ آ‬R79 3/ ( f9‫ ا‬VBA ,H ‫ ا‬,Y R ) ‫ر‬27 ‫ ول ا م ا‬3; Arena ] .‫;ة م ا" دي‬2 ^ ‫ة‬9- ‫ات‬6‫و‬
., ‫ ا‬,[ 0‫ ا‬3; UV" ‫ف‬2‫و‬
162
‫أو‪ :f‬أ‪ U/2 /#‬ا‪ /.‬ت ا'' ‪:‬‬
‫‪#‬ل ‪:1‬‬
‫‪2‬ف أ ء ‪2‬ذج أو‪ M' `I 59G %X w 3‬أآ[ ‪ M 6‬إ إ"اض "‪%N‬‬
‫‪ 2/‬ت ‪.Arena‬‬
‫ ء ‪2‬ذج ج إ ‪ 2I‬ا‪ ? /‬ت ا‪ 3; M `I 3‬ا‪ N‬م و ! ‪ %X‬ج إ ا‹ ! ه‪5.‬‬
‫ا‪ ? /‬ت‪.‬‬
‫‪ 2‬آ ? ت م و‪6‬ة ‪ Create Module‬و‹ ‪ U‬م ا‪62‬ة ‪Dispose Module‬‬
‫و)ة و) )‪Create Module () 4‬‬
‫‪ 2I %9‬ا‪ ? /‬ت ‪62‬ة ‪ Create Module‬إ‪ %‬ا‪62‬ة ‪ 3; S/9‬دا‪ U‬و;‪ 3‬ا‪7‬ف ا‪! 90‬‬
‫ا`‪ -29 3‬د ا‪) 2‬و‪ (`' 6 UN9‬آ ‪ -29‬ج وا‪ ! 6‬ا‪62‬ة )‬
‫‬
‫(‪.‬‬
‫‪ M‬ه‪.‬ة ا‪62‬ة ! ‪ S‬أ‪.; ! U2:9‬ة ا" ت ا‪ Basic Process , 0‬وا‪3‬‬
‫‪ Arena ] 3; -2I‬وه‪ 5.‬ا ;‪.‬ة ‪ " ‹I‬ت ا‪ , 0‬وا‪ "I 3‬أه‪ %‬وأول ا" ت‬
‫;‪ Arena 3‬وا‪0‬آ[ ‪ %N" 3; 2‬ا‪., N0‬‬
‫‪ 2I‬ا‪ ? /‬ت ء ‪ Schedule WJ2‬او از ‪,‬‬
‫! ‪Inter Creation Time 2I‬‬
‫)‪ .(ICT‬و‪ I‬ك ا‪ ? /‬ت ;‪ 3‬ا‪ N‬م ‪ , U %‬أو ت `‪ .,‬و‪ 9‬د ‪2‬ع ا‪ !? /‬أ‪ X‬ء‬
‫‪ 3; 52I‬ه‪ 5.‬ا‪62‬ة‪.‬‬
‫و‪I‬م ا‪62‬ة ‪ ^ Create‬آ ‪:3‬‬
‫ آا‪ @ ,9‬ج ‪.R I w 3; ,"7J‬‬‫ و'‪2‬ل و‪ SC M[ ) ,:X‬أو أ 'ف أو إ رة ا‪ HI , " (d‬ر‪.,9‬‬‫‪ -‬و'‪2‬ل ز ‪2‬ن " ‪ %"7 M[ ) , ,‬أو ‪ g‬أو ‪ , :‬أو ‪ _ƒ2‬إم ا‪.(d‬‬
‫‪163‬‬
‫اص‬2 ‫ة‬.; UN; !I ‫ ` رة‬U wYf‫ و‬Create ‫ة‬6‫ و‬S U'‫ا‬2 ‫ة‬.; ‫ ر‬Uƒ@
, ‫ ا‬Create
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‫اص‬2‫ة ا‬.; :3 ‫ ا‬M/O‫ ا‬3; ‫ه‬/ 3‫وا‬
164
Random(Expo) 3?‫ا‬2O Type ‫ع‬2 ‫ار‬26 ‫ة‬.; 165
Schedule (,‫و‬-) WJ2I Type ‫ع‬2 ‫ار‬26 ‫ة‬.; Constant W X Type ‫ع‬2 ‫ار‬2 ‫ة ا‬.; Expression "I Type ‫ع‬2 ‫ار‬26 ‫ة‬.; Expression "I Expression "I Type ‫ع‬2 ‫ار‬26 ‫ة‬.; 166
:O‫ ا‬, `' ‫ر‬2C 3; ‫اص‬2‫ة ا‬.; Random(expo) 3?‫ا‬2O Type ‫ع‬2 ‫ار‬26 ‫ة‬.; Schedule (,‫و‬-) WJ2I Type ‫ع‬2 ‫ار‬26 ‫ة‬.; Constant W X Type ‫ع‬2 ‫ار‬2 ‫ة ا‬.; 167
Expression "I Type ‫ع‬2 ‫ار‬26 ‫ة‬.; :3Ih ‫?‹ آ‬
‫ ا‬.;‫ا‬2 M `‫و‬
_'2‫ا‬
‫ب‬27 ‫ا‬
6‫ و‬Module Identifier ‫ة‬62 ‫ "ف‬2‫وه‬
Name %‫إ‬
.‫ة‬62‫ ا‬M/ UN9‫ر و‬/9T
.2 ‫ي‬.‫ ?! ا‬/‫ ا‬%‫إ‬
Entity Type !? /‫ع ا‬2
‫ي‬.‫ ا‬Arrival Streem "‫ل‬2'2‫ ا‬M" ‫ع‬2
Type ‫ع‬2
‫ أو‬Random "3?‫ا‬2O" M O9‫ و‬2
‫ أو‬Constant "W X" ‫ أو‬Schedule "WJ2 "
.Expression ""I"
"3?‫ا‬2O" ‫ع‬2‫ن ا‬2/9 w:; ‫م‬9‫و‬
Value , J
, J 7"I‫" )و‬W X" ‫( أو‬w2 ‫ ا‬37";)
.(20 M[ , X
.‫ي م‬.‫" ا‬WJ2‫ ا‬%‫"ف "إ‬9‫و‬
Schedule Name WJ2‫ ا‬%‫إ‬
.‫ م‬N ‫ ? ت‬/‫ل ا‬2'‫ و‬w ‫"ف‬9 "WJ2‫"ا‬
."WJ2I" ‫ع‬2‫ن ا‬2/9 w:; ‫م‬9‫و‬
."2‫! ا‬
! ‫ د "ز‬I , J ‫ أو‬R9‫ز‬2I ‫أي‬
Expression "I
.""I" ‫ع‬2‫ن ا‬2/9 w:; ‫م‬9‫و‬
"2‫ ـ" ! ا‬, ‫ ! ا‬G‫ات ا‬6‫و‬
Units ‫ات‬6‫و‬
First Creation Time "2I ‫أوـ"ز ! أول‬
."WJ2I" ‫ع‬2‫ن ا‬2/9 ‫م‬9T‫و‬
.2I M‫ م آ‬N‫ ا‬M 3‫ ? ت ا‬/‫د ا‬
Entities per Arrival ‫ل‬2'‫ و‬M/ !? ‫آ‬
M 9 ‫ و‬.2 3‫ ? ت ا‬/ ‫ د‬J‫أ‬
Max Arrival ‫ل‬2'‫ و‬J‫أ‬
168
.2‫_ ا‬J29 %J‫ا ا‬.U ‫ة‬2 ‫ ? ت ا‬/‫د ا‬
.‫ م‬N‫ ا‬M9 !? ‫ أول آ‬2 ‫ز ! ائ‬
First Creation 2I ‫أول‬
."WJ2I" ‫ع‬2‫ن ا‬2/9 ‫م‬9T‫و‬
: SIMAN u/ Create ) 4 ‫و)ة‬
: T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Create
1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude");
PICTURES:
Picture.Airplane:
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
169
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
ENTITIES:
Entity
1,Picture.Report,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,,)
;
:‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
Create 1
;
0$
CREATE,
1,HoursToBaseTime(0.0),Entity
1:HoursToBaseTime(EXPO(1)):NEXT(1$);
1$
ASSIGN:
Create 1.NumberOut=Create
1.NumberOut + 1;
Dispose Module (‫ء‬W‫ )إ‬z/$4 ‫و)ة‬
.& U ‫ م‬I‫ م " إ‬N‫ ا‬3; !? /‫د ا‬2-‫ ء و‬[email protected] ‫ة‬62‫ ا‬5.‫م ه‬I‫و‬
: ^ ‫م‬9‫و‬
.‫ق‬2 R
‫ در ا‬YI ,"
‫اء‬G-‫ أ‬-
.,9‫ ر‬HI , ‫ ء‬U‫ إ‬-
170
., : ‫ درو‬Y9 !? ‫ ز‬:‫ ا@ ب‬w7 ‫ر‬2C 3; ‫اص‬2‫ة ا‬.; ‫و‬
:O‫ ا‬, `' ‫ر‬2C 3; ‫اص‬2‫ة ا‬.; ‫و‬
:‫ي‬2 I‫و‬
_'2‫ا‬
‫ب‬27 ‫ا‬
M/ UNI‫ة و‬62‫_ ا‬9" 6‫ و‬%‫إ‬
Name %‫إ‬
.‫ة‬62‫ا‬
‫ دم‬:‫ ?! ا‬/‫ءات ا‬
6‫ إ‬W ‫ د ; إذا آ‬I‫و‬
Record Entity !? /‫ءات ا‬
.T‫ أو‬MHI
6‫ إ‬MH
Statistics
: SIMAN u/ Dipose z/$4 ‫و)ة‬
: T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Dispose
1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude");
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
:‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
171
Dispose 1
;
0$
ASSIGN:
Dispose 1.NumberOut=Dispose
1.NumberOut + 1;
1$
DISPOSE:
Yes;
‫ درو‬Y9‫ و‬2 9 !? G .Dispose ‫ و‬Create !I62‫ا ا [ ل "اض ا‬.‫ ه‬3; ‫م‬2: ‫ف‬2
:‫ ا@ ب‬w7 ‫ر‬27 Create ‫اص‬2 ‫ة‬.; ‫ إ‬N
Customer 2‫ ه‬Entity Type !? /‫ع ا‬2‫ و‬Customers Arrive 2‫ة ا‬6‫ و‬Name %‫“ إ‬6T
w2 , J‫ و‬Random (Expo) 2‫ ه‬Type &2 Time Between Arrivals ‫ل‬2'2‫! ا‬
! ‫ز‬
Minutes ? J‫ ه د‬Units ! G‫ات ا‬6‫ وو‬1 3‫ ه‬Value 30‫ ا‬R9‫ز‬2 ‫ل‬2'2‫! ا‬
! ‫ز‬
‫ ? ت‬/ ‫ د‬J‫ وأ‬1 ‫ ه‬Entities per Arrival ‫ل‬2'‫ث و‬6 M‫ آ‬2I 3‫ ? ت ا‬/‫د ا‬
0.0 ‫ ه‬First Creation (‫ل‬2'‫ )و‬2I ‫ وز ! أو‬Infinite 3? UT ‫ ه‬Max Arrival M I 3‫ا‬
:O‫ ا‬, `' ‫ر‬27 Create ‫اص‬2 ‫ة‬.; ‫ إ‬N
172
‫ه‪.‬ا ا ‪2‬ذج ا‪- w‬ا ‪2 9T‬ي ‪2‬ي آ ? ت ‪ M I‬و‪ YI‬در‪2 .‬ف ‪ N‬إ أ‪ 6‬و‪6‬ات‬
‫ا ت ‪ Data Modules‬وه‪3‬‬
‫و)ة ا‪Entity Module B‬‬
‫‪ wYf‬و‪6‬ة ا‪2 3; !? /‬د ا ‪O‬وع ‪.; W I‬ة ا" ت ا‪ ,'0‬وا‪.‬ي & ا‪M/O‬‬
‫‪.; 3; UN9‬ة ا ‪2‬ذج ) ‪ , `' N‬ا‪ (O‬ا‪ 7‬ا ‪:3‬‬
‫و‪ & : & V2‬إ ‪!97‬‬
‫وو‪6‬ة ا‪"I !? /‬ف _ أ‪2‬اع ا‪ ? /‬ت و'‪2‬ره ا‪0‬و‪ ,‬و‪ U7"I ,`/I‬و‪ ,`/I‬ا‪, :‬‬
‫ا ‪ ,; f‬ا‪0‬و‪ ,‬و‪ , J‬ا‪ ^ , :‬ا ‪ ,; f‬ا‪0‬و‪ ,‬و‪ ,`/I‬ا@‪ N‬ر ا‪0‬و‪ 3‬و‪ ,`/I‬ا@‪ :‬ل ا‪0‬و‬
‫وأي ‪ _ /I‬أو‪ ,‬اي آ ‪ 9 I R7‬إذا أرد ‪ MHI‬إ‪6‬‬
‫و‪9‬م دة‪:‬‬
‫‪3; ]I R7J -‬‬
‫‪.R‬‬
‫ ات ;‪.S/ 3‬‬‫‪ -‬ز ?! ;‪.g 3‬‬
‫‪173‬‬
‫ءات أم ‪.T‬‬
,-. ‫ة ا‬.; 3; UN9‫و‬
wYf ‫ ر‬I !? /‫ة ت ا‬6‫ و‬w‫ذج ا‬2 :(aV2 !?G- W J) 3 ‫( ا‬O‫ ا‬, `')
Initial ,‫رة أو‬2' ,? 7‫ إ‬M[ 2 ‫ ?! ا‬/‫ إد ل ت ! ا‬R7 ‫ر‬27‫ا ا‬.‫ ه‬3; “6T
M7" , ‫ ا‬3; ,`/‫! إد ل ا‬/ 9 ‫( آ‬Picture Man M-‫رة ر‬2' ‫ )ه أ‬Picture
,; f ‫ ^ ا‬,‫و‬0‫ ا‬, :‫ وا‬Initial VA Cost ,; f ‫ ا‬,‫و‬0‫ ا‬, :‫ وا‬Holding Cost/Hour
Initial ,‫و‬0‫ ا‬M:‫ ا‬,`/I‫ و‬Initial Waiting Cost ,‫و‬0‫ ر ا‬[email protected]‫ ا‬,`/I‫ و‬Initial NVA Cost
,7‫ا‬2 YI ‫! أن‬/ 9 %:‫ة ا‬.‫“ ان ه‬6T) Initial Other Cost ,‫ أو‬,`/I ‫ وأي‬Tran Cost
‫ءات‬
6‫( وأ إذا أرد إ‬Assign Module ‫ة أ‬6‫ و‬,7‫ا‬2 ‫آ ة أو‬
‫ ء ا‬X‫ أ‬Y ‫" أو‬I
.Report Statistics 3; A ‫ة‬62‫ ا‬5.‫! ه‬
:3 ‫ آ‬5GUH ‫م‬2: ‫ أن‬T ‫ذج‬2 ‫اء ا‬-‫ إ‬MJ
Setup... %X Run ‫ ر‬,?‫ ا‬, ? :‫! ا‬
174
GUH‫ار ا‬26 ‫ة‬.; UN;
M
%‫ وإ‬Project Title ‫وع‬O ‫ان ا‬2 ‫ أد‬Project Parameters ‫وع‬O ‫ ا‬% " 3;
"‫ أ "آ ? ت‬Statistics Collection ," H ‫ءات ا‬
(‫آ ة‬
[email protected]‫ ا‬3;‫ و‬Analyst Name ‫ م‬N‫ا‬
‫اء ا‬-‫ار )د ات إ‬/‫ ا‬% " 3; .(‫ذج‬2 ‫ا ا‬.‫ ه‬3; ‫اه‬2 9 ˆ) Entities
Replication Parameters
175
Warm-up (!‫ )أو ا‬,
‫ ;ة ا‬1 ‫ ه‬Number of Replications ‫ار‬/‫د ات ا‬
&; ‫ي‬H ‫ي‬.‫ ! ا‬G‫ ا‬2‫ );ة ا! ه‬, Time Units UI‫ا‬6‫ وو‬0.0 ‫ ه‬Period
U 9 3‫ ا‬Transient State , :@‫ `ة ا‬I g‫? ت وذ‬
6‫ أي إ‬MHI ‫آ ة ون‬
‫ا‬
‫ ه‬Replication Length ‫ار‬/‫ل ا‬2C .(Steady State ‫ازن‬2‫ ا‬,6 ‫ إ‬M 9 6 ‫ذج‬2 ‫ا‬
‫ا‬.‫ض ! ه‬Y‫ ) ا‬, &I‫ا‬6‫ وو‬24 ‫ ه‬Hours Per Day ‫م‬2‫ ا‬3; ‫ د ا ت‬.‫ ت‬10
Base Time ! G , 0‫ة ا‬62‫ وا‬.(‫ ت‬8 ‫ن‬2/9 J [ M "‫م ا‬29 ‫ ت‬9 I 2‫ه‬
Run Control ‫اء‬[email protected] %/ ‫ وا‬Speed ,‫ ا‬M[ %:‫ ا‬,: . Hours , ‫ وه‬Units
.Default ,V‫ ا@;ا‬U J 3; U: Reports 9‫ ر‬:‫وا‬
:‫ا^=اء‬
! Run ‫ أو ر‬F4 ‫ ` ح‬wYf g‫ذج وذ‬2 ‫آ ! ا‬e ‫م‬2: ‫آ ة‬
‫اء ا‬-‫ إ‬MJ
Check Model %X ,?‫ ا‬, ? :‫ا‬
176
‫إذا آ ن ا ‪2‬ذج ‪ ! %‬ا ‪ ,6‬ا ‪ UNI ,:7‬ا ;‪.‬ة‬
‫‪ R‬ا ‪ -2IT " ,‬أ‪ 7‬ء أو ‪9. I‬ات ;‪ 3‬ا ‪2‬ذج"‬
‫! ‪ , ? J‬ا‪0‬دوات ا‪, :‬‬
‫@‪-‬اء ا ‪2‬ذج إ ‪ ` wYf‬ح ‪ F5‬أو ‬
‫;‪ 3‬ا‪ , ? :‬ا?‪ ,‬أو ! ‪Go %X Run‬‬
‫ا*‬
‫‪177‬‬
.]? ‫` ا‬I‫ و‬9:‫ ا‬a` I S 7 ‫ك‬9 :!9 I
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"First Example ( Create - Dispose )","Dr.
A. Barry",,,No,Yes,No,No,No,No,No;
VARIABLES:
Customers
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Customers
Leave.NumberOut,CLEAR(Statistics),CATEGORY("Exclude");
PICTURES:
Picture.Airplane:
178
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
REPLICATE,
1,,HoursToBaseTime(10),Yes,Yes,,,,24,Hours,No,No;
ENTITIES:
Customer,Picture.Man,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Ye
s,,);
‫ذج‬1‫ ا‬9/#
;
179
;
Model statements for module:
Create 1
;
1$
CREATE,
1,MinutesToBaseTime(0.0),Customer:MinutesToBaseTime(EXPO(
1)):NEXT(2$);
2$
ASSIGN:
Customers
Arrive.NumberOut=Customers Arrive.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Dispose 1
;
0$
ASSIGN:
Customers
Leave.NumberOut=Customers Leave.NumberOut + 1;
5$
DISPOSE:
Yes;
180
:2 ‫ل‬#
‫ ? ت‬/‫ & ا‬9 Resource ‫رد‬2 ‫ م‬N‫ ا‬3; M"H P
‫ أو‬
‫ذج ا‬2 ‫ر ا‬27 ‫ف‬2
M " ‫م‬2:I 3‫ وا‬Process Module , "‫ة ا‬6‫ض م و‬Y‫ا ا‬.U ‫ م‬N‫ ا‬%U2‫د‬
:3 ‫ ا‬S‫ اآ‬U‫ ? ت و‬/
:Process Module /.‫و)ة ا‬
M ‫ة‬62‫ '` و‬6 2‫ وه‬U`‫ ا‬3; S/9 ‫ة‬62‫ى ا‬2 ‫ و‬U‫ دا‬3; S/9 ‫ة‬62‫ ا‬%‫إ‬
.(
‫ارد‬2 ‫ك ا‬I‫ي رات @ ك و‬2 I‫آ ة و‬
) 6‫( و ج وا‬
) 6‫وا‬
‫ ا‬3; M "‫ أو ا‬,H " ‫م‬2:I ‫ة‬62‫ة ا‬.‫وه‬
‫ي‬.‫ ا‬3:7 ‫ ا‬M‫ ا‬9 I‫ و‬Submodel 3; ‫ذج‬2 ‫ ر إام‬U -29 ‫ آ‬.,6 ‫ا‬
3; !? / 7"9 ,H " ‫ ز ! ا‬.Hierarchical User-defined Logic ‫ ا م‬,7‫ا‬2 7"9
, J ! 9GI , "‫ أن ا‬3"9 ‫ا‬.‫ ) وه‬Value Added ",; f , J" ‫ن‬2/9 ‫! ان‬/ 9‫ة و‬62‫ ا‬5.‫ه‬
‫ أو‬Non-value Added ",; f ^ , J" ‫ ?!( أو‬/‫_ † إ ا‬fI ‫ن أو‬e ! R;I ‫أو‬
M "‫ ا‬,I ‫ _ ا‬/‫ ا‬.Other "( †" ‫ أو اي‬Wait "‫ ر‬N‫ أو "إ‬Transfer "‫ ل‬:‫"إ‬
., ‫ ا‬,b` ‫ ف‬fI ‫ف‬2
181
‫وإا ‪2/I UI‬ن ^ آ ‪:3‬‬
‫ " ‪.,— ,"7J ,H‬‬‫ ا‪ ,"-‬و‪.,:X‬‬‫ ‪ C : I‬ت‪.‬‬‫ ‪ ,‬ز ‪2‬ن‪.‬‬‫ ;‪.‬ة ا‪2‬اص ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ‪: Type‬‬
‫‪182‬‬
: Action ‫ ف‬I Logic 7 ‫ار ا‬26 ‫ة‬.; (Triangular 3[[ R9‫ز‬2I) Delay Type e‫ع ا‬2 ‫ار‬26 ‫ة‬.; 183
(Constant W X) Delay Type e‫ع ا‬2 ‫ار‬26 ‫ة‬.; (Normal 3"C) Delay Type e‫ع ا‬2 ‫ار‬26 ‫ة‬.; 184
(Uniform ‫ ) وي‬Delay Type e‫ع ا‬2 ‫ار‬26 ‫ة‬.; (Expression "I) Delay Type e‫ع ا‬2 ‫ار‬26 ‫ة‬.; 185
Allocation !"‫ار ا‬26 ‫ة‬.; :O‫ ا‬, `' ‫ر‬2C 3; ‹?
‫ة ا‬.; ‫ع‬2 ‫ار‬26 ‫ة‬.; R
186
‫ ;‪.‬ة ‪26‬ار ا ف‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ا‪("I , 6 3;) e‬‬
‫ ;‪.‬ة ‪26‬ار ا"!‬
‫ ;‪.‬ة ‪26‬ار ‪"I‬‬
‫و` ‪.; M‬ة ا‬
‫?‹ آ ‪:3Ih‬‬
‫ا ‪27‬ب‬
‫ا‪_'2‬‬
‫إ‪Name %‬‬
‫وه‪" 2‬ف ‪62‬ة ‪ Module Identifier‬و‪6‬‬
‫‪/9T‬ر و‪ M/ UN9‬ا‪62‬ة‪.‬‬
‫‪2‬ع ‪Type‬‬
‫‪ 9 I ,:9C‬ا ‪ 7‬دا‪ M‬ا‪62‬ة‪,H " .‬‬
‫‪187‬‬
‫"‪ I Standard ", J‬د ان آ‪ M‬ا ‪2 7‬ف‬
‫‪G9‬ن دا‪ M‬و‪6‬ة ا " ‪ ,H‬و‪"9‬ف ‪2‬ا‪,7‬‬
‫إ‪-‬اء "!‪2 " .‬ذج ;‪Submodel "3‬‬
‫‪ 9‬د أن ا ‪2 7‬ف ‪"9‬ف ‪3I M/O‬‬
‫;‪2 3‬ذج ;‪ 3‬وا‪.‬ي ‪ M O9 J‬أي د !‬
‫و‪6‬ات ا ‪.7‬‬
‫إ‪-‬اء ‪Action‬‬
‫‪2‬ع ا " ‪ ,H‬ا‪ 3‬ث دا‪ M‬ا‪62‬ة‪.‬‬
‫"‪ 9 Delay "eI‬د ‪ ,C‬ا& ث‬
‫‪ 3; eI‬ا" ‪ ,‬ون إ‪ 7‬ء ‪2‬رد‪" .‬إ ك‬
‫‪ 3"9 Seize Delay "eI‬أن ‪2‬رد ‪2‬ف‬
‫‪6 R 7"9‬وث ‪ eI‬و‪I !/‬ك ا ‪2‬رد ‪%‬‬
‫ و‪" .( WJ‬إ ك ‪I eI‬ك" ‪Seize‬‬
‫‪ 3"9 Delay Release‬أن ‪2‬رد ‪2‬ف ‪7"9‬‬
‫‪I %9 %X eI , " R9‬ك ا ‪2‬رد‪eI" .‬‬
‫‪I‬ك" ‪ 3"9 Delay Release‬أن ا ‪2‬رد ‪J‬‬
‫ا‪ : 37‬وأ& ث "‪9" %X "eI‬ك"‬
‫ا ‪2‬رد‪ .‬وه‪.‬ا ا‪2/9 w:; 79 0‬ن‬
‫ا‪2‬ع "‪."3 J‬‬
‫أو‪Priority ,‬‬
‫‪ , J‬ا‪0‬و‪ !? / ,‬ا‪.‬ي ‪ N9‬ه‪ 5.‬ا‪62‬ة‬
‫ ‪2‬رد ا د‪ .‬و‪9‬م ‪2/9‬ن آ ?! أو‬
‫أآ[ ! و‪6‬ة اى ‪ ˆ` N9‬ا ‪2‬رد‪.‬‬
‫و‪9T‬م ‪2/9‬ن ا@‪-‬اء "‪ "eI‬أو‬
‫"‪I eI‬ك" أو ‪2/9‬ن ا‪2‬ع " ‪2‬ذج‬
‫;‪."3‬‬
‫‪2‬ارد ‪Resources‬‬
‫و‪"9‬د ا ‪2‬ارد أو ‪2 ,2 H‬ارد وا‪3‬‬
‫‪I‬م " ‪ ,H‬ا‪IT .!? /‬م ‪2/9‬ن‬
‫ا@‪-‬اء "‪ "eI‬أو ‪2/9‬ن ا‪2‬ع " ‪2‬ذج‬
‫;‪."3‬‬
‫‪188‬‬
.e‫ ا‬% " 9 I ,:9C ‫ أو‬R9‫ز‬2‫ع ا‬2
Delay Type e‫ع ا‬2
Expression ""I" ‫ و‬Constant "W X"
"3"C" ‫" ت‬9‫ز‬2‫ة ا‬6‫ وا‬, J ‫ ج‬I
"3[[ "‫ و‬Uniform "‫ و " وي‬Normal
.% " ‫ ج ة‬I Triangular
.e‫ ا‬% " ! G‫ات ا‬6‫و‬
Units ‫ات‬6‫و‬
M "‫ ا‬,`/I‫ و‬M "‫ ‹ ز ! ا‬I ,`‫ د آ‬I‫و‬
Allocation ‹ I
, J" 5" ‫! ان‬/ 9 M "‫ وا‬.‫ ? ت‬/
",; f ^ , J" ‫ أو‬Value Added ",; f
‫ أو‬Transfer "‫ ل‬:‫ أو "إ‬Non-value Added
Other "g‫ أو "^ ذ‬Wait "‫ ر‬N‫"إ‬
, ‫ ا‬,b` ‫ ف‬fI ‫ف‬2 ,' ‫ ا‬,`/‫وا‬
., "‫ ?! وا‬/
R9‫ز‬2 ‫ى‬Y ‫ ا‬, :‫ ا‬9 %" ‫ ا‬, Minimum , J Y'‫أ‬
."3[[ ‫"ا وي" أو "ا‬
"3"C" R9‫ز‬2 w2 ‫ ا‬9 %" ‫ ا‬, Value , J
‫ال‬2 ‫ أو ا‬3 ‫ ز‬e "W X" , J ‫أو‬
."3[[ " R9‫ز‬2
R9‫ز‬2 ‫ى‬/‫ ا‬, :‫ ا‬9 %" ‫ ا‬, Maximum , J ‫أآ‬
."3[[ " ‫" وي" أو‬
R9‫ز‬2 ‫ ا@ اف ا " ري‬9 %" ‫ ا‬, Std Dev ‫ا@ اف ا " ري‬
."3"C"
" & J ‫م‬I ""I" 9 %" ‫ ا‬, Expression "I
., "‫" ا‬eI" ! ‫ ز‬U"I
,?
[email protected]‫ ت ا‬2" ‫ ا‬W ‫ د ; إذا آ‬9
Report Statistics 3?
6‫ إ‬9:I 37‫أ‬
.T ‫ أو‬I‫ ذا‬R HI ‫ف‬2
Process Module – Resources Dialog , "‫ة ا‬62 ‫ارد‬2 ‫ار ا‬26 ‫ة‬.; :3 ‫ارد‬2 ‫ة ا‬.; M/ Y9 Seize Delay Release ‫ إ ر‬
189
‫و‪ SH9‬إ‪2 ,; V‬ع ا ‪2‬رد ; ‪.; UNI Add… wYf‬ة ‪26‬ار ا ‪2‬ارد‪:‬‬
‫و‪2 I‬ي‪:‬‬
‫ا ‪27‬ب‬
‫ا‪_'2‬‬
‫‪2‬ع ‪Type‬‬
‫‪2 9 I‬رد "! أو إ ر ‪2‬رد ! ‪,2 H‬‬
‫‪190‬‬
.Resource Set ‫ارد‬2
.&‫آ‬I ‫أو‬/‫ب إ آ& و‬27 ‫رد ا‬2 ‫ ا‬%‫إ‬
Resource Name ‫رد‬2 ‫ ا‬%‫إ‬
."‫رد‬2 " ‫ع‬2‫ن ا‬2/9 w:; ‫م‬9‫و‬
‫ إ ك‬% U 3‫ارد وا‬2 ,2 H %‫إ‬
Set Name,2 H ‫ ا‬%‫إ‬
‫ن‬2/9 w:; ‫م‬9 ."‫رد‬2 " ‫ك‬I ‫أو‬/‫و‬
.Set ",2 H " ‫ع‬2‫ا‬
,2 H ! ‫د أو‬
%‫ارد ذات إ‬2 ‫د ا‬
Quantity , ‫آ‬
. U‫آ‬I ‫أو‬/‫ و‬U‫ إ آ‬% 3‫دة وا‬
‫ارد‬2 ‫"! د ا‬I , :‫ ا‬5.‫ ه‬،‫ ت‬2 H ‫و‬
:C U‫آ‬I ‫أو‬/‫ و‬U‫ إ آ‬% 3‫ا رة وا‬
3‫ ا‬,2 H ‫رد وˆ د ا;اد ا‬2 ‫ ا‬,"
.‫ك‬I/g I ‫ف‬2
3; ,6 ‫ارد ا‬2 ‫ ا@ ر ! ا‬,:9C
‫ ا@ ر‬%9‫ و‬Cyclical "‫ "دوري‬.,2 H
.!6 ‫ ء ا‬f0‫ دوري ! ا‬M/O
?‫ا‬2O ‫ ا@ ر‬%9‫ و‬Random "3?‫ا‬2O"
"Mf;0‫ ا‬SII" .‫ ء‬f0‫! ! ا‬
‫ ح‬2f ‫ إ ر اول‬%9‫ و‬Preferred Order
"‫د‬
2f" .‫ا‬./‫ وه‬3 [‫ ا‬%X ‫ول‬0‫ا‬
‫ ج إد ل‬9 ‫ا ا@ ر‬.‫ وه‬Specific Member
J ‫ن‬2/I 3‫ )وا‬Attribute Value ",`' , J"
Save ",`' ‫ن‬G ‫ ل‬H " 3; WG
! 2f ‫ أي‬9 ( Attribute Field
",: ," ‫ "أآ‬.‫ب‬27 ,2 H ‫ا‬
‫ د‬MJ‫ و "ا‬Largest Remaining Capacity
‫م‬I Smallest Number Busy"‫ل‬2YO
w:; ‫م‬I‫ارد ذات " ت "دة و‬2 .",2 H " ‫ع‬2‫ن ا‬2/9
191
Selection Rule ‫ ة ا@ ر‬J
‫‪G‬ن '`‪Save Attribute ,‬‬
‫إ‪ %‬ا `‪ ,‬ا ‪ “` ,‬ر‪ %J‬ا@ د ;‪3‬‬
‫‪ ,2 H‬ا‪ f0‬ء ا‪ 3‬ات‪.‬ه‪ 5.‬ا `‪,‬‬
‫‪ !/ 9‬ان ‪2 I‬ا‪ J ,7‬ة ا@ ر‬
‫"‪2f‬‬
‫د" ‪IT .Specific Member‬م‬
‫ ‪2/I‬ن ‪ J‬ة ا@ ر "‪2f‬‬
‫د"‪ .‬إذا‬
‫! ا‪ O‬ط ا& "‪I eI‬ك" ;ن ا‪, :‬‬
‫ا دة ‪ !"I‬أي ! ا‪ f‬ء ا ‪% ,2 H‬‬
‫‪I‬آ&‪ .‬وإذا ‪ I %‬د '`‪; ,‬ن ا‪2 !? /‬ف‬
‫‪9‬ك ‪ 2f‬ا ‪ ,2 H‬ا‪.‬ي أ ‪ 3; g‬ا‪.h‬‬
‫"ر‪ %J‬ا@ د" ‪,2 H 3; Index Number‬‬
‫ ا ‪Set Index ,2 H‬‬
‫ا‪ f0‬ء ا ‪ .! 27‬و‪I‬م ;‪2/I w:‬ن‬
‫‪ J‬ة ا@ ر ه‪2f" 3‬‬
‫د"‪ .‬إذا ‪6‬د‬
‫ا‪ O‬ط ا& "‪I eI‬ك" ;ن ا‪, :‬‬
‫ا دة ‪"I‬ف أي ‪) 2f‬ر‪ %J‬ا@ د( !‬
‫ا ‪ ,2 H‬ا‪.‬ي ‪I %‬آ&‪.‬‬
‫‪2‬ف ‪:‬م و‪ ! !I6‬و‪6‬ات ا ت ‪ Data Modules‬ه‪:3‬‬
‫و)ة ارد ‪Resource Module‬‬
‫و‪ U‬ا‪ M/O‬ا ‪3‬‬
‫و ا‪ UN9 U wYf‬ا‪ , `' 3; 7‬ا‪O‬‬
‫و‪"9‬ف ا ‪2‬ارد ;‪ 3‬ا‪ N‬م و‪ 2" M OI‬ت ! ‪ ;2I‬ا ‪2‬ارد و‪2‬ع ا"‪ ,‬و ‪:‬ار ا"‪ ,‬و‪,`/I‬‬
‫ا ‪2‬رد إ‪62 & Y‬ة ز ! و‪; ,`/I‬ا^‪ ,‬و‪ ,`/I‬آ‪ M‬إام وإ‪ ,2 H %‬ا ‪ ,‬و;‪MO‬‬
‫ا ‪2‬رد وإ‪ 7‬ء إ‪6‬‬
‫ءات‪.‬‬
‫و)ة ا‪ D‬ر ‪Queue Module‬‬
‫‪192‬‬
3 ‫ ا‬7‫ ا‬UN9‫و‬
3 ‫ ا‬M/O‫ ا‬U‫و‬
‫ر‬2 7‫ر وإذا آ ن ا‬2 7‫ م ا‬N Y‫ م و‬N‫ ا‬3; ‫ا‬27‫_ ا‬9" ‫م‬I ‫ر‬2 7‫ة ا‬6‫وو‬
Service !9‫ر‬2 C -29 ‫ ا‬M/O‫ ا‬3; “6T .‫ءات‬
6‫ إ‬MH9 M‫ك وه‬O
.File.Queue ‫ و‬Station.Queue
SIMAN u/ Process Module /2 ‫و)ة‬
T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Process
1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Process
1.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Process
1.NumberIn,CLEAR(Statistics),CATEGORY("Exclude");
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
‫ذج‬1‫ ا‬9/#
;
Model statements for module:
Process 1
;
0$
ASSIGN:
Process 1.NumberIn=Process
1.NumberIn + 1:
Process 1.WIP=Process
1.WIP+1;
2$
DELAY:
Triangular(.5,1,1.5),,VA;
49$
ASSIGN:
Process 1.NumberOut=Process
1.NumberOut + 1:
193
Process 1.WIP=Process 1.WIP1;
194
%X ," , %U ‫ى‬HI‫ر و‬2 7 2: 9‫ م و‬N ‫ل ز ?! إ‬2'2 g‫ر ا [ ل ا وذ‬27
‫ م‬N‫ ! ا‬2; 9
3 ‫ آ‬Create ‫اص‬2 M9" J
Process ‫اص‬2 ‫ة‬.; "‫ك‬I - eI - ‫ "إ ك‬Action ‫اء‬[email protected]‫ ا‬Standard U2 Customers Service , "‫ ا‬%‫إ‬
: Resources ‫ارد‬2 ‫ ا‬Medium(2) 2 ‫ أو‬,72 Priority ,f;0‫ ا‬Seize Delay Release
195
‫دة‬2" ‫ و‬.1 ‫ ه‬Quantity U ‫ آ‬Server ‫ ه دم‬Resource Name ‫رد‬2 ‫ ا‬%‫رد" إ‬2 " ‫ع‬2‫ا‬
‫ وإ اف‬5 w2
"C ‫زع‬2 Delay Type e‫ع ا‬2 ‫ أ‬, "‫اص ا‬2 ‫ة‬.; .",; f ^ , J" ‹ ‫ ? وا‬J‫ د‬, G‫ات ا‬62‫ ا‬1 ‫" ري‬
O‫ ا‬, ` ‫اص‬2‫ة ا‬.; ! ‫ ت‬2" ‫ ه `ˆ ا‬O ‫ أن‬R7
wYf U M
3‫ا وا‬27‫ة ت ا‬.; ‫ إ‬N
T‫ أو‬M9 ! " Type ‫ر‬2 7‫ع ا‬2 I‫_ ذا‬V‫ ا‬Customer Service Queue ‫ر‬2 7‫ ا‬%‫“ إ‬6T
.,V‫ ا@;ا‬U : W‫آ‬I %:‫ ا‬,: FIFO ‫ أو‬First In First Out "T‫ج أو‬9
wYf U M
196
3‫ارد وا‬2 ‫ة ت ا‬.; ‫ إ‬N
Server ‫رد‬2 ‫ ا‬Name %‫ إ‬M/O‫ ا‬3; aV2 2‫ه‬
‫ آ‬.M/O‫ ا‬aV2 !?G- J ‫آ‬
Busy/Hour , , ,`/I 1 Capacity &"‫ و‬Fixed Capacity ", X ,"" Type &2
%:‫ ا‬,: ‫ و‬0.0 Per Use 6‫ا‬2‫ام ا‬z &`/I 0.0 Idle/Hour , &^‫ ;ا‬,`/I 0.0
.,V‫إ;ا‬
:,‫م ا آ‬2‫_ † ! ا‬f ‫ذج‬2 ‫اء ا‬-‫ إ‬MJ
‫ة ا" ت‬.; 3; Entity ,2:9‫ أ‬wYf ‫ م‬N ‫ و‬9 %‫ ?! وه‬G‫ر ا‬2' UN 3/
UN; ‫وع‬O ‫د ا‬2 ! , 0‫ا‬
. Picture Man M-‫رة ر‬2' ‫ ر‬Initial Picture W I ‫ ط‬:z‫ة ا‬.; ! (‫ ح‬f9z ‫? ه‬G-)
3‫وا‬
Resource ,2:9‫ أ‬wYf g‫ ا دم وذ‬M[ I ,‫م آ‬2‫ ر‬,; V‫! إ‬/ 9
‫آ‬
‫ أ ر‬%?‫ا‬2:‫ة إ ر ا‬.; UN; Toolbars... %X View ‫ ر‬,?‫ ا‬, ? :‫ ده ! ا‬H9‫! إ‬/ 9
,‫م ا آ‬2‫ أدوات ا‬, ? J UN; ‫! رة‬/I % ‫ إن‬Animate
‫ارد‬2 ‫م ا‬2‫ة ر‬.; UNI
197
Resource ,2:9‫ أ‬wYf‫ ا‬
[ S ‫ ا‬%‫م ر ا‬2‫ة ا‬.; ! %X ‫ ا`اغ دم‬RV‫أي و‬
M/O‫ ا‬a ;
‫ ر‬
wYf‫و‬
3; ‫ ا دم‬M[ ‫ا‬.‫ وه‬Idle RV2‫ ا‬State ! ‫ و‬Server ‫رد‬2 ‫ ا‬Identifier ! ‫“ أ أ‬6T
a ; S ‫ ا‬M/O‫م ر ا‬2: Busy ‫ل‬2YO RV2 M[ .‫ ا`اغ‬RV‫و‬
198
. ‫ ه‬%U ! 0 Default 3V‫ ا@;ا‬RV2‫ ا‬3; !9h‫"! ا‬V2‫ك ا‬
+ A ‫ ا‬M/ a 9‫ارد و‬2 ‫م ا‬2‫ة ر‬.; 3`I OK %X Seize Area ‫ و‬Auto Scale ‫ ر‬
M/O‫ ا‬a ; ‫ ء‬OI `‫ آ‬U H6 M/ ‫رة ا دم‬2' UN; S ‫ ن ا‬/ ‫ ا‬3; wYV‫أ‬
:‫اء‬[email protected]‫ ا‬GUHI
199
‫ ‪ ! :‬ا ‪2‬ذج ‪ H; F4 wYf‬أ& ‪ -29T‬أ‪ 7‬ء أو ‪9. I‬ات ‪H %X‬ي ا‬
‫‪F5 wYf‬‬
‫‪200‬‬
‫آة‬
‫ا‪:9:‬‬
‫‪ a` I :!9 I‬ا‪ 9:‬وأج ا ?]‪.‬‬
‫‪2‬ف ‪ " _f‬ا ت ‪2‬ذج وذ‪ ! , ,; V g‬ز ! ا‬
‫آ ة وآ‪%92:I g.‬‬
‫@‪ 7‬ء ا ر‪ d9‬ودات "د ا‪ !? G‬ا ‪ Y‬در‪ !9‬وا‪ :‬د ! ر‪ %‬ا رج ا‪/‬اري "د ا‪!? G‬‬
‫ا‪ !9.‬أآ ‪ 2‬ا ‪ ,‬ور‪" %‬د ا‪ !? G‬اا!‪ , ? J ! .‬ا‪2‬م ا آ‪,‬‬
‫‪201‬‬
‫‪ wYf‬‬
‫‪ wYf‬‬
‫‪.; UNI‬ة ‪26‬ار ا ‪ wYf ,‬‬
‫‪.; UNI‬ة ‪26‬ار ا ‪Y‬‬
‫و ‪ U‬ر ا" ! ;‪.‬ة ا@‪ :‬ط‬
‫@‪2 ,; V‬ص `ة ‪ wYf‬‬
‫! ‪ , ? J‬ا‪2‬م‬
‫;‪.; UN‬ة إد ل ا ‪2‬ص‬
‫‪202‬‬
‫‪.; UNI‬ة ‪26‬ار ا‪%92:‬‬
‫" آ ‪ ,‬ا‹ ا اد ‪ A a ; OK wYf‬ا` رة ‪ +‬و‪ 3; wYf‬ا`اغ ا ‪UN; S‬‬
‫ا‹‪ ,; [email protected] .‬ا رج ا‪/‬اري ‪wYf‬‬
‫‪ M‬ا ت ا ‪ , 27‬وآ‪wYf % g.‬‬
‫‪ M‬ا ت ا ‪, 27‬‬
‫ا‪ M/O‬ا ‪ !9 3‬ا ‪2‬ذج " إد ل ه‪ 5.‬ا ت‪.‬‬
‫‪203‬‬
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"Unnamed
Project","amb",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Service
Station.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Service
Station.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Service
Station.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Customers
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Finish
Service.NumberOut,CLEAR(Statistics),CATEGORY("Exclude");
QUEUES:
Service
Station.Queue,FIFO,Shared,AUTOSTATS(Yes,,);
PICTURES:
Picture.Airplane:
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
204
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
RESOURCES:
Server,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources
),,AUTOSTATS(Yes,,);
REPLICATE,
10,,MinutesToBaseTime(480),Yes,Yes,,,,24,Hours,No,No;
ENTITIES:
Customer,Picture.Man,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Ye
s,,);
T‫ ا‬9/#
;
;
Model statements for module:
Create 1
;
2$
CREATE,
1,MinutesToBaseTime(0.0),Customer:
MinutesToBaseTime(DISC(0.125,1,0.25,2,0.375,3,0.5,4,0.625
,5,0.75,6,0.875,7,1.0,8)):NEXT(3$);
3$
ASSIGN:
Customers
Arrive.NumberOut=Customers Arrive.NumberOut + 1:NEXT(0$);
205
;
;
;
Model statements for module:
Process 1
;
0$
ASSIGN:
Service
Station.NumberIn=Service Station.NumberIn + 1:
Service Station.WIP=Service
Station.WIP+1;
9$
QUEUE,
Service Station.Queue;
8$
SEIZE,
2,VA:
Server,1:NEXT(7$);
7$
DELAY:
MinutesToBaseTime(DISC(
0.1,1,0.3,2,0.6,3,0.85,4,0.95,5,1.0,6 )),,VA;
6$
RELEASE:
Server,1;
54$
ASSIGN:
Service
Station.NumberOut=Service Station.NumberOut + 1:
Service Station.WIP=Service
Station.WIP-1:NEXT(1$);
;
;
;
Model statements for module:
Dispose 1
;
1$
ASSIGN:
Finish
Service.NumberOut=Finish Service.NumberOut + 1;
57$
DISPOSE:
Yes;
:3 ‫ل‬#
‫ م‬N‫ ا‬3; ‫ ? ت‬/‫ار ور ا‬J ‫ ذ‬I‫ ن إ‬/ @‫ ا‬3; ‫ن‬2/9 P
‫ذج ا‬2 ‫ر ا‬27 ‫ف‬2
:3 ‫ ا‬S‫ اآ‬U 3‫ار ا‬:‫ة ا‬6‫ا و‬.U ‫م‬2:9 .‫ ل و ط‬6‫ أو إ‬, ‫ أو‬,; "I
206
‫و)ة ا*ار ‪Decide Module‬‬
‫و‪.U‬ة ا‪62‬ة ‪ M‬وا‪) 6‬‬
‫ا‪) e7‬‬
‫( و ‪ !-‬أ‪6‬ه ‪:‬ار ا ‪) a‬‬
‫( وا‪: h‬ار‬
‫( ‪ “6T‬د ا‪:‬ارات آ‪; M‬ع ‪ 6‬و‪.` 9‬‬
‫ه‪ 5.‬ا‪62‬ة ‪ ! !/ I‬ت أ‪J .‬ار ;‪ 3‬ا‪ N‬م‪ .‬و‪ M OI‬ة رات ‪J .0‬ار إ دا ‬
‫ط أو أآ[ ) [‪ :M‬إذا آ ن ‪2‬ع ا‪ ,J 7 !? /‬ذه‪ (,‬أو إ‪ 6‬ل أو أآ[ ) [‪a' 75% :M‬‬
‫‪ .(e7 25% ،‬و‪ !/ 9‬ان ‪ "I‬ا‪O‬وط ‪ `' %J‬ت ) [‪ :M‬ا‪0‬و‪ (,‬أو ‪:M[ ) Y %J‬‬
‫ا"د ا ;‪2‬ض( أو ‪2‬ع ا‪ !? /‬أو ا"‪.‬‬
‫‪ ! !- -29‬و‪6‬ة ا‪:‬ار ‪2/9‬ن ‪ U2‬ا د‪ ،‬إ ‪ !:9C‬إ‪ 6‬ل او ‪!:9C‬‬
‫ط‪ ،‬و‪ -29‬ج وا‪ ? / 6‬ت ا‪ "True a'" : I 3‬ووا‪ ? / 6‬ت ا‪e7" : I 3‬‬
‫‪ 9 ."False‬د ة ‪C‬ق إ‪ 6‬ل ‪ N-way Chance‬أو وط ;‪2/‬ن ه ك ة رج‬
‫‪ M/‬إ‪ 6‬ل أو ط و ج وا‪ Y 6‬ذ‪ .Else g‬د ا‪ ? /‬ت ا‪I 3‬ج ! آ‪2 M‬ع‬
‫)'‪.w:; !:97 UNI (e7/a‬‬
‫إا ت و‪6‬ة ا‪:‬ار ا " دة‪:‬‬
‫ إر ل ‪ @ , ' ^ ,"7J‬دة ا" ‪. U M‬‬‫ إر ل ا‪ /O‬ت ا ‪ ,UH ,2:‬وا‪ ,UH ,2: Y‬اى‪.‬‬‫ إر ل ز ?! ‪ %U‬أ;‪ ,f‬إ ‪.,' ,‬‬‫ ;‪.‬ة ا‪2‬اص ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫‪207‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫‪.; R‬ة ا ‪2‬ار ‪2‬ع‬
‫و‪2 I‬ي‪:‬‬
‫ا ‪27‬ب‬
‫ا‪_'2‬‬
‫‪208‬‬
‫إ‪Name %‬‬
‫إ‪ %‬و‪ _9" 6‬ا‪62‬ة و‪M/ UNI‬‬
‫ا‪62‬ة‪.‬‬
‫‪2‬ع ‪Type‬‬
‫و‪ ; !I‬إذا آ ن ا‪:‬ار ‪" "9‬ط"‬
‫) [‪ (IF X>Y :M‬أو "إ‪ 6‬ل" أو "‪",‬‬
‫) [‪ (60%, yes; 40%, no:M‬و‪9 I !/ 9‬‬
‫ا‪2‬ع آ‪ !:97‬أو ة ‪C‬ق‪a 9 "!:9C" .‬‬
‫‪ !"I‬ط وا‪ 6‬أو إ‪ 6‬ل ) @‪ ,; V‬ج‬
‫‪" (False‬ة ‪C‬ق" ‪ !" a 9‬ة وط‬
‫أو إ‪T 6‬ت @‪ ,; V‬ج ‪.Else‬‬
‫وط ‪Conditions‬‬
‫‪"I‬ف ط أو اآ[ ‪9‬م ‪ &-2‬ا‪ ? /‬ت‬
‫إ و‪6‬ات `‪ .,‬و‪9‬م ;‪2/9 w:‬ن‬
‫ا‪2‬ع "ة ‪C‬ق ‪O‬ط"‪.‬‬
‫‪Percentages ,92b S‬‬
‫و‪ I‬د ‪ ,‬أو أآ[ ‪I‬م ‪ &-2‬ا‪ ? /‬ت‬
‫إ و‪6‬ات `‪ .,‬و‪I‬م ;‪2/9 w:‬ن‬
‫ا‪2‬ع "ة ‪C‬ق ‪ 6‬ل"‪.‬‬
‫‪Percent True a' ,‬‬
‫و‪ I‬د ‪ , !" , J‬ا‪ ? /‬ت ا‪I 3‬ج‬
‫! ج "'‪.7" "a‬‬
‫إذا ‪IF‬‬
‫ ‪Named‬‬
‫أ‪2‬اع ا‪O‬وط ا ‪.%: ,6‬‬
‫‪ I‬د إ "إ‪ "Y %‬أو "'`‪ ",‬أو "‪2‬ع‬
‫آ ?!" وا‪.‬ي ‪:‬ر ‪ M9‬ا‪ !? /‬ا‪62‬ة‪.‬‬
‫و‪IT‬م ‪2/9‬ن ا‪2‬ع "‪.""I‬‬
‫ه‪IS M‬‬
‫‪:‬ر ‪O‬ط‪ .‬و‪9‬م ;‪2/9 w:‬ن "ط‬
‫'`‪ ",‬أو " ‪."Y‬‬
‫‪Value , J‬‬
‫‪ "I‬وا‪.‬ي ‪ :9 J‬رن‬
‫`‪ ,‬أو ‪ Y‬أو ا‪.‬ي‬
‫‪:‬ر آ" وا‪ 9 6‬إذا آ ن "'‪ "a‬أو‬
‫"‪9T ."e7‬م ‪2‬ع "آ ?! ‪ ."3C‬إذا‬
‫آ ن ا‪2‬ع "‪; ""I‬ن ه‪ 5.‬ا‪ T , :‬ان‬
‫‪ M OI‬ا ‪:‬ر ) [‪.(Color<>Red :M‬‬
‫‪209‬‬
SIMAN u/ Decide Module ‫و)ة ار‬
T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Decide 1.NumberOut
True,CLEAR(Statistics),CATEGORY("Exclude"):
Decide 1.NumberOut
False,CLEAR(Statistics),CATEGORY("Exclude");
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
‫ذج‬1‫ ا‬9/#
;
Model statements for module:
Decide 1
;
0$
BRANCH,
1:
With,50/100,1$,Yes:
Else,2$,Yes;
1$
ASSIGN:
Decide 1.NumberOut
True=Decide 1.NumberOut True + 1;
2$
ASSIGN:
Decide 1.NumberOut
False=Decide 1.NumberOut False + 1;
h‫ وا‬w:; "O‫‹ ا‬: ‫م‬2:9 %‫ه‬6‫! أ‬J6 &; M "9 ,J M
& ‫ل‬2'2‫! ا‬
! ‫ أن ز‬P
3‫ف آ‬2 ‫ا ا [ ل‬.‫ ه‬3;
3?‫ا‬2O M/O M ‫ ?! إ ا‬G‫ ا‬M 9 .& :9‫" و‬O‫ ا‬MY9
‫ي‬.‫ ا ق ا‬.w:; " ‹J ‫و‬99 !? G‫ ! ا‬25% .,:J‫ ا‬3; !? ‫ ز‬4 ‫ "ل‬3‫& ا‬9‫ز‬2I
1 ‫ ? وإ اف " ري‬J‫ د‬3 w2 3"C R9‫ز‬2I & ‫ن‬2/9 ! ‫ ز‬3; g. ‫م‬2:9 "O‫‹ ا‬:9
.,:J‫ د‬2 ‫ ? وإ اف " ري‬J‫ د‬5 w2 3"C ! G g. ‫م‬2:9 ‹:‫ وا‬MY‫ق ا‬6 .,:J‫د‬
.5‫ س أداؤ‬J‫ م و‬N‫ا ا‬.‫آ ة ه‬
‫ب‬27 ‫ا‬
:‫ذج‬2 ‫ا‬
210
‫ ا@ ب‬w7 ‫ر‬2C 3; Create ‫اص‬2 ‫ة‬.; O‫ ا‬, `' ‫ر‬2C 3; Create ‫اص‬2 ‫ة‬.; ‫ ا@ ب‬w7 ‫ر‬2C 3; Decide ‫اص‬2 ‫ة‬.; 211
O‫ ا‬, `' ‫ر‬2C 3; Decide ‫اص‬2 ‫ة‬.; ‫ ا@ ب‬w7 ‫ر‬27 w:; "O‫ ا‬,J Process ‫اص‬2 ‫ة‬.; w:; "O‫رد ق ا‬2 ‫ار ا‬26 ‫ة‬.; O‫ ا‬, `' ‫ر‬27 w:; "O‫ ا‬,J Process ‫اص‬2 ‫ة‬.; 212
‫ ا@ ب‬w7 ‫ر‬2C "O‫ ا‬,J6‫ و‬MY Process ‫ار‬26 ‫ة‬.; ‫ ا@ ب‬w7 ‫ر‬2C "O‫ ا‬,J6‫ و‬MY ‫رد‬2 ‫ار ا‬26 ‫ة‬.; 213
‫ ;‪.‬ة ‪26‬ار‪2‬اص ‪ ,J Process‬ا‪ "O‬و‪ MY‬و‪ ,J6‬ا‪27 "O‬ر '` ‪ ,‬ا‪O‬‬
‫‪ 3; “6T‬ه‪.‬ا ا‪27‬ر ‪ 9 I R7‬ا" ! " ‪.‬‬
‫وأا ‪2‬ا;‪26 .‬ار ‬
‫?‹ ‪Dispose‬‬
‫ ;‪.‬ة و‪6‬ة ا ت ‪ ? /‬ت‬
‫ ;‪.‬ة ‪26‬ار و‪6‬ة ا ت ‪27‬ا ‬
‫‪214‬‬
‫و ;‪.‬ة ‪26‬ار و‪6‬ة ا ت ‪2‬ارد‬
‫‪ " _f‬ا‪ 2‬ت‬
‫‪ “6T‬ه أ‪2J `V‬ل ا;‪G ) Level 3:‬ان ‪ :‬س ا@ ء(‬
‫! ‪ , ? J‬ا‪2‬م ا آ‪,‬‬
‫! ‪:‬ار إ ء و‪2Y‬ل‬
‫ا ‪2‬رد‪.‬‬
‫وأا ‪ MJ‬إ‪-‬اء ا‬
‫آ ة ‪ GUH‬ا ‪2‬ذج‬
‫‪215‬‬
.F5 wYV ‫آ ة‬
‫ي ا‬H %X F4 wYf ‫ذج‬2 ‫ ! ا‬: 216
9:‫ا‬
.‫ ن‬J ‫ ا‬, "; 37"I M/O‫ ا‬3; , ‫ ا‬, ` ‫ وا‬, `' 14 ! ‫ن‬2/9 9:‫ا‬
., 27 ‫داء ا‬0‫ˆ ا‬9 : ‫ واج‬9:‫ ا‬a` I :!9 I
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"Barber Shop","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,Yes;
VARIABLES:
Hair Cut Only?.NumberOut
False,CLEAR(Statistics),CATEGORY("Exclude"):
Hair
Cut.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
217
Customers
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Hair
Cut.NVATime,CLEAR(Statistics),CATEGORY("Exclude"):
Hair
Cut.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Hair Cut and
Shampoo.VATime,CLEAR(Statistics),CATEGORY("Exclude"):
Hair
Cut.WaitTime,CLEAR(Statistics),CATEGORY("Exclude"):
Hair Cut and
Shampoo.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Customer
Finish.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Hair Cut and
Shampoo.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Hair Cut and
Shampoo.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Hair
Cut.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Hair Cut and
Shampoo.WaitTime,CLEAR(Statistics),CATEGORY("Exclude"):
Hair Cut Only?.NumberOut
True,CLEAR(Statistics),CATEGORY("Exclude");
QUEUES:
Hair Cut and
Shampoo.Queue,FIFO,,AUTOSTATS(Yes,,):
Hair Cut.Queue,FIFO,,AUTOSTATS(Yes,,);
PICTURES:
Picture.Airplane:
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
218
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
RESOURCES:
Shampoo,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resource
s),,AUTOSTATS(Yes,,):
Hair Cut
Server,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources
),,AUTOSTATS(Yes,,);
TALLIES:
Hair
Cut.TotalTimePerEntity,,DATABASE(,"Total
Time","Process","Hair Cut"):
Hair Cut and
Shampoo.VATimePerEntity,,DATABASE(,"VA
Time","Process","Hair Cut and Shampoo"):
219
Hair Cut.NVATimePerEntity,,DATABASE(,"NVA
Time","Process","Hair Cut"):
Hair Cut.WaitTimePerEntity,,DATABASE(,"Wait
Time","Process","Hair Cut"):
Hair Cut and
Shampoo.WaitTimePerEntity,,DATABASE(,"Wait
Time","Process","Hair Cut and Shampoo"):
Hair Cut and
Shampoo.TotalTimePerEntity,,DATABASE(,"Total
Time","Process","Hair Cut and Shampoo");
OUTPUTS:
Hair Cut.NVATime,,Hair Cut Accum NVA
Time,DATABASE(,"Accum NVA Time","Process","Hair Cut"):
Hair Cut.NumberIn,,Hair Cut Number
In,DATABASE(,"Number In","Process","Hair Cut"):
Hair Cut and Shampoo.VATime,,Hair Cut and
Shampoo Accum VA Time,DATABASE(,"Accum VA
Time","Process",
"Hair Cut and Shampoo"):
Hair Cut.WaitTime,,Hair Cut Accum Wait
Time,DATABASE(,"Accum Wait Time","Process","Hair Cut"):
Hair Cut and Shampoo.NumberIn,,Hair Cut and
Shampoo Number In,DATABASE(,"Number In","Process",
"Hair Cut and Shampoo"):
Hair Cut and Shampoo.NumberOut,,Hair Cut
and Shampoo Number Out,DATABASE(,"Number Out","Process",
"Hair Cut and Shampoo"):
Hair Cut.NumberOut,,Hair Cut Number
Out,DATABASE(,"Number Out","Process","Hair Cut"):
Hair Cut and Shampoo.WaitTime,,Hair Cut and
Shampoo Accum Wait Time,DATABASE(,"Accum Wait
Time","Process",
"Hair Cut and Shampoo");
220
REPLICATE,
1,,MinutesToBaseTime(200),Yes,Yes,,,,8,Hours,No,No;
ENTITIES:
Customer,Picture.Man,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Ye
s,,);
T‫ ا‬9/#
;
;
;
Model statements for module:
Create 1
;
4$
CREATE,
1,MinutesToBaseTime(0.0),Customer:MinutesToBaseTime(EXPO(
4)):NEXT(5$);
5$
ASSIGN:
Customers
Arrive.NumberOut=Customers Arrive.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Decide 1
;
0$
BRANCH,
1:
With,25/100,8$,Yes:
Else,9$,Yes;
8$
ASSIGN:
Hair Cut Only?.NumberOut
True=Hair Cut Only?.NumberOut True + 1:NEXT(1$);
9$
ASSIGN:
Hair Cut Only?.NumberOut
False=Hair Cut Only?.NumberOut False + 1:NEXT(2$);
221
;
;
;
Model statements for module:
Process 1
;
1$
ASSIGN:
Hair Cut.NumberIn=Hair
Cut.NumberIn + 1:
Hair Cut.WIP=Hair Cut.WIP+1;
39$
STACK,
1:Save:NEXT(13$);
13$
QUEUE,
Hair Cut.Queue;
12$
SEIZE,
2,NVA:
Hair Cut Server,1:NEXT(11$);
11$
DELAY:
MinutesToBaseTime(Normal(3,1)),,NVA:NEXT(54$);
54$
ASSIGN:
Hair Cut.WaitTime=Hair
Cut.WaitTime + Diff.WaitTime;
18$
TALLY:
Hair
Cut.WaitTimePerEntity,Diff.WaitTime,1;
20$
TALLY:
Hair
Cut.TotalTimePerEntity,Diff.StartTime,1;
44$
ASSIGN:
Hair Cut.NVATime=Hair
Cut.NVATime + Diff.NVATime;
45$
TALLY:
Hair
Cut.NVATimePerEntity,Diff.NVATime,1;
10$
RELEASE:
Hair Cut Server,1;
59$
STACK,
1:Destroy:NEXT(58$);
58$
ASSIGN:
Hair Cut.NumberOut=Hair
Cut.NumberOut + 1:
Hair Cut.WIP=Hair Cut.WIP1:NEXT(3$);
222
;
;
;
Model statements for module:
Dispose 1
;
3$
ASSIGN:
Customer
Finish.NumberOut=Customer Finish.NumberOut + 1;
61$
DISPOSE:
Yes;
;
;
;
Model statements for module:
Process 2
;
2$
ASSIGN:
Hair Cut and
Shampoo.NumberIn=Hair Cut and Shampoo.NumberIn + 1:
Hair Cut and
Shampoo.WIP=Hair Cut and Shampoo.WIP+1;
91$
STACK,
1:Save:NEXT(65$);
65$
QUEUE,
Hair Cut and Shampoo.Queue;
64$
SEIZE,
2,VA:
Shampoo,1:NEXT(63$);
63$
DELAY:
MinutesToBaseTime(Normal(5,2)),,VA:NEXT(106$);
106$
ASSIGN:
Hair Cut and
Shampoo.WaitTime=Hair Cut and Shampoo.WaitTime +
Diff.WaitTime;
70$
TALLY:
Hair Cut and
Shampoo.WaitTimePerEntity,Diff.WaitTime,1;
223
72$
TALLY:
Hair Cut and
Shampoo.TotalTimePerEntity,Diff.StartTime,1;
96$
ASSIGN:
Hair Cut and
Shampoo.VATime=Hair Cut and Shampoo.VATime + Diff.VATime;
97$
TALLY:
Hair Cut and
Shampoo.VATimePerEntity,Diff.VATime,1;
62$
RELEASE:
Shampoo,1;
111$
STACK,
1:Destroy:NEXT(110$);
110$
ASSIGN:
Hair Cut and
Shampoo.NumberOut=Hair Cut and Shampoo.NumberOut + 1:
Hair Cut and
Shampoo.WIP=Hair Cut and Shampoo.WIP-1:NEXT(3$);
224
‫‪#‬ل ‪:4‬‬
‫;‪ 3‬ه‪.‬ا ا [ ل ‪2‬ف "ض و‪6‬ة أ ‪ Assign Module‬وا‪ U 3‬اآ‪ S‬ا ‪:3‬‬
‫و)ة أ'‪Assign Module )1‬‬
‫و‪I‬م ه‪ 5.‬ا‪62‬ة @ د ‪9- %J‬ة ‪Y‬ات أو آ ? ت أو '` ت أو أ‪2‬اع آ ? ت أو '‪2‬ر‬
‫آ ? ت أو اي ‪Y‬ات ‪ N‬م‪ .‬و‪ !/ 9‬إ د ة أ ء ‪62‬ة إ د وا‪6‬ة‪.‬‬
‫ا@ا ت ا" د‪:,9‬‬
‫ ‪I‬اآ‪ %‬د أ‪G-‬اء ا‪ R H‬ا ‪.R I ,"7: ,; f‬‬‫ ‪2 YI‬ع آ ?! [‪ , M‬ا" ‪2I ` M‬رة‪.‬‬‫ إ‪ 7‬ء ز ‪2‬ن أ;‪.,f‬‬‫و ;‪.‬ة ا‪2‬اص ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫ ;‪.‬ة ‪26‬ار إ دات ‪Assignments‬‬
‫‪225‬‬
‫ ;‪.‬ة ‪26‬ار إ دات ‪2‬ع‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫ ;‪.‬ة ا ‪2‬ار ‪ z‬دات‬
‫و‪2 I‬ي‪:‬‬
‫ا ‪27‬ب‬
‫ا‪_'2‬‬
‫إ‪Name %‬‬
‫إ‪ %‬و‪ _9" 6‬ا‪62‬ة و‪M/ UNI‬‬
‫ا‪62‬ة‪.‬‬
‫إ د ‪Assignment‬‬
‫و‪ 9‬د إ د أو أآ[ وا‪.‬ي "‪ 7‬‬
‫‪ M9‬آ ?! ا‪62‬ة‪.‬‬
‫‪2‬ع ‪Type‬‬
‫‪2‬ع ا@ د ا‪.‬ي ‪ .%‬ا‪2‬ع "^ذ‪"g‬‬
‫‪ !/ 9 Other‬أن ‪Y M OI‬ات ‪ N‬م [‪," M‬‬
‫ا ‪2‬رد أو ز ! إ‪ U‬ء ا‬
‫إ‪ %‬ا ‪Variable Name Y‬‬
‫آ ة‪.‬‬
‫إ‪ %‬ا ‪ Y‬ا‪.‬ي إ& ‪9- , J‬ة ‬
‫د‪2‬ل ا‪ !? /‬ا‪62‬ة‪ .‬و‪9‬م ;‪ w:‬‬
‫‪2/9‬ن ا‪2‬ع " ‪."Y‬‬
‫‪226‬‬
‫ة‬9- , J U‫ إ‬3‫ ?!" ا‬/‫ ا‬,`'" %‫إ‬
Attribute Name ,`
‫ ا‬%‫إ‬
w:; ‫م‬I‫ و‬.‫ة‬62‫ ?! ا‬/‫ل ا‬2‫ د‬
.",`'" ‫ع‬2‫ن ا‬2/9
,2‫ي إ& د‬.‫ ا‬9H‫ ?! ا‬/‫ع ا‬2
Entity Type !? /‫ع ا‬2
‫ع‬2" ‫ع‬2‫ن ا‬2/9 w:; ‫م‬9‫ و‬.‫ة‬62‫ا‬
Entity Type "!? ‫آ‬
Entity Picture !? ‫رة آ‬2'
&‫ إ‬3‫ة وا‬9H‫رة آ ?!" ا‬2'" ‫ع‬2
‫ن‬2/9 w:; ‫م‬I‫ و‬.‫ة‬62‫& ا‬2‫ د‬
."!? ‫رة آ‬2'" ‫ع‬2‫ا‬
&‫ي إ‬.‫ م ا ص وا‬N‫ ا‬Y !"I‫و‬
Other g‫^ ذ‬
‫م‬9‫ و‬.‫ة‬62‫ ?! ا‬/‫ل ا‬2‫ة د‬9- , J
."g‫ع "^ذ‬2‫ن ا‬2/9 ! g‫ أو ^ذ‬Y ‫ أو ا‬,` ‫ ا@ د‬, J
New Value ‫ة‬9H‫ ا‬, :‫ا‬
‫ع‬2‫ن ا‬2/9 ‫م‬9T .‫ م‬N‫ات ا‬Y
."!? ‫رة آ‬2'" ‫ع آ ?!" أو‬2"
SIMAN u/ Assign Module )1'‫و)ة أ‬
T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
;
0$
ASSIGN;
227
Assign 1
‫ور‪" a I ,‬ات ‪ ! U M "9 .,:X‬أ‪6‬ه‪ %‬ه و‪2:9‬م ت ا‪ 6 O ,"9‬ت‬
‫ا ‪Y‬ة ذات ا‪ 3; ,f;T‬ا ‪ a‬وا‪2 3IeI 3‬ر‪e ,‬ز ‪,‬‬
‫! و'‪2‬ل ‪2‬ز‪ ,‬ا‬
‫ رة آ‪ 15 M‬د‪ ,:J‬و‪Y9‬ق ;‪ 3‬إ'‪ U6‬ز ! ‪2‬زع ‪"C‬‬
‫‪ 5 w2‬د‪ ? J‬وإ اف‬
‫" ري ‪ 1‬د‪ .,:J‬ا‪ 6 O‬ت ا‪/‬ة وا‪ 3IeI 3‬ت ‪2 M I , -‬ر‪e ,‬ز ‪,‬‬
‫و'‪2‬ل ‪2‬ز‪ ,‬ا‬
‫"ل‬
‫!‬
‫"ل رة آ‪ 10 M‬د‪ ? J‬و‪2:9‬م '‪ ^ M U6‬ه ;‪ 3‬ز !‬
‫‪2‬زع ‪ 6 w2 3"C‬د‪ ? J‬وإ اف " ري ‪ 1‬د‪.,:J‬‬
‫‪ 6‬آ‪ 3‬ا‪ N‬م وأو‪ ˆ9 : -‬ا@داء‪.‬‬
‫ا ‪2‬ذج‪:‬‬
‫و‪ %:‬ا‪aV2 M/O‬‬
‫‪228‬‬
w:; O‫ ا‬, `' ‫ر‬2C 3; ‹?
229
‫ ا‬.;‫ا‬2 ! ‫ف‬2
Cteate ‹?
‫ة‬.; Assign ‹?
‫ة‬.; .‫ ت‬6 O‫اع ا‬2‫ع ! أ‬2 M/ ,` ‫ع ا‬2 S6 ,f;‫“ ه أ أ‬6T
Decide ‹?
‫ة‬.; .S ‫ ا‬M "‫( إ ا‬,6 O‫ ?! )ا‬/‫ ا‬MI 3/ ,f;0‫ ا‬,`' ‫ ام‬W J Decide ‫ة‬6‫و‬
230
Process ‹?
231
‫ة‬.; 9:‫ا‬
.]? ‫ إاج ا‬S 7 ‫ك‬9 :!9 I
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"WorkShop","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
ATTRIBUTES:
Priority;
VARIABLES:
Which Worker?.NumberOut
True,CLEAR(Statistics),CATEGORY("Exclude"):
Skilled.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
232
Not
Skilled.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Normal
Repair.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Skilled.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Not
Skilled.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Not
Skilled.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Finished
Repair.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Which Worker?.NumberOut
False,CLEAR(Statistics),CATEGORY("Exclude"):
Fast
Repair.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Skilled.WIP,CLEAR(System),CATEGORY("Exclude-Exclude");
QUEUES:
Skilled.Queue:
Not Skilled.Queue,FIFO,,AUTOSTATS(Yes,,);
PICTURES:
Picture.Airplane:
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
233
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
RESOURCES:
Skilled
Worker,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources
),,AUTOSTATS(Yes,,):
Not Skilled
Worker,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources
),,AUTOSTATS(Yes,,);
REPLICATE,
1,,MinutesToBaseTime(480),Yes,Yes,,,,8,Hours,No,No;
ENTITIES:
Van,Picture.Van,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,,):
Truck,Picture.Truck,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes
,,);
‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
;
234
Create 1
6$
CREATE,
1,MinutesToBaseTime(0.0),Truck:MinutesToBaseTime(EXPO(10)
):NEXT(7$);
7$
ASSIGN:
Normal
Repair.NumberOut=Normal Repair.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Assign 1
;
0$
ASSIGN:
Priority=2:NEXT(2$);
;
;
;
Model statements for module:
Decide 1
;
2$
BRANCH,
1:
If,Priority==1,10$,Yes:
Else,11$,Yes;
10$
ASSIGN:
Which Worker?.NumberOut
True=Which Worker?.NumberOut True + 1:NEXT(3$);
11$
ASSIGN:
Which Worker?.NumberOut
False=Which Worker?.NumberOut False + 1:NEXT(4$);
;
;
;
Model statements for module:
;
235
Process 1
3$
ASSIGN:
Skilled.NumberIn=Skilled.NumberIn + 1:
Skilled.WIP=Skilled.WIP+1;
15$
QUEUE,
Skilled.Queue;
14$
SEIZE,
2,VA:
Skilled Worker,1:NEXT(13$);
13$
DELAY:
MinutesToBaseTime(Normal(5,1)),,VA;
12$
RELEASE:
60$
ASSIGN:
Skilled Worker,1;
Skilled.NumberOut=Skilled.NumberOut + 1:
Skilled.WIP=Skilled.WIP1:NEXT(5$);
;
;
;
Model statements for module:
Dispose 1
;
5$
ASSIGN:
Finished
Repair.NumberOut=Finished Repair.NumberOut + 1;
63$
DISPOSE:
Yes;
;
;
;
Model statements for module:
Process 2
;
4$
ASSIGN:
Not Skilled.NumberIn=Not
Skilled.NumberIn + 1:
Not Skilled.WIP=Not
Skilled.WIP+1;
67$
QUEUE,
Not Skilled.Queue;
236
66$
SEIZE,
2,VA:
Not Skilled
Worker,1:NEXT(65$);
65$
DELAY:
MinutesToBaseTime(Normal(6,1)),,VA;
64$
RELEASE:
Not Skilled Worker,1;
112$
ASSIGN:
Not Skilled.NumberOut=Not
Skilled.NumberOut + 1:
Not Skilled.WIP=Not
Skilled.WIP-1:NEXT(5$);
;
;
;
Model statements for module:
Create 2
;
115$
CREATE,
1,MinutesToBaseTime(0.0),Van:MinutesToBaseTime(EXPO(15)):
NEXT(116$);
116$
ASSIGN:
Fast Repair.NumberOut=Fast
Repair.NumberOut + 1:NEXT(1$);
;
;
;
Model statements for module:
Assign 2
;
1$
ASSIGN:
Priority=1:NEXT(2$);
237
:5 ‫ل‬#
‫م‬2:I‫ و‬Separate Module ‫ و‬Batch Module M ; ‫م و‬G6 !I62‫ا ا [ ل "ض ا‬.‫ ه‬3;
3; Uf" R !" "I ‫ أو ط أو‬,`' : I 3‫ ? ت ا‬/‫ " ا‬R - ‫م أو‬G
‫و‬T‫ا‬
‫ إ‬%U ` M ; ‫ة‬6‫م و‬2:I WJA ‫م ا‬G ‫ ا‬, 6 3;‫ و‬WJA ‫ أو‬%?‫ دا‬M/O 9- !? ‫ آ‬M/
:, ‫ ا‬S‫ ااآ‬%U‫ و‬.,'0‫ ا‬%UI 2/
Batch Module ‫م‬G6 ‫ة‬6‫و‬
3‫ ? ت ا‬/‫ة د ا‬62‫ ا‬M`‫ أ‬3; %J‫ ا‬37"9‫ و‬6‫ و ج وا‬6‫ وا‬M U ‫ة‬62‫ ا‬5.‫وه‬
.‫م‬G I
‫ أ ي أو‬M/O R HI ‫! ان‬/ 9 ‫م‬G ‫ ا‬.‫آ ة‬
‫ذج ا‬2 M‫ دا‬R HI ,—‫ة آ‬62‫ ا‬5.‫م ه‬I‫و‬
.“Separate Module” M ; ‫ة‬62‫ ا‬,7‫ا‬2 M `I ‫`ق أو‬I ‫ ان‬SH9 ,JA ‫م ا‬G ‫ ا‬.WJA
.," ,`' : I ‫ة أو آ ? ت‬62‫ ا‬MI 3‫ ? ت ا‬/‫د ! ا‬
‫ إ د‬%9 %9G ‫ا‬
" ‫ و‬. U ‫ب‬27 ‫ ا"د ا‬R H9 6 ‫ر‬2 C 3; RV2I ‫م‬G6 ‫ة‬6‫ إ و‬M I 3‫ ? ت ا‬/‫ا‬
. U[ 9 9- !? ‫ آ‬29 U" HI
:,9‫ا@ا ت ا" د‬
.‫ ز‬U- R I MJ R7:‫ د ! ا‬R HI . U ; ,Y' ! d R HI ‫ إ دة‬.SC &2‫ د‬MJ &` R 9 R - :‫ ا@ ب‬w7 ‫ر‬2C 3; ‫اص‬2‫ة ا‬.; 238
‫ ;‪.‬ة ا ‪2‬ار ‪2‬ع‬
‫ ;‪.‬ة ا ‪2‬ار " ر ا `“ ‪Save Criterion‬‬
‫ ;‪.‬ة ا ‪2‬ار ‪ :‬ة‬
‫‪239‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫‪.; R‬ة ‪26‬ار ا‪2‬ع‬
‫ ;‪.‬ة ‪26‬ار " ر ا `“‬
‫ ;‪.‬ة ا ‪2‬ار ‪ :‬ة‬
‫و‪2 I‬ي‪:‬‬
‫ا ‪27‬ب‬
‫ا‪_'2‬‬
‫إ‪Name %‬‬
‫إ‪ %‬و‪ _9" 6‬ا‪62‬ة و‪M/ UNI‬‬
‫ا‪62‬ة‪.‬‬
‫‪2‬ع ‪Type‬‬
‫‪G6 ,:9C‬م ا‪ ? /‬ت " ‪.‬‬
‫‪ %H6‬ا ‪Batch Size , G‬‬
‫د ا‪ ? /‬ت ا‪G 3‬م‪.‬‬
‫‪240‬‬
‫ و "ف‬,2 H ‫ ا‬M[ 9 !? ‫ إ د آ‬,:9C
Save Criterion “` ‫" ر ا‬
.‫ م‬
‫ "أي‬.‫ة‬62 , ‫ د‬:‫ ? ت ا‬/‫م ا‬G6 ,`‫ د آ‬I‫و‬
Rule ‫ ة‬J
%H6" ‫ أول‬.eI ‫ف‬2 Any Entity "‫ة‬6‫و‬
. " U G I‫ و‬, ‫ د‬:‫ ? ت ا‬/‫" ! ا‬, G6
%H6" " ‫م‬G I By Attribute ",` "
U 3‫ م وا‬N , ‫ د‬:‫ ? ت ا‬/‫ ا‬M‫" آ‬, G6
.," ,`'
3‫ ? ت ا‬/‫ ا‬M‫ آ‬SH9 3‫ ا‬,` ‫ ا‬%‫إ‬
Attribute Name ,`
‫ ا‬%‫إ‬
‫م‬I‫ و‬. U; ‫ك‬OI ‫م " أن‬G ",` " ‫ ة‬:‫ن ا‬2/I
SIMAN u/ Batch Module ‫و)ة >م‬
T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Batch
1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude");
QUEUES:
Batch 1.Queue,FIFO,,AUTOSTATS(Yes,,);
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
Batch 1
;
0$
QUEUE,
Batch 1.Queue;
1$
GROUP,
,Permanent:2,Last:NEXT(2$);
241
‫‪Batch 1.NumberOut=Batch‬‬
‫‪ASSIGN:‬‬
‫‪2$‬‬
‫;‪1.NumberOut + 1‬‬
‫و)ة ‪Separate Module A‬‬
‫و‪ M U‬و ‪ d !-‬ا‪ ,'0‬و‪ 37"9‬ده ;‪2‬ق ا ج و‪ d‬ا ‪ ,-‬و‪7"9‬‬
‫ده ا`‪ M‬ا‪62‬ة‪.‬‬
‫ه‪ 5.‬ا‪62‬ة ‪ !/ 9‬ان ‪I‬م إ ‪ d‬آ ?! ‪ J‬دم إ ة ‪ ! d‬ا‪ ? /‬ت أو ` ‪ M‬آ ? ت ‪%I‬‬
‫‪ . : U G6‬آ ‪2J 7"I‬ا ‪ _ /I ‹ I‬وأز ‪ d ,‬ا ‪G6 M ; .,HI‬م ;ن‬
‫ا [‪ g M‬ا ‪G‬م ‪ %9‬ا‹ & و‪ R-I‬ا‪ ? /‬ت ا‪ .,'0‬و‪ I‬ك ا‪ ? /‬ت ا ‪M/O ,HI‬‬
‫‪ S6 3" I‬ا‪ SI‬ا‪.‬ي ‪ 3; U" HI & %I‬ا ‪ d ., G‬آ ? ت ;ن ا"د ا ‪27‬ب !‬
‫ا‪ & %9 d‬وإر & ! ا‪62‬ة آ أن ا‪ !? /‬ا‪ Y9 3'0‬در ا‪62‬ة‪.‬‬
‫ا@ا ت ا " دة‪:‬‬
‫ إر ل آ ? ت ` ‪ ' M[ I ,‬د‪ 6 ! ,- 9‬و‪.,9‬‬‫ إر ل أ'‪ M‬إ رة ‪2 U M "9 3/ U R‬ازي‪.‬‬‫ ; ‪ ! ,2 H M‬ا ات ‪. : W" -‬‬‫ ;‪.‬ة ا‪2‬اص ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫‪242‬‬
‫وه‪26 M/ 3; 3‬ار ا‪2‬ع ‪ d‬ا‪.M'0‬‬
‫ ;‪.‬ة ‪26‬ار ا‪2‬ع‬
‫‪243‬‬
, G6 M ; , 6 3; ‫ع‬2‫ار ا‬26 ‫ة‬.; :O‫ ا‬, `' ‫ر‬2C 3; ‫اص‬2‫ة ا‬.; ‫ع‬2‫ار ا‬26 ‫ة‬.; ‫ر‬2Uƒ R
, G6 M ; , 6 3; ‫ع‬2‫ار ا‬26
:‫ي‬2 I‫و‬
_'2‫ا‬
‫ب‬27 ‫ا‬
M/ UNI‫ة و‬62‫_ ا‬9" 6‫ و‬%‫إ‬
Name %‫إ‬
.‫ة‬62‫ا‬
"M'0‫ ا‬d" ., ‫ د‬:‫ ? ت ا‬/‫ ا‬M ; ,:9C
! ‫د‬
‫ د‬d %9‫ و‬Duplicate Original
244
Type ‫ع‬2
"‫دة‬2-2 ‫ ا‬, G ‫ ا‬%J" .3'0‫ ?! ا‬/‫ا‬
3; !? ‫ آ‬M ; %9 ‫ وه‬Split Existing Batch
‫م" إ‬G6" ‫ة‬62‫ ا‬,7‫ا‬2 W" - , G6 M/
.,'0‫ ? ت ا‬/‫ا‬
,-‫ ا ر‬d ‫ دم‬:‫ ?! ا‬/‫ وز ! ا‬,`/I 37"I
Percent Cost to d‫ ا‬,`/I ,
, 0‫ ا‬,`/‫ ! ا‬,‫ د آ‬I , :‫ ا‬5.‫وه‬
Duplicates
,‫ ا‬5.‫( وه‬100-0 ! ) 3'0‫ ?! ا‬/
! :9 ‫ و‬,HI ‫ ا‬d‫زع وي ! ا‬2I
w:; M "I‫ و‬.3'0‫ ?! ا‬/ MNI ,
."M'0‫ ا‬d" ‫ع‬2‫ن ا‬2/9
‫ة‬62‫ در ا‬Y 3‫ وا‬,HI ‫ ? ت ا‬/‫د ا‬
# of Duplicates d‫د ا‬
w:; M "I .3'0‫ ?! ا‬/‫ إ ا‬,; [email protected]
."M'0‫ ا‬d" ‫ع‬2‫ن ا‬2/9 !? /‫ '` ت ا‬%J ‫ إ د‬,`‫"! آ‬I ,:9C
Member Attributes 2f"‫'` ت ا‬
5.‫ ه‬.,'0‫ ? ت ا‬/‫ إ ا‬,2 H M[ ‫ا‬
,' ‫ ! ا ` ت ا‬6 ‫د إ‬2"I ‫ا@ رات‬
Entity.Type, Entity.Picture, )
Entity.Station, Entity.Sequence,
( Entity.HoldCostRate, and Entity.Jobstep
‫م‬I‫ و‬.‫ م‬,;" ‫ ا ` ت ا‬M/‫و‬
."," H ‫ ا‬, G ‫ ا‬%J" ‫ع‬2‫ن ا‬2/9 W ‫ آ‬3‫ وا‬M[ ‫ ?! ا‬/‫ أو '` ت ا‬,`' %‫إ‬
Attribute Name ,`
‫ ا‬%‫إ‬
‫م‬9‫ و‬, G ‫ ا‬3; ,'0‫ ? ت ا‬/ ‫ة‬
“Take 3‫" ه‬2f"‫ن "'` ت ا‬2/9
w:;
Specific Representative Value”
SIMAN u/ Separate Module A ‫و)ة‬
T‫ ا‬9/#
245
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
Separate 1.NumberOut
Dup,CLEAR(Statistics),CATEGORY("Exclude"):
Separate 1.NumberOut
Orig,CLEAR(Statistics),CATEGORY("Exclude");
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
‫ذج‬1‫ ا‬9/#
;
Model statements for module:
Separate 1
;
0$
DUPLICATE,
100 - 50:
1,3$,50:NEXT(2$);
2$
ASSIGN:
Separate 1.NumberOut
Orig=Separate 1.NumberOut Orig + 1;
3$
ASSIGN:
Separate 1.NumberOut
Dup=Separate 1.NumberOut Dup + 1;
246
‫و"‪ 3; %UV‬ا [ ل ا ‪:3‬‬
‫آ‪C ,‬ان '‪? C g I ,‬ات '‪Y‬ة ‪ 10 M I‬رآ ب ;‪2:I .w:‬م ه‪ 5.‬ا‪O‬آ‪6 ,‬ت‬
‫إ ‪-‬ة وا م وا ‪ .,9‬اآ ب ا ‪ Y‬درون إ ‪e 2 9 5-‬ز ‪,‬‬
‫ا‪" 3T‬ل ‪ 7‬رآ ب ;‪ 3‬ا‪ ,:J‬ورآ ب ا م ‪e 2 9‬ز ‪,‬‬
‫"ل ‪ 6‬رآ ب ;‪ 3‬ا‪ ,:J‬و ورآ ب ا ‪e 2 9 ,9‬ز ‪,‬‬
‫! و'‪2‬ل ‪ RI‬ا‪2‬ز‪R9‬‬
‫! و'‪2‬ل ‪ RI‬ا‪2‬ز‪ R9‬ا‪3T‬‬
‫! و'‪2‬ل ‪ RI‬ا‪2‬ز‪ R9‬ا‪3T‬‬
‫"ل ‪ 8‬رآ ب ;‪ 3‬ا‪ .,:J‬ا‪? 7‬ة ‪ M /9 6 R:IT‬د اآ ب‪ .‬ز ! ا‪H ,6‬ة & ‪2I‬ز‪R9‬‬
‫ وي ! ‪ 1.9‬و ‪ , 2.2‬و م & ا‪2I f9‬ز‪ R9‬وي ! ‪ 0.9‬و ‪ , 1.1‬و ‪,9‬‬
‫ا‪2I f9‬ز‪ R9‬وي ! ‪ 1.15‬و ‪ 6 ., 1.25‬آ‪ 3‬ا‪ N‬م وأو‪ ˆ9 : -‬ا‪0‬داء‪.‬‬
‫ا ‪2‬ذج‪:‬‬
‫و‪aV2 & :‬‬
‫‪247‬‬
248
O‫ ا‬, `' ‫ر‬27 ‫ات‬62‫?‹ ا‬
‫ "ض‬3`/
Create ‹?
Batch ‹?
(‫ ?ة‬7‫ ا‬,") 10 2‫ ه‬Batch Size , G ‫ ا‬%H6 .Temporary WJA Type ‫م‬G ‫ع ا‬2 ‫“ أن‬6T
(“` ) ‫ ة‬:‫ وا‬M 9 (S‫ آ ?! )راآ‬Last ( 2‫ ه‬Save Criterion , G ‫`“ ا‬6 ‫و " ر‬
Entity.Type !? /‫ع ا‬2 2‫ ه‬Attribute Name ,`
249
‫ ا‬%‫ وإ‬By Attribute ,` Rule
Decide ‹?
Process ‹?
‫ارد‬2 ‫?‹ ا‬
.;‫ا‬2
Separate ‫اص‬2
‫ ء‬f0‫ ا‬,`'‫ و‬Split Existing Batch ‫دة‬2-2 ‫ ا‬, G ‫ ا‬M ; 2‫ ه‬Type M `‫ع ا‬2 ‫“ ه‬6T
.Retain Original Entity Values ,'0‫ ? ت ا‬/‫ ا‬%J ‫ ء‬: @‫ ا‬2‫ ه‬Member Attribute
.Dispose ‫اص‬2 ‫أا‬
250
9:‫ا‬
.]? ‫ إاج ا‬S 7 ‫ك‬9 :!9 I
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"Private
Air","amb",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
To
Madina.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
To
Jedda.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
251
To
Dammam.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
To Madina
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
To
Jedda.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
To Dammam
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Fly
To.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Dispose
1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
To
Madina.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
To Jedda
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
To
Jedda.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
To
Dammam.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
To
Madina.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Arrival Terminal.NumberOut
Orig,CLEAR(Statistics),CATEGORY("Exclude"):
To
Dammam.WIP,CLEAR(System),CATEGORY("Exclude-Exclude");
QUEUES:
Fly To.Queue,FIFO,,AUTOSTATS(Yes,,):
To Dammam.Queue:
To Jedda.Queue,FIFO,,AUTOSTATS(Yes,,):
To Madina.Queue;
PICTURES:
Picture.Airplane:
Picture.Green Ball:
252
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
RESOURCES:
Flight
Three,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources)
,,AUTOSTATS(Yes,,):
Flight
One,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,
AUTOSTATS(Yes,,):
Flight
Two,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,
AUTOSTATS(Yes,,);
253
REPLICATE,
1,,HoursToBaseTime(10),Yes,Yes,,,,24,Hours,No,No;
ENTITIES:
To Dammam
Passinger,Picture.Man,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Y
es,,):
To Madina
Passinger,Picture.Man,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Y
es,,):
To Jedda
Passinger,Picture.Man,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Y
es,,);
‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
Create 1
;
7$
CREATE,
1,MinutesToBaseTime(0.0),To
Jedda Passinger:MinutesToBaseTime(EXPO(7)):NEXT(8$);
8$
ASSIGN:
To Jedda Arrive.NumberOut=To
Jedda Arrive.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Batch 1
;
0$
QUEUE,
11$
GROUP,
Fly To.Queue;
Entity.Type,Temporary:10,Last:NEXT(12$);
12$
ASSIGN:
Fly To.NumberOut=Fly
To.NumberOut + 1:NEXT(3$);
254
;
;
;
Model statements for module:
Decide 1
;
3$
BRANCH,
1:
If,Entity.Type==To Jedda
Passinger,6$,Yes:
If,Entity.Type==To Dammam
Passinger,4$,Yes:
If,Entity.Type==To Madina
Passinger,5$,Yes:
Else,2$,Yes;
;
;
;
Model statements for module:
Dispose 1
;
2$
ASSIGN:
Dispose 1.NumberOut=Dispose
1.NumberOut + 1;
15$
DISPOSE:
Yes;
;
;
;
Model statements for module:
Process 4
;
6$
ASSIGN:
To Jedda.NumberIn=To
Jedda.NumberIn + 1:
To Jedda.WIP=To Jedda.WIP+1;
19$
QUEUE,
To Jedda.Queue;
18$
SEIZE,
2,NVA:
Flight One,1:NEXT(17$);
255
17$
DELAY:
Uniform(1.9,2.2),,NVA;
16$
RELEASE:
Flight One,1;
64$
ASSIGN:
To Jedda.NumberOut=To
Jedda.NumberOut + 1:
To Jedda.WIP=To Jedda.WIP1:NEXT(1$);
;
;
;
Model statements for module:
Separate 1
;
1$
SPLIT::NEXT(67$);
67$
ASSIGN:
Arrival Terminal.NumberOut
Orig=Arrival Terminal.NumberOut Orig + 1:NEXT(2$);
;
;
;
Model statements for module:
Process 2
;
4$
ASSIGN:
To Dammam.NumberIn=To
Dammam.NumberIn + 1:
To Dammam.WIP=To
Dammam.WIP+1;
73$
QUEUE,
To Dammam.Queue;
72$
SEIZE,
2,NVA:
Flight Two,1:NEXT(71$);
71$
DELAY:
Uniform(0.9,1.1),,NVA;
70$
RELEASE:
Flight Two,1;
256
118$
ASSIGN:
To Dammam.NumberOut=To
Dammam.NumberOut + 1:
To Dammam.WIP=To Dammam.WIP1:NEXT(1$);
;
;
;
Model statements for module:
Process 3
;
5$
ASSIGN:
To Madina.NumberIn=To
Madina.NumberIn + 1:
To Madina.WIP=To
Madina.WIP+1;
124$
QUEUE,
To Madina.Queue;
123$
SEIZE,
2,NVA:
Flight Three,1:NEXT(122$);
122$
DELAY:
Uniform(1.15,1.25),,NVA;
121$
RELEASE:
Flight Three,1;
169$
ASSIGN:
To Madina.NumberOut=To
Madina.NumberOut + 1:
To Madina.WIP=To Madina.WIP1:NEXT(1$);
;
;
;
Model statements for module:
Create 4
;
172$
CREATE,
1,MinutesToBaseTime(0.0),To
Dammam Passinger:MinutesToBaseTime(EXPO(6)):NEXT(173$);
257
173$
ASSIGN:
To Dammam
Arrive.NumberOut=To Dammam Arrive.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Create 5
;
176$
CREATE,
1,MinutesToBaseTime(0.0),To
Madina Passinger:MinutesToBaseTime(EXPO(8)):NEXT(177$);
177$
ASSIGN:
To Madina
Arrive.NumberOut=To Madina Arrive.NumberOut + 1:NEXT(0$);
258
‫@آ ل إ"اض ‪:‬رات ‪2 Arena‬ف ‪:‬م ‪ ,:‬ا‪62‬ات ;‪ ,62 3‬ا‪62‬ات ا‪ , 0‬وه‪:3‬‬
‫و)ة ‪Record Module T 4‬‬
‫‪I‬م ه‪ 5.‬ا‪62‬ة ‪ R H‬إ‪6‬‬
‫? ت ;‪2 3‬ذج ا‬
‫آ ة‪.‬‬
‫ا@ا ت ا " دة‪:‬‬
‫ ‪ R HI‬د ا ‪ U‬م ا‪ 3‬اآ ‪ W‬آ‪., M‬‬‫ آ‪. U:: I eI SC %‬‬‫ ‪ MH‬ا‪ ! G‬ا‪.‬ي ‪ 5 fJ‬ز ‪2‬ن ‪2 C 3; ,f;e‬ر ا` ‹ ا‪0‬و‪.3‬‬‫ ;‪.‬ة ا‪2‬اص ;‪27‬ر ‪ w7‬ا@ ب‪:‬‬
‫و‪ UNI‬ا‪2‬ع ‪Count‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ;‪ , 6 3‬إ‪6‬‬
‫? ت ا‪!? /‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ;‪; , 6 3‬ة ز ‪,‬‬
‫‪259‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ;‪ , 6 3‬ا‪! ! G‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ;‪"I , 6 3‬‬
‫ ;‪.‬ة ا‪2‬اص ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫‪.; R‬ة ‪26‬ار ‪2‬ع ƒ هة‬
‫‪260‬‬
:‫ي‬2 I‫و‬
_'2‫ا‬
‫ب‬27 ‫ا‬
M/ UNI‫ة و‬62‫_ ا‬9" 6‫ و‬%‫إ‬
Name %‫إ‬
.‫ة‬62‫ا‬
‫ب‬27 3‫ هة أو وا‬O ‫ءات‬
[email protected]‫ع ا‬2
Type ‫ع‬2
, J ‹:9 ‫ أو‬9G9 Count "" . U" ‫ءات‬
‫ءات‬
6‫ "إ‬.‫ ا دة‬, : ‫ ة‬,?
6‫إ‬
6‫ إ‬29 Entity Statistics "!? /‫ا‬
Time Interval "! ‫ ";ة ز‬.!? /‫ ! ا‬, ‫دة‬
,`' , J ! ‫ ا`ق‬MH9‫ و‬S 9
Time "! ! ‫ "ز‬.3 ‫آ ة ا‬
‫وز ! ا‬
‫ ? ت‬/‫ ! ! ا‬G‫ ا‬MH9‫ و‬R 9 Between
MHI Expression ""I" .‫ة‬62‫ ا‬MI 3‫ا‬
.7" ‫ ا" ا‬, J
‫? ت‬
[email protected] U J ‫ م‬3‫ ا‬,` ‫ ا‬%@
Attribute Name ,`
‫ ا‬%‫إ‬
."‫ع ";ة‬2‫ إذا آ ن ا‬w:; ‫م‬I‫ و‬.‫ا`ة‬
‫ هة‬O ‫ ا‬,?
6z MH 3‫ ا‬, :‫ا‬
Value , J
‫ ف إ ا"اد‬fI ‫"" أو‬I" ‫ع‬2‫ن ا‬2/9
."" ‫ع‬2‫ن ا‬2/9 ‫ي‬.‫ وا‬MH‫ ا‬G ‫ ر‬%‫"ف إ‬I , ‫ ا‬5.‫ه‬
w:; ‫م‬9‫ هات و‬O ‫ ;& ا‬MH
‫ع ";ة ز !" أو "ز ! !" أو‬2‫ن ا‬2/9
.""I"
261
Tally Name MH‫ ا‬%‫إ‬
‫اد أو‬G ‫ي‬.‫ "اد ا‬G ‫ ا‬%‫"ف إ‬9‫و‬
Counter Name ‫ ا"اد‬%‫إ‬
."‫ع "اد‬2‫ إذا آ ن ا‬w:; ‫م‬9‫ و‬.‹:9
‫ د ; إذا آ ن‬9 3/ ‫آ‬e‫ ر 'وق ا‬9‫و‬
Record into Set ,2 H 3; MH
,2 H ‫ أو‬MH ,2 H T ‫م أم‬
.‫اد‬
‫ي م‬.‫ ا‬MH‫ ا‬,2 H %‫إ‬
‫م‬9‫ و‬.‫ ه‬O ‫ع ا‬2‫? ت ! ا‬
Tally Set Name MH ,2 H %‫إ‬
6z
‫ع ";ة ز !" أو "ز ! !" أو‬2‫ن ا‬2/9
.""I"
‫ع‬2 MH ‫ م‬3‫ ا"اد ا‬,2 H %‫إ‬
‫ن‬2/9 ‫م‬I‫" و‬I 3‫? ت ا‬
Counter Set Name ‫ اد‬,2 H %‫إ‬
[email protected]‫ا‬
."" ‫ع‬2‫ا‬
.‫ د‬,2 H ‫ او‬MH ,2 H 3; A
Set Index ,2 H ‫ ا‬A
:3‫ات ا ت ه‬6‫! ! و‬I6‫ و‬g.‫وآ‬
Schedule Module t 4 ‫و)ة‬
3 ‫ ا‬7‫ ا‬UN9‫و‬
M/O‫ ا‬U‫و‬
WJ2I _9" 2‫ة ا‬6‫ و‬R ‫رد أو‬2 MYOI WJ2I _9" ‫رد‬2 ‫ة‬6‫ و‬R ‫م‬9‫و‬
.‫ل‬2'‫و‬
:&I ‫وإا‬
.‫ت " ل‬7"‫ ا‬M O9‫ و‬R
3; MY WJ2I .‫ت‬Th‫ ا‬M7"I w -
.H !'‫ا‬2‫ ?! ا‬G‫ ا‬%H6 .‫د‬H‫ " ل ا‬%"‫ ' ا‬Set Module 2T‫و)ة ا‬
262
‫و& ا‪M/O‬‬
‫و‪57‬‬
‫و‪"9‬ف _ أ‪2‬اع ا ‪ 2 H‬ت‬
‫;‪ U‬ا ‪2‬ارد وا"ادات وا‪H‬ت وأ‪2‬اع ا‪ ? /‬ت و'‪2‬ر‬
‫ا‪ ? /‬ت‪ .‬آ ان ‪ R H‬ا ‪2‬ارد ‪ !/ 9‬ان ‪I‬م ;‪ 3‬و‪6‬ة ا" ‪ ,‬و وا"ادات وا‪H‬ت ‪!/ 9‬‬
‫ان ‪I‬م ;‪ 3‬و‪6‬ة ا‪.MH‬‬
‫وإا ‪: UI‬‬
‫‪ -‬ا ‪ !? /‬ا‪2:I 3‬م `ˆ ا" ‪3; ,‬‬
‫‪. R‬‬
‫ ا ‪ !;O‬وا ا;! ;‪ 2 3‬رآ‪.W‬‬‫ ا ‪.S/ 3; !`ƒ2‬‬‫ ‪2' ,2 H‬ر ?ة ‪ ! ,2 H‬أ‪2‬اع ا‪ ? /‬ت‪.‬‬‫و)ة ‪Variable Module u#‬‬
‫و‪ U‬ا‪M/O‬‬
‫و‪7‬ه‬
‫و‪"9‬ف أ " د ا ‪ Variable Dimension Y‬و‪ & J‬ا‪0‬و‪ .,‬و‪ !/ 9‬أن ‪_ 3; R-I‬‬
‫ا‪62‬ات ) [‪ M‬و‪6‬ة ا‪:‬ار( أو ‪ "9‬د إ د ‪ M[ ) U %J‬و‪6‬ة ا( و‪ !/ 9‬ان ‪I‬م ;‪ 3‬أي‬
‫‪."I‬‬
‫إا ‪: UI‬‬
‫ د ا ات ا ‪ , /‬آ‪., M‬‬‫ أر‪ J‬م ‪ ! R7: 7"I ,I‬أ‪ M-‬ا"‪._9‬‬‫ ا`اغ ا ح ;‪.,UI 3‬‬‫و)ة ‪SIMAN u/ T 4‬‬
‫‪ 9/#‬ا‪ T‬‬
‫‪263‬‬
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
COUNTERS:
Record 1,,,,DATABASE(,"Count","User
Specified","Record 1");
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
Record 1
;
0$
COUNT:
Record 1,1;
264
Case
,‫ت درا‬T 6 3; U ‫رة و‬27 ‫ات ا" ت ا‬6‫ف "ض و‬2
.Studies
‫رة‬D‫ ت ا‬/.‫ا‬
Flowchart Modules ‫ب‬
^‫ ا‬8D$# ‫و)ات‬
Delay Module 0v4 ‫ و)ة‬-1
U ‫ إا‬,[ ‫ وأ‬.! G‫د ! ا‬
‫ار‬: !? /‫ ا‬e ‫م‬2:I e‫ة ا‬6‫و‬
.g 3; g ! : ‫ ا‬-1
.M " ,( GUHI -2
.( %J ‫ إ‬M: -3
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‹?
‫ة ا‬.; Allocation !"‫ار ا‬26 ‫ة‬.; (‫أ‬
Delay Time e‫ ا‬WJ‫ار و‬26 ‫ة‬.; (‫ب‬
265
Units ! G‫ات ا‬6‫ار و‬26 ‫ة‬.; (‫ج‬
:O‫ ا‬, `' ‫ر‬2C 3; ‹?
‫ة ا‬.; Allocation !"‫ار ا‬26 ‫ة‬.; (‫أ‬
Delay Time e‫ ا‬WJ‫ار و‬26 ‫ة‬.; (‫ب‬
266
Units ! G‫ات ا‬6‫ار و‬26 ‫ة‬.; (‫ج‬
SIMAN u/ ‫ا)ة‬
DELAY:
0.0,,Other;
Dropoff Module (‫و)ة إ'*ط )إ)اع‬
‫ة اى‬6‫ إ و‬%UI‫ ? ت و‬/‫ ! ا‬,2 H ! ‫ ? ت‬/‫ د ! ا‬,‫م زا‬2:I ‫ ط‬:@‫ة ا‬6‫و‬
UI ‫ إا‬,[ ‫ وأ‬.Graphical Connection ,77 ,'2 ‫ د‬I
.R? f _;‫ أر‬M I -1
.‫ م‬J‫ ة أ‬,7‫ا‬2 ‫ام‬z ‫ر‬2' ‫ ! ة‬M ; -2
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‹?
267
‫ة ا‬.; 2f"‫ار '` ت ا‬26 ‫ة‬.; :O‫ ا‬, `' ‫ر‬2C 3; ‹?
‫ة ا‬.; 2f"‫ار '` ت ا‬26 ‫ة‬.; f9‫ أ‬UN‫و‬
SIMAN u/ ‫ا)ة‬
DROPOFF,
1,1:,
268
‫;*‬
‫و)ة إ‪ #‬ك )‪Hold Module (!1#‬‬
‫ه‪ 5.‬ا‪62‬ة ‪2:I‬م ك آ ?! ;‪2 C 3‬ر ‪ N‬إ رة ) ! و‪6‬ة ا@ رة ;‪ 3‬ا ‪2‬ذج( أو‬
‫ ‪ :‬ط "! أو ‪^ 0 g 9‬‬
‫د ) ‪G9 3/‬ال " ذ‪62 g‬ة إزا‪ .(,‬وأ [‪ ,‬‬
‫إا ‪ &I‬ه‪3‬‬
‫‪ -1‬إ‪ N‬ر إ رة ور ‪2‬ل إ ا‪2‬ن ا‪.f0‬‬
‫‪.& ` e9 6 g -2‬‬
‫‪ ,( , 6 ‹ ; -3‬أو ‪ M /I 6 M‬ا‪.MYO‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ‪Type‬‬
‫‪269‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ا‪2 7‬ر ‪Queue Type‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫و‪ UN‬أ‪.; f9‬ة ‪26‬ار ‪2‬ع‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ا‪2 7‬ر‬
‫‪270‬‬
SIMAN u/ ‫ا)ة‬
QUEUE,
Hold 1.Queue;
WAIT:
1;
Match Module [ D4 ‫و)ة‬
3; `I 3‫ وا‬,` ‫ا‬2C 3; ‫ة‬N ‫ ? ت ا‬/‫د ! ا‬
‫ " د‬R R HI 7‫ة ا‬6‫و‬
3‫ ا‬,7:‫ ا‬S6 g‫ا وذ‬2C 5 ! 6‫ وا‬3; RV29 7I ‫ة‬6‫ل آ ?! و‬2‫ د‬.," ,`'
3‫ ? ت ا‬/‫ در ا‬YI %X ! ‫ و‬7I M
9 6 ‫ر‬2 7‫ ا‬3; :I‫ة و‬62‫ ?! إ ا‬/‫ ا‬U M‫د‬
U ‫ إا‬,[ ‫ وأ‬.‫ة‬62‫ ا‬U: 7I %I
.‫ إ ج‬w 3; ,"7J R HI -1
.‫ن‬2 ‫ ز‬SC S6 ‫ ت‬H ‫ ة‬R HI -2
.," ,H ` ‫ رات‬,7
3; ‫ د ! اآ ب‬R HI -3
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‹?
271
‫ة ا‬.; ‫ ;‪.‬ة ‪26‬ار د ا‪Number of Match 7‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ‪Type‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫و‪.; UNI‬ة ‪26‬ار د ا‪ 7‬‬
‫ ;‪.‬ة ‪26‬ار ا‪2‬ع‬
‫‪272‬‬
SIMAN u/ ‫ا)ة‬
0$
QUEUE,
Match
1.Queue1:DETACH;
3$
QUEUE,
Match
1.Queue2:DETACH;
MATCH:
0$:
3$;
Pickup Module ‫و)ة إ*ط‬
3; ," ,I‫ ا ر‬7" ‫ر‬2 C ! ," ‫ ? ت ا‬/‫ ط د ! ا‬: ‫ة‬62‫ ا‬5.‫م ه‬2:I‫و‬
,[ ‫ وأ‬.‫ ? ت‬/‫ ! ا‬, ‫ د‬J ,2 H ,9 U ‫ ف إ‬fI ,7: ‫ات ا‬62‫ ا‬.‫ر‬2 7‫ا‬
UI ‫إا‬
.,` RJ‫ا‬2 3; ‫ا‬2C ! SC R HI -1
.‫ م‬J0‫ ! _ ا‬,U ”' R HI -2
.,' ,‫ ر‬,;
273
. ‫ ا‬R HI -3
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‹?
‫ة ا‬.; :O‫ ا‬, `' ‫ر‬2C 3; ‹?
‫ة ا‬.; ‫ا)ة ‪SIMAN u/‬‬
‫‪PICKUP:‬‬
‫;‪Queue 1,1,1‬‬
‫و)ة اءة وآ ‪ReadWrite Module‬‬
‫و‪I‬م ه‪ 5.‬ا‪62‬ة ‪:‬ا?‪ ,‬ت ! _ إد ل أو ! ‪ ,62‬ا ` ‪ aI‬وإ د ا‪Y %:‬ات أو‬
‫'` ت )أو أي ‪ (( "I‬وآ‪9 g.‬م ‪ , /‬ت إ _ إاج أو إ ا‪ ., O‬وأ [‪,‬‬
‫ إا ‪U‬‬
‫‪J -1‬اءة "‪ 2‬ت و'‪2‬ل و ‪ Y‬درة ر‪6‬ت ا‪7‬ان‪.‬‬
‫‪ -2‬ا‪ ! S7‬ا م @د ل ت ! ا ‪2‬ذج أ‪ X‬ء ‪ MYOI‬ا‬
‫‪ -3‬آ ‪ 2" ,‬ت ! ‪._ 3; SC‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫‪274‬‬
‫آ ة‪.‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع‬
‫ ;‪.‬ة إ‪Add.. ,; V‬‬
‫‪2‬ع‬
‫‪275‬‬
‫و@‪ %‬ا `‪,‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫‪ R‬إƒ‪ U‬ر ;‪.‬ة ‪26‬ار ا‪2‬ع‬
‫ ;‪.‬ة ‪26‬ار‪J‬اءة ! ‪ ,62‬ا ` ‪aI‬‬
‫ ;‪.‬ة ‪26‬ار ‪J‬اءة ! _‬
‫ا)ة ‪SIMAN u/‬‬
‫;‪READ:‬‬
‫‪276‬‬
‫و)ة إ‪rC‬ق )‪Release Module ({A‬‬
‫و‪I‬م ه‪ 5.‬ا‪62‬ة @‪C‬ق و‪6‬ات ! ا ‪2‬ارد وا‪ 3‬آ ‪W‬‬
‫‪ .!? / ,/‬و‪9 J‬م @‪C‬ق‬
‫‪2‬ارد `دة أو ! ‪2 M/ .,2 H‬رد ‪9‬اد إ‪ I ,JC‬د إ & ود ا‪62‬ات ا ‪27‬ب‬
‫إ‪ . UJC‬د‪2‬ل آ ?! ه‪ 5.‬ا‪62‬ة ;‪9 ,‬ك ا ‪2‬رد ا‪.‬ي أ ‪ & g‬وأي آ ?! ‪3; N9‬‬
‫‪2 C‬ر ه‪.‬ا ا ‪2‬رد ‪ R79‬إ آ& ;‪2‬را‪ .‬وأ [‪ ,‬إا &‬
‫‪ -1‬إ‪ U‬ء ! ‪ SC‬ز ‪2‬ن ) ‪ 79‬ا دم(‪.‬‬
‫‪ Y -2‬درة ا ‪ 79) `O‬ا‪ C0‬ء وا ‪ !V‬و^;‪ ,‬ا"ج(‪.‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫ ;‪.‬ة ‪26‬ار إ‪Add... ,; V‬‬
‫‪277‬‬
‫ع‬2 ‫ار‬26 ‫ة‬.; ,`' ‫ع‬2 , 6 3;
:O‫ ا‬, `' ‫ر‬2C 3; ‹?
‫ة ا‬.; ,`' ‫ع‬2 ‫ار‬26 ‫ة‬.; R
SIMAN u/ ‫ا)ة‬
RELEASE;
278
‫و)ة إزا ‪Remove Module‬‬
‫و‪2:9‬م زا‪ ,‬آ ?! وا‪RJ2 ! 6‬‬
‫د ;‪2 C 3‬ر وإر & إ و‪6‬ة "‪ .,‬وأ [‪ ,‬‬
‫إا &‬
‫‪ -1‬إزا‪ %J U ‹9T , SC ,‬إ ‪.( %J‬‬
‫‪ -2‬إ ء ‪H6 3; 9‬ة ا@‪ N‬ر " دة "‪.,‬‬
‫‪ -3‬أ‪ .‬راآ‪ ! S‬رآ ب ا@‪ N‬ر ‪ R -‬ا‪6‬ت `‪.‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫ا)ة ‪SIMAN u/‬‬
‫‪REMOVE:‬‬
‫;‪1,Queue 1‬‬
‫‪279‬‬
‫و)ة إ‪ #‬ك )أ‪Seize Module (30‬‬
‫و‪2:9‬م ‪ 7‬ء ا‪ !? /‬و‪6‬ات ! ‪2‬رد أو أآ[ ‪ ,` "I‬أو ‪ ."I‬د‪2‬ل آ ?! ه‪ 5.‬ا‪62‬ة‬
‫;& ‪2 C 3; N9‬ر ‪ R - ;2I 6‬ا ‪2‬ارد ا‪ U79 3‬ة وا‪6‬ة ) " ( آ ان ‪2‬ع‬
‫‪ ‹ I‬إام ا ‪2‬رد ‪ 9‬د ه ‪ .‬و ! أ [‪ ,‬إ ‪&I‬‬
‫‪ -1‬ا‪ SC ,9‬ز ‪2‬ن )إ ‪ g‬ا دم(‪.‬‬
‫‪ -2‬د‪2‬ل ‪) `O‬إ ك ^;‪ ,‬و‪ SC‬ا‪.(d‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫‪280‬‬
!"‫ار ا‬26 ‫ة‬.; Priority ,f;0‫ار ا‬26 ‫ة‬.; 281
‫ ;‪.‬ة ‪26‬ار إ‪,; V‬‬
‫ ;‪.‬ة ‪26‬ار إ‪2 ,; V‬ع‬
‫‪282‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع ا‪2 7‬ر‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫‪ R‬إƒ‪ U‬ر ;‪.‬ة ‬
‫?‹ ا"!‬
‫ ;‪.‬ة ‪26‬ار ا ‪2‬ارد‬
‫‪283‬‬
‫ر‬2 7‫ع ا‬2 ‫ار‬26 ‫ة‬.; SIMAN u/ ‫ا)ة‬
QUEUE,
Seize 1.Queue;
SEIZE,
2,Other;
DELAY:
0.0,,VA;
Search Module
‫و)ة‬
: 9 ( J ) ‫ م‬Y , J ‫ ?! أو‬/‫ ا‬,I‫ ر‬H "I ‫ أو‬,2 H ‫ر أو‬2 C 3; P ‫م‬2:9‫و‬
:3; [ ‫م‬9‫ و‬.‫د‬
P
‫ط‬
.‫ر‬2 C 3; ," ,I‫ ر‬%J‫ ! ر‬P ‫ ا‬-1
.R7:‫ع "! ! ا‬2 ! ,2 H 3; P ‫ ا‬-2
.("I 3; P ) ‫رد‬2 ‫; ا‬2I ‫ ?! إ دا‬/‫ ا‬U9 ‫ أي ! ا" ت‬9 I -3
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‹?
284
‫ة ا‬.; ‫ع‬2‫ار ا‬26 ‫ة‬.; :O‫ر '` ت ا‬2C 3; ‹?
‫ة ا‬.; ‫ع‬2‫ار ا‬26 ‫ة‬.; R
SIMAN u/ ‫ا)ة‬
0$
SEARCH,
Queue 1;
285
1$
BRANCH,
1:
If,J<>0,2$,Yes:
Else,3$,Yes;
2$
DELAY:
0.0,,VA;
3$
DELAY:
0.0,,VA;
Signal Module ‫رة‬7^‫و)ة ا‬
S‫ا‬2:‫ ا‬3; N‫ )أ‬Wait
Module ‫ ر‬N‫ة إ‬6‫ و‬M/ ‫ إ رة‬,
J ‫م ر ل‬2:9‫و‬
&I ‫ و ! إا‬.‫ ? ت ا د‬/‫ اآ د ! ا‬79‫ذج و‬2 ‫ ا‬3; (Blocks
.(fq ‫ء‬2f‫ل ا‬2 9 A9 ) ‫ق‬C RC :I ‫ أ ط ا‬M I -1
.‫ ^ ر‬,"7J N9 ‫ آ ن‬SC M /9 3/ M " e‫ ا‬-2
:‫ ا@ ب‬w7 ‫ر‬2C 3; ‹?
‫ة ا‬.; :O , `' ‫ر‬2C 3; ‹?
‫ة ا‬.; SIMAN u/ ‫ا)ة‬
SIGNAL:
1;
286
‫و)ة ‪Store Module >$4‬‬
‫و‪ _f9‬آ ?! إ ‪G‬ن‪ .‬آ ا& ‪9‬م "ض '‪2‬ر آ‪ ? / ,‬ت ل ا" ‪3; U M‬‬
‫و‪6‬ات اى @‪ ,; V‬إ ‪ R -‬إ‪6‬‬
‫? ت ! ا‪ ? /‬ت‪ .‬وأ [‪ ,‬إا &‬
‫‪ -1‬ض '‪2‬ر آ‪" I ,"7J ! ,‬ة ت‪.‬‬
‫‪ RI -2‬د ا‪ !? G‬دا‪., : M‬‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر ‪ w7‬ا@ ب‪:‬‬
‫‪287‬‬
‫ ;‪.‬ة ‪26‬ار ‪2‬ع‬
‫ ;‪.‬ة ا‬
‫?‹ ;‪2C 3‬ر '` ‪ ,‬ا‪:O‬‬
‫ا)ة ‪SIMAN u/‬‬
‫‪STORE:‬‬
‫;‪Storage 1‬‬
‫و)ة إ‪0‬ج ‪>$#‬ون ‪Unstore Module‬‬
‫‪2:9‬م اج آ ?! ! ‪G‬ن أن د& ! ل ا‪62‬ة ‪G‬ن‪ .‬و& ‪ ˆ/‬إا ت‬
‫ا‪62‬ة ‪G‬ن‪.‬‬
‫ ;‪.‬ة ا‬
‫?‹ ‪27‬ر ‪ w7‬ا@ ب‪:‬‬
‫ ;‪.‬ة ‪26‬ار ا‪2‬ع‬
‫‪288‬‬
:O‫ ا‬, `' ‫ر‬2C 3; ‹?
‫ة ا‬.; SIMAN u/ ‫ا)ة‬
UNSTORE;
289
:‫رة‬D‫ ت ا‬6‫و)ات ا‬
Advanced Set Module ‫رة‬D‫ت ا‬2T‫و)ة ا‬
‫ ت‬2 H ‫ وأي‬Storage Sets ‫ ت ا زن‬2 H ‫ و‬Queue Sets ‫ا‬27‫ ت ا‬2 H ‫ د‬9‫و‬
! Group ,2 H ‫"ف‬I Set ,2 H ‫ وا‬.‫ ت‬2 H ‫ة ا‬.‫ ء ه‬f‫"ف أ‬I U‫اى آ أ‬
‫ ت‬2 H .Set Index ,2 H A ‫ك و‬O % I 3‫ وا‬,U O ‫ا" ' ا‬
‫اد‬2 ‫ ا‬R M "9 ‫ي‬.‫ع ا‬2‫ة ! ا‬6‫ أو أي و‬Seize g ‫ة أ‬62‫ ا‬M‫"ف دا‬I ‫! أن‬/ 9 ‫ا‬27‫ا‬
!9GI ‫ات‬6‫ و‬3; ‫"ف‬I ‫! أن‬/ 9 ‫ ت ا زن‬2 H .Material Handling Type Module
.Unstore ‫ون‬G ‫ وإاج‬Store
Expression Module 6.4 ‫و)ة‬
‫ذج‬2 ‫ ا‬3; "‫ ا‬I‫ و‬. U ," ‫ ا‬%:‫ وا‬Expressions "I ‫"ف‬I ‫ة‬62‫ ا‬5.‫وه‬
M/OI !/ 9‫ و‬.!9" ‫ ذات " أو‬Arrays ‫ف‬2` ‫_ ا" آ‬9"I !/ 9 . U? ‫ام أ‬
‫" ت‬9‫ز‬2I‫ز و‬2 ‫ وأ ء ر‬,:: ‫اد ا‬0‫ وا‬, ‫اد ا‬0‫ ! ا‬S‫اآ‬I ‫ا" ام‬
< M[ ) ,:7 ‫اس و ت‬2J‫ و*( وأ‬+ M[ ) , 6 ‫( و ت‬NORM(10,2) M[ ) ,?
6‫إ‬
3; " a 9T !/‫" ( و‬I 3; "I ‫! إام‬/ 9 .‫ات‬Y ‫( و'` ت و‬.GT. ‫و‬
.&` ‫إام‬
290
Failure Module JA ‫و)ة‬
R ‫ام‬z ,
3‫ وه‬.MO`9 &‫رد آ‬2 ‫ ;ن ا‬MO; ‫وث‬6 .‫ارد‬2 ‫ ا‬R ‫م‬9‫و‬
.WJ2‫ `ˆ ا‬3; " UI 2/ M‫ آ‬MO`I 3‫ وا‬,"‫ أو "دة ا‬,"‫ ا‬,9‫ د‬6‫ارد أ‬2 ‫ا‬
File Module 9/# ‫و)ة‬
5.‫ وه‬.ReadWrite ‫ة‬62‫ ا‬,7‫ا‬2 3-‫اد إام _ ر‬9 ‫دا‬2-2 ‫ن‬2/9 ‫ أن‬SH9‫و‬
.‫ى‬T‫اص ا _ ا‬2‫ و‬M/O‫ل وا‬2'2‫ ا‬,:9C‫ و‬3-‫ ا _ ا ر‬%‫ د إ‬I ‫ة‬62‫ا‬
StateSet Module 2T# ‫و)ة‬
,I‫ ذا‬,
,7I ‫ن‬2/I ‫! أن‬/ 9 ‫ت‬T ‫ وا‬.‫ارد‬2 ‫رد أو د ! ا‬2 ‫ت‬T 6 9 ‫م‬9‫و‬
,2 H 3I , 0‫ ا" ت ا‬3; Resource ‫ة‬6‫ و‬.‫رد‬2 ‫ة‬9- ‫ت‬T
‫ أو‬Autostate
.!" ‫رد‬2 ‫م‬I ‫ف‬2 3‫ وا‬, ‫ا‬
Statistic Module ‫و)ة إء‬
.‫آ ة‬
‫ ء ا‬X‫ ا‬R HI 3/ ,; V‫? ت إ‬
6‫ إ‬9 ‫م‬9‫و‬
Storage Module >$4 ‫و)ة‬
. UI ‫ة‬6‫ي و‬e I‫ ذا‬2I ‫! ان‬/ 9 ‫ وا زن‬.‫ن‬G %‫"ف إ‬9‫و‬
:Advanced Modules #)*‫ا)ات ا‬
3‫ ه‬3‫ وا‬SIMAN ,Y S‫اآ‬I ,:: ‫ ا‬3; ‫ات‬62‫ة ا‬.‫ات اي )ه‬6‫ و‬Arena ] -29
Advanced Transfer Modules , : ‫ ل ا‬:@‫ات ا‬6‫ و‬M[
291
(Arena 3; 3`‫ا ك ا‬
(SIMAN ,Y ‫ ت‬2/ ! ) Blocks S‫ا‬2:‫ات ا‬6‫وو‬
(SIMAN ,Y ‫ ت‬2/ ! ) Elements ' "‫ات ا‬6‫وو‬
292
‫وو‪6‬ات ا ‪G‬م ‪Packaging‬‬
‫و^ه ! ا‪62‬ات ا ‪- , :‬ا‪2 .‬ف ‪O‬ح أي و‪6‬ة ‪ ! U-‬ه‪ 5.‬ا‪62‬ات ا‪G‬وم‪.‬‬
‫‪293‬‬
:Case Studies '‫ت درا‬f
:)‫ اا‬9‫ ر ا‬C
U M `9 3?‫ا‬2O M/O R;‫ ا‬,7: ‫ ?! إ‬G‫ ا‬M 9 .6‫ وا‬S
ˆ` U ‫ل‬2'‫! و‬
& Y' , : M
, ‫ز‬0‫ ا‬5.‫ ? وه‬J‫ د‬8 ‫ و‬1 ! Interarrival times ‫ل‬2'‫! و‬
, ‫أز‬
:3 ‫ول ا‬H‫ ا‬3; ‫ ل آ‬[email protected]‫ا‬
:‫ل‬2'2‫! ا‬
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Time between
Arrivals
(Minutes)
Cumulative
Probability
Probability
1
0.125
0.125
2
0.125
0.250
3
0.125
0.375
4
0.125
0.500
5
0.125
0.625
6
0.125
0.750
7
0.125
0.875
8
0.125
1.000
:3 ‫ول ا‬H‫ ا‬3; ‫ت آ‬T 6 ? J‫ د‬6 ‫ و‬1 !
294
‫اوح‬I Sevice times , ‫ ا‬, ‫أز‬
‫ول ‪2I‬ز‪ R9‬أز ‪ ,‬ا ‪:,‬‬‫‪Cumulative‬‬
‫‪Probability‬‬
‫ا ‪27‬ب ‪ M I‬ا‪ N‬م‬
‫‪Service Time‬‬
‫‪Probability‬‬
‫)‪(Minutes‬‬
‫‪0.10‬‬
‫‪0.10‬‬
‫‪1‬‬
‫‪0.30‬‬
‫‪0.20‬‬
‫‪2‬‬
‫‪0.60‬‬
‫‪0.30‬‬
‫‪3‬‬
‫‪0.85‬‬
‫‪0.25‬‬
‫‪4‬‬
‫‪0.95‬‬
‫‪0.10‬‬
‫‪5‬‬
‫‪1.00‬‬
‫‪0.05‬‬
‫‪6‬‬
‫آ ة و'‪2‬ل و ‪ 500 ,‬ز ‪. 2‬‬
‫ ء ا ‪2‬ذج‪:‬‬
‫ا ‪2‬ذج ‪- w‬ا‪ ،‬ز ‪2‬ن ‪ &H9‬اف و‪2 7 9‬ر‪:‬‬
‫‪ -1‬ا‪2 7‬ر ‪:3‬‬
‫أ‪ -‬ا اف ‪9 :3‬أ ا ‪ ,‬ة و‪ 9‬ف " ‪.& ,9 U‬‬
‫ب‪ -‬ا اف ‪2YO‬ل‪ 2 6 N9 :‬ا دم ‪ %9 %X‬ا دم و‪9‬أ ا ‪ ,‬و‪ 9‬ف " ‪,9 U‬‬
‫ &‪.‬‬
‫‪ -2‬ا‪2 7‬ر ^ ‪:3‬‬
‫أ‪ ,9 U 9 -‬ا‪2 7‬ر و‪ a 9 6 N9‬ا‪0‬ول ;‪ 3‬ا‪2 7‬ر و‪ 9‬ا ‪ ,‬و‪ 9‬ف "‬
‫‪.& ,9 U‬‬
‫ب‪ !/ 9T -‬أن ‪ Y9‬در ا‪ N‬م إ‪ ! T‬ل ‪.& ,9 U ,7:‬‬
‫ ج إ ‪ 2I‬ز ?! وذ‪ g‬ام ‪ Create‬أ‪ wYV‬وأ ‪ S‬أ‪Create ,2:9‬‬
‫‪295‬‬
‫ا دم ‪ M[ 9‬ام ‪Process‬‬
‫‪ “6T‬ا‪ w‬ا‪2‬ا'‪ U M‬وا‪.‬ي ‪ 9‬ث ‪eI) ? :I‬آ ! أن ا‪ M'2‬ا‪.‬ا‪ 3I‬ر آ ‪:3‬‬
‫وإ‪ R H %J T‬ا@ رات آ ه‪ 3; aV2 2‬ا‪ M/O‬ا‪(5‬‬
‫‪ 9 %X‬ف ا‪2 G‬ن و‪9‬ج ! ا‪ N‬م ! ل ‪Dispose‬‬
‫‪296‬‬
‫ا‪h‬ن ‪ M‬ا "‪ 2‬ت ! ‪ ,:9C‬ا‪ 2‬وا ‪ ,‬واوج ! ا‪ N‬م‪.‬‬
‫أ ر ‪ Create‬وأ‪.; UN; !I U wYV‬ة ‪2‬ا'‪U‬‬
‫‪ †"I‬ا ت آ ;‪ 3‬ا‪.M/O‬‬
‫‪26 3; “6T‬ار "‪2‬ع" ‪ Type‬أ "‪ Expression ""I‬و;‪26 3‬ار "‪ ""I‬ا‬
‫)…‪DISC(P1,V1,‬‬
‫وا‪ 3"I 3‬أن ا‪2‬ز‪0 R9‬ز ‪,‬‬
‫! ا‪2'2‬ل ه‪2I 2‬ز‪H 7" M ` R9‬ول و ا‪G‬وج ‪P1,V1‬‬
‫ه‪ 2‬ا‪ , :‬ا‪0‬و ا‪ ,‬ا‪2‬ز‪ R9‬ااآ ‪ 3‬وا‪ , :‬ا‪0‬و ا ‪ Y ,/‬ا"‪2O‬ا?‪" 3‬ز !‬
‫!‬
‫ا‪2'2‬ل" وا ‪ M‬ه‪2‬‬
‫) ‪( x1 ) , x1, F ( x2 ) , x2 ,..., F ( xn ) , xn‬‬
‫‪DISC( F‬‬
‫‪ " “6T‬ا@‪ U‬ء ! إد ل ا "‪ 2‬ت و ‪2/I‬ن ‪ Create‬رة ‪ , `' 3; UN9‬ا‪ O‬ه‪5.‬‬
‫ا "‪ 2‬ت‬
‫‪297‬‬
. ‫اص إذا أرد‬2‫ ا‬YI ‫ ! ه‬R7
!I wYf U'‫ا‬2 ‫ة‬.; UN‫ و‬Process ‫ ر‬
‫ة‬.; ‫ت ا‬UN; Add… 7YV Resources "‫ارد‬2 " ‫ار‬26 3; “6T
.OK %X OK wYf %X.aV2 2‫ ت آ ه‬2" ‫ ا‬b ‫و‬
(aV2 !?G- W J) O‫ ا‬, `' ‫ة‬.; “6T
298
.‫ ء‬O ,' ‫ أي‬M9"I ‫ أو‬YI ‫ ! ه‬R7
U'‫ا‬2 ‫ة‬.; UN; !I U wYf‫ و‬Dispose ‫وأا ر‬
O‫ ا‬, `'‫و‬
Setup ‫ و‬Run ‫دوات ر‬0‫ة ا‬.; ! .‫اء‬-z G‫ ه‬- ‫ذج‬2 ‫ن ا‬h‫ا‬
GUH‫ار ا‬26 ‫ة‬.; N;
299
Number of ‫ارات‬/‫ د ا‬M Replication Parameters ‫ار‬/‫ ا‬% " ‫ة‬.; !
‫ ود‬,:J‫ د‬480 Replication Length ‫ار‬/‫ل ا‬2C‫ارات و‬/I 10 ‫ وه أ‬Replications
3‫ي آ ه‬0‫ ا‬.;‫ا‬2‫ ا‬3; % " ‫ ا‬,: 3:‫ و‬0.0 !‫ و ة ا‬, 24 ‫م‬2‫ ا‬3; ‫ا ت‬
.Default Values
UN9‫ ء و‬[email protected]‫ ا‬6 ‫آ ة‬
‫ي ا‬HI Go %X Run ‫ ر‬
Yes wYf 9:‫ ه ا‬O 3/
300
‫ا‪:9:‬‬
‫ا‪ 9:‬ا‪.‬ي ‪2 9 ) M ` Arena 5UNI‬ي ه ‪ `' 9‬ت ( و‪2‬ف ‪ 3; ,OJ‬ا‬
‫‪ “6T‬ا" ‪2‬د ا‪ 90‬وا‪.‬ي ‪9‬م ‪2H‬ال ;‪ 3‬ا‪.9:‬‬
‫وه‪.‬ة ‪ ! ,7:‬ا‬
‫آة‬
‫‪301‬‬
‫‪V‬ة‬
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"mm1","amb",,,No,Yes,Yes,Yes,No,No,No;
VARIABLES:
FinishedService.NumberOut,CLEAR(Statistics),CATEGORY("Excl
ude"):
Customers.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Service.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Service.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Service.WIP,CLEAR(System),CATEGORY("ExcludeExclude");
QUEUES:
Service.Queue,FIFO,,AUTOSTATS(Yes,,);
PICTURES:
Picture.Airplane:
302
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
RESOURCES:
service1,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resource
s),,AUTOSTATS(Yes,,);
REPLICATE,
1,,MinutesToBaseTime(100),Yes,Yes,,,,24,Hours,No,No;
303
ENTITIES:
Arrival,Picture.Report,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Y
es,,);
SETS:
Servers,service1;
‫ذج‬1‫ ا‬9/#
;
;
;
Model statements for module:
Create 1
;
2$
CREATE,
1,MinutesToBaseTime(0.0),Arrival:MinutesToBaseTime(EXPO(1
)),100:NEXT(3$);
3$
ASSIGN:
Customers.NumberOut=Customers.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Process 1
;
0$
ASSIGN:
Service.NumberIn=Service.NumberIn + 1:
Service.WIP=Service.WIP+1;
9$
QUEUE,
Service.Queue;
8$
SEIZE,
2,VA:
SELECT(Servers,POR,
),2:NEXT(7$);
7$
DELAY:
MinutesToBaseTime(Uniform(.5,1.5)),,VA;
6$
RELEASE:
SELECT(Servers,LAST),2;
304
54$
ASSIGN:
Service.NumberOut=Service.NumberOut + 1:
Service.WIP=Service.WIP1:NEXT(1$);
;
;
;
Model statements for module:
Dispose 1
;
1$
ASSIGN:
FinishedService.NumberOut=FinishedService.NumberOut + 1;
57$
DISPOSE:
Yes
305
. ‫ ا‬#)$/ B ‫أ) و‬
.‫ر‬2 C _' ‫د اآ[ ! ر او‬2-‫آ ة و‬
‫ ا‬,:9C ‫ ض‬2‫ا ا [ ل ه‬.‫ض ! ه‬Y‫ا‬
‫ رات‬S7‫ ا‬M'2I‫ و‬.0 ! ‫ ت د‬7‫ ا‬,I ‫م‬2:9 ‫ رات‬,"9 , %"7
:, ‫ل ا‬2'2‫! ا‬
, ‫ از‬R9‫ز‬2I S6 %"7 ‫ ا رات إ ا‬M I .%"7 ,'‫ا‬2‫ا‬
:‫ل‬2'2‫! ا‬
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Time between
Arrivals
(Minutes)
Cumulative
Probability
Probability
1
0.25
0.25
2
0.40
0.65
3
0.20
0.85
4
0.15
1.00
S^‫ ا‬,f`9 g.‫ )و‬/ ! ‫رة وة‬J [‫ اآ‬6‫ ا‬،/ 3 [‫ وا‬6‫ ا‬%‫ه‬6‫ ا‬9 ! ‫ا د‬
3‫ ه‬/ ‫ و‬6‫ ! ا‬M/ , ‫ ا‬, ‫ از‬R9‫ز‬2I ،!? G‫ ا‬, 3; ‫ ?!( آ ا& اع‬G‫ا‬
:3‫ا‬2‫ا‬
: 60 , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
(Minutes)
Cumulative
Probability
Probability
2
0.30
0.30
3
0.28
0.58
4
0.25
0.83
5
0.17
1.00
:/ , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
(Minutes)
Cumulative
Probability
Probability
3
0.35
0.35
4
0.25
0.60
306
‫ا ‪27‬ب‬
‫‪0.80‬‬
‫‪0.20‬‬
‫‪5‬‬
‫‪1.00‬‬
‫‪0.20‬‬
‫‪6‬‬
‫آ ة ا‪ N‬م ";‪ ,‬أدا?&‪.‬‬
‫‪ ,-. !/ 9‬ه‪.‬ا ا‪ N‬م "ة ‪C‬ق‪ .‬أ‪2 3Ih‬ذج ‪:‬ح و ا‪ † S 7‬ا ت ا ‪3; , 27‬‬
‫‪2‬ا;‪ .‬‬
‫?‹ ‪ R -‬ا‪62‬ات‬
‫و‪aV2 &?GH‬‬
‫‪ 6 :!9 I‬ول ‪ ,-.‬ه‪.‬ا ا‪ N‬م "ة ‪C‬ق اى و‪ J‬رن ‪. U‬‬
‫‪307‬‬
SIMAN u/ ‫ال‬
T‫ ا‬9/#
PROJECT,
"Unnamed
Project","amb",,,No,Yes,Yes,Yes,No,No,No;
ATTRIBUTES:
Ahmad Service.Busy;
VARIABLES:
Wait
Line.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Ahmad Available?.NumberOut
True,CLEAR(Statistics),CATEGORY("Exclude"):
Bakur
Service.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Customers
Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Ahmad Available?.NumberOut
False,CLEAR(Statistics),CATEGORY("Exclude"):
Customers
Leave.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Ahmad
Service.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Bakur
Service.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Wait
Line.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"):
Wait
Line.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Bakur
Service.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"):
Ahmad
Service.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Ahmad
Service.WIP,CLEAR(System),CATEGORY("Exclude-Exclude");
308
QUEUES:
Wait Line.Queue,FIFO,,AUTOSTATS(Yes,,);
PICTURES:
Picture.Airplane:
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Green Page:
Picture.Red Ball;
RESOURCES:
Ahmad,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),
,AUTOSTATS(Yes,,):
Bakur,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),
,AUTOSTATS(Yes,,);
309
REPLICATE,
1,,MinutesToBaseTime(480),Yes,Yes,,,,24,Hours,No,No;
ENTITIES:
Customr,Picture.Van,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,
,);
‫ذج‬2 ‫_ ا‬
;
;
;
Model statements for module:
Create 1
;
5$
CREATE,
1,MinutesToBaseTime(0.0),Customr:MinutesToBaseTime(EXPO(3)
):NEXT(6$);
6$
ASSIGN:
Customers
Arrive.NumberOut=Customers Arrive.NumberOut + 1:NEXT(0$);
;
;
;
Model statements for module:
Process 1
;
0$
ASSIGN:
Wait Line.NumberIn=Wait
Line.NumberIn + 1:
Wait Line.WIP=Wait
Line.WIP+1;
12$
QUEUE,
Wait Line.Queue;
11$
SEIZE,
2,NVA:
Ahmad,1:
Bakur,1:NEXT(10$);
310
10$
DELAY:
0.016666666666667,,NVA;
57$
ASSIGN:
Wait Line.NumberOut=Wait
Line.NumberOut + 1:
Wait Line.WIP=Wait Line.WIP1:NEXT(1$);
;
;
;
Model statements for module:
Decide 1
;
1$
BRANCH,
1:
If,Ahmad
Service.Busy==0,60$,Yes:
Else,61$,Yes;
60$
ASSIGN:
Ahmad Available?.NumberOut
True=Ahmad Available?.NumberOut True + 1:NEXT(2$);
61$
ASSIGN:
Ahmad Available?.NumberOut
False=Ahmad Available?.NumberOut False + 1:NEXT(3$);
;
;
;
Model statements for module:
Process 2
;
2$
ASSIGN:
Ahmad Service.NumberIn=Ahmad
Service.NumberIn + 1:
Ahmad Service.WIP=Ahmad
Service.WIP+1;
63$
DELAY:
MinutesToBaseTime(NORM( 3 ,
RELEASE:
Ahmad,1;
0.5 )),,VA;
62$
311
110$
ASSIGN:
Ahmad Service.NumberOut=Ahmad
Service.NumberOut + 1:
Ahmad Service.WIP=Ahmad
Service.WIP-1:NEXT(4$);
;
;
;
Model statements for module:
Dispose 1
;
4$
ASSIGN:
Customers
Leave.NumberOut=Customers Leave.NumberOut + 1;
113$
DISPOSE:
Yes;
;
;
;
Model statements for module:
Process 3
;
3$
ASSIGN:
Bakur Service.NumberIn=Bakur
Service.NumberIn + 1:
Bakur Service.WIP=Bakur
Service.WIP+1;
115$
DELAY:
MinutesToBaseTime(NORM( 4 , 1
114$
RELEASE:
Bakur,1;
162$
ASSIGN:
Bakur Service.NumberOut=Bakur
)),,VA;
Service.NumberOut + 1:
Bakur Service.WIP=Bakur
Service.WIP-1:NEXT(4$);
312
{1 ‫آة‬#
:3‫ ه‬,7O‫ أ‬,XX &; %I g w ‫ذج‬2 ‫ف "ض‬2
ATM Transactions 3( : S ‫ " ت‬-1
Teller Operation ,;‫ ت 'ا‬-2
"Drive Thru" Transactions ‫ة ا رة‬.; ! ‫ " ت‬-3
.M " M/ ‫ ر‬[email protected]‫ وز ! ا‬, ‫! ا‬9N ‫ ?! ا‬G‫? ت ! د ا‬
6‫ إ‬R HI
‫ م‬N :‫ذج‬2 ‫ا‬
‫ء " ت ا رات‬G-
,;‫ء ت ا ا‬G-
313
3h‫ ا‬S ‫ء ا‬G-
Advanced Transfer Mdules ‫رة‬27 ‫ ا‬M:‫ات ا‬6‫ة ! و‬9- !I6‫ذج و‬2 ‫ا ا‬.‫ ه‬3; “6
.Route Module ‫ و‬Station Module ‫ه‬
Station Module ,7
314
‫ة‬6‫و‬
‫ ث‬I P6 3:7 ‫ ن دي أو‬/ ‫ج‬. I 3‫ ت( وا‬7
,2 H ‫ )أو‬,7
‫"ف‬I ‫ة‬62‫ ا‬5.‫وه‬
.‫"ف ة أ آ! " ت‬9 U9 ‫ا‬.U; ‫ ت‬7 ‫ ! ا‬,2 H &`9"I , 6 3;‫ و‬., "‫ا‬
:3 ‫ آ‬,[ ‫ أ‬3; ^ ‫م‬9‫و‬
.,C‫ت اا‬T( ,:7 -1
.‫م‬J ‫ آة‬S" ‫اآ‬.I ‫ اء‬.;‫ا‬2 ,2 H -2
.‫ي‬G‫ق آ‬2 3; % 7 ,:7 -3
: U'‫ا‬2 .;‫ا‬2‫و‬
SIMAN u/ T‫ ا‬9/#
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
STATIONS:
Station 1;
315
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
SIMAN u/ ‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
Station 1
;
0$
STATION,
Station 1;
3$
DELAY:
0.0,,VA;
Route Module ‫ة ر‬6‫و‬
.!? / ‫ار‬G 3‫ ت ا‬7 ‫ ا‬, ? J 3; , ‫ ا‬,7 ‫ أو ا ا‬," ,7
‫ آ ?! إ‬M: ‫م‬2:I‫و‬
.‫ ل‬:z eI ! ‫ ز‬9 I !/ 9‫و‬
:[ ‫ن‬2/I UI ‫وإا‬
.‫ ا ر‬, : "I ‫ ت‬,7
‫ إ‬R ‫ر ا‬2C 3; ,"7J ‫ إر ل‬-1
.," ,‫ و‬7 %"7 3; !? ‫ إر ل ز‬-2
U'‫ا‬2 .;‫ا‬2‫و‬
SIMAN u/ T‫ ا‬9/#
316
PROJECT,
"Unnamed Project","Dr. A.
Barry",,,No,Yes,Yes,Yes,No,No,No;
STATIONS:
Station 1;
REPLICATE,
1,,,Yes,Yes,,,,24,Hours,No,No;
SIMAN u/ ‫ذج‬1‫ ا‬9/#
;
;
Model statements for module:
Route 1
;
0$
ROUTE:
0.,Station 1;
317
‫ [ ل ا‪" g‬ض ‪2‬اص ا‪62‬ات آ ‪:3Ih‬‬
‫ا ‪2‬ذج ‪2 9‬ي ‪ ,XX‬و‪6‬ات ‪.; Create‬ة ‪2‬ا'‪U‬‬
‫و‪ ,XX‬و‪6‬ات ‪Process‬‬
‫و‪2 M `I‬ارده آ ‪3Ih‬‬
‫‪318‬‬
U'‫ا‬2 ‫ة‬.; (‫رة‬27 ‫ ) ! ا" ت ا‬Station Module ‫ ت‬7
8 -29 ‫آ‬
U'‫ا‬2 ‫ة‬.; (‫رة‬27 ‫ ) ! ا" ت ا‬Route Module ‫ رات‬6 -29 ‫و‬
U'‫ا‬2 ‫ة‬.; Dispose !I6‫وو‬
319
Arena A ‫ت‬r0)‫ ا‬/4
: M "9 !/‫ ) و‬Arena R -29 ‫ي‬.‫ وا‬Input Analyser ‫ ا ت‬M I ] ‫م‬9
, /‫ ا‬,-. ‫ ا‬3; U ‫ @ا‬g‫ وذ‬, ‫ ت‬, 6‫" ت إ‬9‫ز‬2I 7 ( U
.( Input-Data Modeling , ‫ ا ت ا‬,-. f9‫ ا‬I‫ )و‬Quatitative Modeling
!/ 9‫ واى ;اغ و‬, J M‫ ! آ‬M `I ASCII File 3 _ 3; , ‫ ا ت ا‬RV2I
3; ,9‫ن ^ و‬2/I ‫! ان‬/ 9 70‫ آ ان ا‬6‫ا‬2‫ ا‬7‫ ا‬3; ‫إد ل اي د ! ا ت‬
! ‫ أو‬Arena M‫ ا ت ! دا‬M I ] MY‫* و‬.dst ‫ن ا _ اد‬G . UI ‫د‬
Arena ‫ي‬2 9 ‫ي‬.‫ ا‬H ‫ا‬
‫ة إد ل‬.; UN;
wYV‫ أو أ‬New %X File ‫ أ ر‬,?‫ ا‬, ? :‫! ا‬
320
Use Existing … %X Data File %X File ‫ ا ر‬,?‫ ا‬, b:‫ ! ا‬%X
_ ‫ة إ ر ا‬.; UN
321
‫ا ر ا _ ا‪.‬ي ‪2 9‬ي ا ت وا‪.‬ي & ا@ اد ‪ %X dst‬ا‪]; Open wYV‬‬
‫‪ “6T‬أن ا ] ‪ M/‬رج ‪/I‬اري ت ذا‪" I‬د ‪) ,b; 31‬ه‪.‬ا ه‪ 2‬ا"د ا@;ا‪.(3V‬‬
‫ا‪ ! Fit wYV‬ا‪ , ? :‬ا?‪Fit All %X ,‬‬
‫‪322‬‬
Mf;‫ أ‬37"9 ‫ي‬.‫ ا‬R9‫ز‬2‫ ر ا‬9 %X I‫ ذا‬, ‫" ت ا‬9‫ز‬2‫ ا‬M‫ آ‬79 ] ‫ ا‬M"H ‫ا‬.‫ه‬
:! K-S Test ‫! إ ر‬/ 9 K-S Test ‫ و‬Chi Square Test ‫اء إ ري‬- g‫ وذ‬7I
%X
:3‫ ه‬,H‫ ا‬W ‫ آ‬, ‫ ت ا‬
Distribution Summary
Distribution: Weibull
Expression:
WEIB(4.91, 1.03)
Square Error: 0.000756
Chi Square Test
Number of intervals = 15
Degrees of freedom = 12
323
Test Statistic
= 14.4
Corresponding p-value
= 0.284
Kolmogorov-Smirnov Test
Test Statistic = 0.0176
Corresponding p-value
> 0.15
Data Summary
Number of Data Points
= 1000
Min Data Value
= 0.0022
Max Data Value
= 38.5
Sample Mean
= 4.92
Sample Std Dev
= 5.01
Histogram Summary
Histogram Range
= 0 to 39
Number of Intervals = 31
SUMMARY.OUT ‫ر‬
@‫و _ ا‬
Fit All
Document: C:\Documents and Settings\amb\Desktop\InputAnalysis\exp.dst
Data File: C:\Documents and Settings\amb\Desktop\InputAnalysis\exp.dst
Function
Sq Error
-------------------------------Weibull
0.000756
Gamma
0.000818
Erlang
0.000846
Exponential
0.000846
Beta
0.00203
324
Lognormal
0.00625
Normal
0.0391
Triangular
0.0632
Uniform
0.0957
.‫ ا ت‬7I Mf;0‫ ا‬R9‫ز‬2‫ ا‬2‫ ه‬M9‫ و‬R9‫ز‬2I ‫“ أن‬6T
‫ "د‬,: ‫“ أن ا ?] ا‬6T .7‫اري ا‬/‫ ا‬R9‫ز‬2‫ ت ا‬b; ‫ د‬XeI ‫ف "ض‬2
:! ‫ ت‬b`‫ د ا‬Y .31 ‫ ت‬b;
%X
]9‫ و‬I‫ ذا‬7‫ ;" د ا‬OK %X 20 ‫ ت‬b`‫" د ا‬V‫و‬
Distribution Summary
Distribution: Exponential
Expression:
EXPO(4.92)
Square Error: 0.000421
Chi Square Test
Number of intervals = 11
Degrees of freedom = 9
Test Statistic
= 6.98
Corresponding p-value
= 0.639
325
Kolmogorov-Smirnov Test
Test Statistic = 0.0192
Corresponding p-value
> 0.15
Data Summary
Number of Data Points
= 1000
Min Data Value
= 0.0022
Max Data Value
= 38.5
Sample Mean
= 4.92
Sample Std Dev
= 5.01
Histogram Summary
Histogram Range
= 0 to 39
Number of Intervals = 20
.‫ ا ت‬7I Mf;0‫ ا‬R9‫ز‬2‫ ا‬2‫ن ه‬h‫ ا‬30‫ ا‬R9‫ز‬2‫“ أن ا‬6T
Fit All
Document: C:\Documents and Settings\amb\Desktop\InputAnalysis\exp.dst
Data File: C:\Documents and Settings\amb\Desktop\InputAnalysis\exp.dst
Function
Sq Error
---------------------------------Erlang
0.000421
Exponential
0.000421
Gamma
0.000422
Weibull
0.00048
326
Beta
0.00277
Lognormal
0.00784
Normal
0.06
Triangular
0.101
Uniform
0.148
.]T‫ إر‬R9‫ز‬2I ! ,' , 6 2‫ ه‬30‫ ا‬R9‫ز‬2‫“ أن ا‬6T
10 ‫ ت‬b`‫ آ ن د ا‬2 ‫ذا‬
Distribution Summary
Distribution: Exponential
Expression:
EXPO(4.92)
Square Error: 0.000068
Chi Square Test
Number of intervals = 6
Degrees of freedom = 4
Test Statistic
= 0.959
Corresponding p-value
> 0.75
Kolmogorov-Smirnov Test
Test Statistic = 0.0192
Corresponding p-value
> 0.15
Data Summary
Number of Data Points
= 1000
Min Data Value
= 0.0022
Max Data Value
= 38.5
Sample Mean
= 4.92
Sample Std Dev
= 5.01
Histogram Summary
327
Histogram Range
= 0 to 39
Number of Intervals = 10
Fit All
Document: C:\Documents and Settings\amb\Desktop\InputAnalysis\exp.dst
Data File: C:\Documents and Settings\amb\Desktop\InputAnalysis\exp.dst
Function
Sq Error
--------------------------------Erlang
6.8e-005
Exponential
6.8e-005
Weibull
0.000107
Gamma
0.000166
Beta
0.00158
Lognormal
0.00868
Normal
0.0976
Triangular
0.202
Uniform
0.281
M ; R-‫ را‬.‫ل‬29‫] وو‬T‫"! إر‬9‫ز‬2‫ ! ا‬M‫ ! آ‬,' , 6 2‫ ه‬30‫ ا‬R9‫ز‬2‫ ا‬:,N6
.‫ ا ت‬M I
328
‫‪1 [/#‬‬
‫ا" ل‬
‫‪329‬‬
‫ ‪2‬‬
‫اوال ا‪,V 9‬‬
‫‪330‬‬
331
3 SIMAN S‫اآ‬I ‫ات‬Y
332
333
‫ ‪4‬‬
‫‪-‬ول ‪Y‬ات‬
‫‪334‬‬
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
‫ ‪5‬‬
‫‪ ,/‬ا‪ 2‬ت‬
‫‪351‬‬
352
353
354
355
356
357
358
359
360
361
Arena 3
:, ‫ ا‬,/O ‫ ا‬M ARENA ‫آ ة ام‬
‫ وا‬,-. ‫ ا‬,:9C ‫ف "ض‬2
,:Y ‫ ا‬,‫و‬/@‫ات ا‬62‫! `! ! ا‬2 ‫ة @ ج‬0‫ ا" ت ا‬M[ 9 ‫ م‬N‫ا ا‬.‫ه‬
:3 ‫ ا‬M/O‫ ا‬3; M[ 9 ‫ي‬.‫ وا‬Sealed
Scrapped
20%
Rework
Part A Prep
Part A
EXPO(5)
TRIA(1,4,8)
Sealer
9%
EXPO(45)
80%
Salvaged
and
Shipped
Arrivals
Part B
Part BPrep
Part A
TRIA(1,3,4)
Batch of 4
EXPO(30)
Part B
NORM(2.4,0.5)
91%
Shipped
TRIA(3,5,10
.% I‫ و‬U‫ دا‬RV2 U"' %I 3‫ات ا‬62 ," 9‫ رة ! ' د‬,'‫ا‬2‫ ا‬R7:‫ا‬
-‫ذ‬2 ‫ إ‬M I‫ذج و‬2 ‫ود ا‬6 ‫ ( رج‬%J 3; ]I Part A I 3‫و ا‬0‫ات ا‬62‫ا‬
5.‫ل ه‬2'‫ و‬،? J‫ د‬5 w2
‫زع ا‬2 Interarrival Times ‫ل‬2'‫! و‬
!G
,:7 3; ،? J‫ د‬2 M:‫ا ا‬.‫ق ه‬Y9‫ و‬Part A Prep f ‫ ا‬,:7 ‫ إ‬M:I R7:‫ا‬
‫ق‬Y9 f ‫ا ا‬.‫ا وه‬- ‫ن ا م‬2/9 3/ 9‫ ا د‬5.‫_ ه‬NI‫ و‬M:'‫ د و‬%9 f ‫ا‬
2 M:‫ق ا‬Y9‫ و‬Sealer ‫ء ا ا م‬GH‫ا ا‬.‫ ه‬M:9 %X ،(1,4,8) 3[[ ‫ ا‬R9‫ز‬2‫ ا‬R9 ‫ز‬
.? J‫د‬
‫ات‬6‫ و‬3; R HI‫ذج و‬2 ‫ود ا‬6 ‫ ( رج‬3; ]I Part B I 3‫ ا‬, [‫ات ا‬62‫ا‬
!
! G U I ‫ وا‬Part B Prep f ‫ة ا‬6‫ إ و‬MI ‫ ان‬MJ R7J (4) R ‫! ار‬
"‫ ا‬Uf" ! U ; %9 R7:‫ ا‬5.‫ل ه‬2'‫ " و‬،,:J‫ د‬30 w2 3‫ ا‬R9‫ز‬2I & ‫ل‬2'‫و‬
‫ات‬27 ,X[‫ `ˆ ا‬RI Part B Prep f ‫ ا‬,:7 3; ,H " ‫ ا‬،‫ `اد‬,"7J M‫" ] آ‬I‫و‬
(3,5,10) 3[[ ‫ ا‬R9‫ز‬2‫ ا‬R9 f ‫ ا ان ز ! ا‬Part A Prep f ‫ ا‬,:7 3; ‫آ‬
,‫و‬/@‫ ا‬R7:‫ ا‬RV2 %I ‫ ا م‬, .‫ل‬2'2 ? J‫ د‬2 ,JY ‫ ا ا م‬R7:‫ ا‬MI %X
Part ‫ع‬2 ! ,"7:; ،,"7:‫ع ا‬2 "9 , "‫ ا‬5.‫ ز ! ه‬، U %X ! ‫ و‬9‫ ا د‬M‫دا‬
.(2.4,0.5)3"C R9‫ز‬2I & ‫ن‬2/9 Part B ‫ع‬2 ! ,"7:‫( و‬1,3,4) 3[[ R9‫ز‬2I & ‫ن‬2/9 A
362
MI ,V2; ‫ ا‬R7:‫ ا‬،! O‫ ا‬%: MI‫ ا` ‹ و‬,:7 I , 2 ‫ ا‬R7:‫ ! ا‬91%
9- ! U ‫ و‬U`NI ‫ و‬U:' ‫ وإ دة‬U//`I %9 P6 Rework R ‫ إ دة ا‬,:7 3‫" د إ‬9 3J ‫ ! و ا‬O‫ ا‬%J ‫ إ‬MI‫ ` ‹ و‬I ‫ات‬62‫ ! ا‬80% , "‫ ا‬5.‫و ! ه‬
45 w2 3T‫ ا‬R9‫ز‬2‫ ا‬R9 R ‫ق @ دة ا‬Y ‫ ! ا‬G‫ ا‬.‫ذج‬2 ‫ رج ا‬,'0‫& ا‬U.,:J‫ د‬2 ‫ق‬YI ‫ى‬T ,U- ! ‫ ل‬:@‫ ا‬, ‫ أز‬،R7:‫ ا‬M/ ,:J‫د‬
Resource
‫ارد‬2 ‫ ى إام ا‬,;" ,6 M‫? ت ! آ‬
6‫ إ‬R - ‫ب‬27 ‫ا‬
,"7:‫ ا‬,JYI ‫ي‬.‫ ! ا‬G‫ ا‬، Number in Queue ‫ر‬2 C M‫ آ‬3; R7:‫ د ا‬، Utilization
Flowtime ‫ أو‬Cycletime ‫ذج‬2 ‫ ا‬3; ,"7:‫ث ا‬2/ ! ‫ وز‬Time in Queue ‫ر‬2 7‫ ا‬3;
.3'0‫ره ا‬
. Animation ,‫ر آ‬2
W‫ او ار‬U" I ‫ ! أو ا‬O W‫ ار‬,"7J M/
‫ذج‬2 3 ‫ف‬2‫ و‬,:J‫ د‬2000 ‫ م ة‬N‫ا ا‬.‫ ه‬3‫ف آ‬2
:‫ذج‬1‫ء ا‬1
Common panel ‫ أ ر‬File > New 9- _ a;‫ وأ‬ARENA ] MY
:, ‫اء ا‬G-0‫ وأ ا‬d‫ أ‬U ‫و‬
363
, ‫ة ا‬.; ‫ ا‬UNI Arrive 1 3 !I ‫رة‬e` wYV‫ن أ‬h‫ا‬
364
:3 aV2 2‫ ا ت آ ه‬M‫أد‬
Enter Data
Station
Part A Arrive
Arrival Data
Batch Size
1
Time Between
EXPO(5)
Mark Time Attribute
Arrival Time
Leave Data
Station
Part A Prep
Route Time
2
Assignments
Attribute
Sealer Time
Value
TRIA(1,3,4)
, ‫ة ا‬.; ‫ ا‬UNI Assign… wYV‫ أ‬%X
365
, ‫ة ا‬.; ‫ ا‬UN; Add… wYV‫أ‬
, ‫ة ا م آ‬.; ‫ ا‬3; Sealer Time 3 ‫ ا‬M‫ اد‬%X ‫! رة‬/I % ‫ إذا‬Attribute ‫أ ر‬
..;‫ا‬2‫ ا‬R - M`: OK wYV‫ ا‬%X Value: ‫ة ا م‬.; ‫ ا‬3; TRIA(1,3,4)‫ و‬Attribute:
:39 ‫ ا ت آ‬M‫ وأد‬Arrive 2 R †O‫ `ˆ ا‬M";‫أ‬
Enter Data
366
Station
Part B Arrive
Arrival Data
Batch Size
4
Time Between
EXPO(30)
Mark Time Attribute
Arrival Time
Leave Data
Station
Part B Prep
Route Time
2
Assignments
Attribute
Sealer Time
Value
NORM(2.4,0.5)
, ‫ ا ت ا‬M‫! وأد‬I wYV‫ ا‬Server 1 ‫ إ‬M: ‫ن‬h‫ا‬
Enter Data
Station
Part A Prep
Server Data
Resource
Part A Prep_R
Capacity Type
Capacity
Capacity
1
Process Time
TRIA(1,4,8)
Leave Data
Station
Sealer
Route Time
2
, ‫ة ا‬.; ‫ ا‬3; ‫;و آ‬
367
, ‫ ا ت ا‬M‫! وأد‬I wYV‫ ا‬Server 2 ‫ إ‬M: ‫ن‬h‫ا‬
Enter Data
Station
Part B Prep
Server Data
Resource
Part B Prep_R
Capacity Type
Capacity
Capacity
1
Process Time
TRIA(3,5,10)
Leave Data
Station
Sealer
Route Time
2
, ‫ة ا‬.; ‫ ا‬3; ‫;و آ‬
368
:39 ‫ ا ت آ‬M‫! وأد‬I wYV‫ إ‬Inspect 1 3‫ إ‬M:
Enter Data
Station
Sealer
Server Data
Resource
Sealer _R
Capacity Type
Capacity
Capacity
1
Process Time
Sealer Time
Failure Probability
0.09
Pass Inspection Leave Data
Station
Shipping
Route Time
2
Fail Inspection Leave Data
Station
Rework
Route Time
2
369
, ‫ة ا‬.; ‫ ا‬3; ‫;و آ‬
:39 ‫ ا ت آ‬M‫ وأد‬Inspect 2 R †O‫ `ˆ ا‬M";‫وأ‬
Enter Data
Station
Rework
Server Data
Resource
Rework _R
Capacity Type
Capacity
Capacity
1
Process Time
EXPO(45)
Failure Probability
0.2
Pass Inspection Leave Data
Station
Salvaged Parts
370
Route Time
2
Fail Inspection Leave Data
Station
Scrap
Route Time
2
, ‫ ا ت ا‬M‫ واد‬Depart 3 !I wYV‫ا‬
Enter Data
Station
Shipping
Count
Counter
Shipping_C
Increament
1
Tally
371
Tally
Shipping_Ta
Type of Statistics
Attribute
Arrival Time
, ‫ة ا‬.; ‫ ا‬3; ‫;و آ‬
, ‫ ا ت ا‬M‫ واد‬Depart 2 !I wYV‫ا‬
Enter Data
Station
Salvaged Parts
Count
Counter
Salvaged Parts _C
Increament
1
372
Tally
Tally
Salvaged Parts _Ta
Type of Statistics
Attribute
Arrival Time
, ‫ة ا‬.; ‫ ا‬3; ‫;و آ‬
, ‫ ا ت ا‬M‫ واد‬Depart 1 !I wYV‫ا‬
Enter Data
Station
Scrap
Count
Counter
Scrap _C
Increament
1
Tally
Tally
Scrap _Ta
373
Type of Statistics
Attribute
Arrival Time
, ‫ة ا‬.; ‫ ا‬3; ‫;و آ‬
:3 ‫ ا‬M‫ وأد‬Simulate !I wYV‫وأا إ‬
Replicate
Number of Replications
1
Beginning Time
0.0
Length of Replication
2000
374
‫أ‪h‬ن د رات ا‪G-0‬اء ;‪ 3‬ا ‪2‬ذج وذ‪ g‬ر ` ح ا ر‬
‫! ا‪H‬ول ا‪! 90‬‬
‫;‪ UN‬ا ;‪.‬ة ا ‪,‬‬
‫ا‪2 ; OK wYV‬ل ا ‪ A‬ا ‪ +‬وو'‪ _ M‬ا‪G-0‬اء آ ‪3‬‬
‫‪375‬‬
‫ى‬I ‫ف‬2‫آ ة و‬
‫أ ا‬I ‫ف‬2 RUN > GO wYf g‫آ ة وذ‬
:3 ‫ ا‬9:‫] ا‬9 ‫آ ة‬
‫ي ا‬H ‫ن‬h‫ا‬
‫ ا‬3UI 6‫ذج و‬2 ‫ ! ا‬,` ‫اء ا‬G-0‫ ا‬3; M:I 3‫ات وه‬62‫ا‬
*‫ اآة وا‬T ARENA Simulation Results
amb - License #9400000
Summary for Replication 1 of 1
Project:
Electronics Assembly
Analyst:
Dr.Adnan Barry
Replication ended at time
Run execution date :30/31/2001
Model revision date:
3/11/2001
: 2000.0
TALLY VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Observations
____________________________________________________________________________
Salvaged Parts_Ta
540.48
(Insuf)
101.91
874.90
31
Shipping_Ta
35.911
(Corr)
9.7800
117.85
548
Scrap_Ta
334.79
(Insuf)
76.343
821.27
4
Rework_R_Q Queue Time
429.95
(Insuf)
.00000
782.19
36
Part A Prep_R_Q Queue
6.0259
(Corr)
.00000
28.804
365
Sealer_R_Q Queue Time
1.9247
(Corr)
.00000
12.850
603
Part B Prep_R_Q Queue
42.308
(Insuf)
.00000
105.34
240
376
DISCRETE-CHANGE VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Final Value
____________________________________________________________________________
Rework_R Available
1.0000
(Insuf)
1.0000
1.0000
1.0000
Sealer_R Available
1.0000
(Insuf)
1.0000
1.0000
1.0000
Part A Prep_R Availabl
1.0000
(Insuf)
1.0000
1.0000
1.0000
Part B Prep_R Busy
.72774
(Insuf)
.00000
1.0000
.00000
Part A Prep_R Busy
.79647
(Corr)
.00000
1.0000
1.0000
# in Rework_R_Q
11.615
(Insuf)
.00000
22.000
19.000
# in Part B Prep_R_Q
5.0770
(Insuf)
.00000
19.000
.00000
# in Sealer_R_Q
.58031
(Corr)
.00000
4.0000
.00000
Sealer_R Busy
.77139
(Corr)
.00000
1.0000
.00000
# in Part A Prep_R_Q
1.0999
(Corr)
.00000
6.0000
2.0000
Rework_R Busy
.99029
(Insuf)
.00000
1.0000
1.0000
Part B Prep_R Availabl
1.0000
(Insuf)
1.0000
1.0000
1.0000
COUNTERS
Identifier
Count
Limit
_________________________________________
Scrap_C
Shipping_C
Salvaged Parts_C
4
Infinite
548
Infinite
31
Infinite
Simulation run time: 5.48 minutes.
Simulation run complete.
.‫ة‬V
‫ ا‬3; 9:‫ا ا‬.‫› ه‬J ‫ف‬2
‫ذج‬1‫ ا‬U/2 ‫ت‬1 4 ‫ل‬0‫إد‬
M "I Rework ‫ إ دة ا م‬,7
‫ `ض ان‬،‫ذج‬2 ‫ات ا‬Y‫_ " ا‬f ‫ف‬2
(,:J‫ د‬480) ‫ ت‬8 ‫ ة‬6‫ وا‬M U; M "9 ‫و‬0‫ ا‬,9‫ اور‬Shift !9‫ دور‬
] ‫ ; ت‬[email protected]‫ ا‬5.‫ ه‬,-. ، f9‫ ت ا‬8 ‫ ! ة‬U; M "9 , [‫ ا‬,9‫واور‬
:3 ‫ ا‬M " ARENA
, ‫ ا ت ا‬U; M 3‫ وا‬, ‫ة ا‬.; ‫ ا‬N; Rework ‹ `‫ ا‬,7
Enter Data
Station
Rework
377
3 !I wYV‫ا‬
Server Data
Resource
Rework _R
Capacity Type
Scedule
Scedule
Rework Schedule
Process Time
EXPO(45)
Failure Probability
0.2
Ignore
Pass Inspection Leave Data
Station
Salvaged Parts
Route Time
2
Fail Inspection Leave Data
Station
Scrap
Route Time
2
, ‫ة ا‬.; ‫ ا‬g UNI (‫ة ! ا ر‬.; ‫ ا‬M`‫ )ا‬Schedule wYV‫إ‬
378
‫ة اى‬.; UN; Add… wYV‫إ‬
3 ‫ ة اى آ‬, "‫ آر ا‬%X OK wYV‫إ‬
,? U‫ة ا‬.; ‫] ا‬I‫و‬
379
,"‫ و‬,:J‫ د‬480 ,9‫ق اور‬YI‫ و‬6‫ وا‬M ‫و‬0‫ ا‬," !9‫ دور‬,-. 2‫ ه‬5 ‫ي‬.‫ا‬
.,:J‫ د‬480 f9‫ق ا‬YI‫ ! و‬, [‫ا‬
R9‫ز‬2I ‫ ;ذا آ ن‬h WJ‫ ل ! و‬7 ‫ب‬
‫ وإ دة‬a I ! ‫ وز‬,:J‫ د‬120 w2
I Sealer ‫ ا م‬,7
,/ ‫ ان‬f9‫`ض أ‬
3‫ ا‬2‫ ه‬Uptime ,/ ‫ ا‬,; M "I ‫ي‬.‫ ! ا‬G‫ا‬
wYV‫ا إ‬.‫ ه‬,-. .? J‫ د‬4 w2 3‫ ا‬R9‫ز‬2I f9‫ & ا‬Downtime & 79‫ و‬MYOI
‫ة‬.; ‫ ا‬UN !I Sealer ‹ `‫ ا‬,7
380
‫ة‬.; ‫ ا‬UN;
381
wYV‫إ‬
& ‫ة و† ا ت ا‬.; ‫ ا‬UN; Add… wYV‫ إ‬Failures W I ‫ء‬GH‫ ا‬3;
Failure
Sealer Failure
Failure Based On
Time
Fai When
Wait
Uptime
EXPO(120)
Downtime
EXPO(4)
! ‫ أ ر‬g. :6T U ‫? ت‬
[email protected]‫ " ا‬R H ,?
6‫ إ‬,‫ آ‬-‫ذ‬2 ‫_ إ‬f
Common ,62
‫ذج وأ‬2 ‫ر ا‬
3; , ,:7 ‫ أ ر‬%X Statistics & ‫ب‬2/ ‫ ا‬2‫وه‬
‫ر‬G‫ا‬
,‫ا آ‬
382
‫ة‬.; ‫ ا‬N; Statistics !I wYV‫إ‬
‫ة‬.; ‫ ا‬N; Add… wYV‫ أ‬Time-Persistent W I ‫ء‬GH‫ ا‬3;
383
, ‫ أ † ا ت ا‬%X
Data Object
Queue
select
Queue Name
Part B Prep_R_Q
Save Observation to a File
OS File Name in Double Quotes
check
“Prep B_Q.dat”
:3 ‫آر ا‬
Data Object
Queue
select
Queue Name
Sealer_R_Q
Save Observation to a File
OS File Name in Double Quotes
check
“Sealer_Q.dat”
384
Data Object
Queue
select
Queue Name
Rework_R_Q
Save Observation to a File
OS File Name in Double Quotes
check
“Rework_Q.dat”
, ‫ة ا‬.; ‫ ا‬N; Add… wYV‫ أ‬Tallies W I
, ‫ ا ت ا‬M‫أد‬
Tally Name
Shipping_Ta
Save Observations to a File
check
OS File Name in Double Quotes
“Ship.dat”
, ‫ ا ت ا‬M‫ وأد‬Add… wYV‫ أ‬Frequencies W I ‫أا‬
Expression
NQ(Rework_R_Q)
Constant or Range
Constant
Value
0
Constant or Range
Range
Value
0
High Value
10
Constant or Range
Range
Value
10
High Value
20
385
Constant or Range
Range
Value
20
High Value
30
…
‫ة‬.; ‫;] ا‬
:3 ‫و آ‬I ‫ف‬2 ,?
386
[email protected]‫ة ا‬.; ‫ا‬
.‫ذج‬2 ‫ ا‬9 I ‫ة‬.; ‫د ا‬2"I 6 OK wYV‫أ‬
:3 ‫ ا‬9:‫ ا‬RC‫آ ة آ وأ‬
‫ي ا‬-‫أ‬
*‫ اآة وا‬T ARENA Simulation Results
amb - License #9400000
Summary for Replication 1 of 1
Project:
Electronics Asse
Run execution date :
11/ 1/2001
Analyst:
Dr.Adnan Barry
Model revision date:
3/11/2001
Replication ended at time
: 50000.0
TALLY VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Observations
____________________________________________________________________________
Salvaged Parts_Ta
302.17
(Corr)
19.439
1229.2
1199
Rework_R_Q Queue Time
193.93
48.888
.00000
674.58
1467
Sealer_R_Q Queue Time
6.2386
1.5828
.00000
50.795
16499
Scrap_Ta
285.39
(Insuf)
25.366
1159.2
267
Part B Prep_R_Q Queue
70.972
(Corr)
.00000
541.65
6624
Shipping_Ta
57.472
(Corr)
9.0197
564.91
15031
Part A Prep_R_Q Queue
15.183
2.5646
.00000
99.536
9876
DISCRETE-CHANGE VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Final
Value
____________________________________________________________________________
Part A Prep_R Busy
.85391
.02036
.00000
1.0000
1.0000
# in Rework_R_Q
5.6899
1.6284
.00000
28.000
.00000
# in Sealer_R_Q
2.0586
.59611
.00000
21.000
.00000
Part B Prep_R Availabl
1.0000
(Insuf)
1.0000
1.0000
1.0000
# in Part A Prep_R_Q
2.9990
.61504
.00000
24.000
1.0000
Sealer_R Available
1.0000
(Insuf)
1.0000
1.0000
1.0000
Part A Prep_R Availabl
1.0000
(Insuf)
1.0000
1.0000
1.0000
Rework_R Available
1.4992
(Insuf)
1.0000
2.0000
1.0000
Sealer_R Busy
.84177
.02003
.00000
1.0000
.00000
Rework_R Busy
1.3732
.06088
.00000
2.0000
1.0000
387
Part B Prep_R Busy
.79305
.04708
.00000
1.0000
.00000
# in Part B Prep_R_Q
9.4023
(Corr)
.00000
88.000
.00000
COUNTERS
Identifier
Count
Limit
_________________________________________
Salvaged Parts_C
1199
Infinite
267
Infinite
15031
Infinite
Scrap_C
Shipping_C
FREQUENCIES
--Occurrences--
Standard
Restricted
Identifier
Category
Number
AvgTime
Percent
Percent
____________________________________________________________________________
Value(NQ(REWORK_R_Q))
STATE(Sealer_R)
Constant(0,)
112
81.559
18.27
18.27
Range(0,10)
163
197.97
64.54
64.54
Range(10,20)
63
120.45
15.18
15.18
Range(20,30)
11
91.559
2.01
2.01
BUSY
3635
11.578
84.18
84.18
IDLE
3339
1.9188
12.81
12.81
FAILED
387
3.8871
3.01
3.01
Simulation run time: 1.97 minutes.
Simulation run complete.
.‫ة‬V
‫ ا‬3; 9:‫ا ا‬.‫› ه‬J ‫ف‬2
: Output Analysis ‫=ت‬$‫ ا‬/4
‫آة‬
P
342 ‫ر‬: ‫ ا‬3; ‫ ة‬/ ‫ ا‬3; ‫ ت‬- ‫ ا‬M I ‫ع‬2V2 ‫ إ‬M ` ‫ق‬7 ‫ف‬2
] R 3Ie9 ‫ي‬.‫ وا‬Output Analyser ] ‫ف م‬2 ‫ى‬2 ‫ا ا‬.‫ ه‬3; . 2
. ‫ع ا‬2V2 ‫ ا‬3; ,?
[email protected]‫ ا‬,‫ " ه آ‬- 3‫ ت ا‬w M ARENA
M "9 ] ‫ن ا‬0 ,2:9‫ او ! ا‬ARENA M‫! دا‬
‫ إ‬Output Analyser MYO ‫إ أ‬
‫ة‬.; ‫ ا‬UNI MYO‫ " ا‬،M "9 3/ ARENA ‫ ج‬9T‫ و‬,I‫ا‬.
388
‫ة‬.; ‫ ا‬UN; File > New 3 wYV‫أ‬
‫ ا ` ت‬H UN; Add… 3 wYV‫أ‬
389
Data Group Files ‫ ` ت ت‬,2 H ‫ آ‬: WG 3‫أ ر ا ` ت ا‬
UN; Graph > Plot ‫ أ ر‬، Prep B_Q , [‫ ا‬R7:‫ ا‬f I ‫ر‬2 C 3; Y‫ ا‬% ‫ن‬h‫ا‬
‫ة‬.; ‫ا‬
390
OK %X Prep B_Q.dat ‫ وا ر‬Add… wYV‫ا‬
, [‫ ا‬R7:‫ ا‬f I ‫ر‬2 C 3; ‫ات‬62‫ "د ا‬%‫ ر‬2‫وه‬
R ‫ر إ دة ا‬2 C ‫ ( ت‬%‫ ر‬%
391
‫;‬
‫وأا ‪ N‬ا ا رج ا‪/‬اري ‪2 7‬ر إ دة ا ‪R‬‬
‫‪392‬‬
‫‪ M‬ا‪%‬‬
3 ‫ ا‬%‫ ا‬37"9 ‫ي‬.‫وا‬
Uf" ‫ف "ض‬2 Output Analyser ] 3; ‫ آ[ة‬3?
6‫ إ‬M I ‫ق‬C -2I
.‫ة‬V
393
‫ ا‬3; R9 M/O
:!'‫ا ا‬
:/# GPSS World ‫;م اآة‬
1‫ل‬#
,`‫ م وآ‬N‫ ا‬3; Transactions ! ` ‫ " ! او‬2I ,`‫ف "ض آ‬2 ‫ا ا [ ل‬.‫ ه‬3;
.%U U ‫ أو‬%U`? ƒ‫ ء و‬U‫ م " إ‬N‫ ! ا‬%U-‫ أو إا‬%U ‹‫ا‬
S‫ م و& اآ‬N‫ ا‬3; ‫ل‬2 ! " 2 GENERATE S :‫م ا‬9
The GENERATE Block:
GENERATE
A,B,C,D,E
Operands ‫ ا" ل‬P6
%‫( او إ‬Null) †T ‫ن‬2/9 ‫! ان‬/ 9‫ إ ري و‬2‫ وه‬، 2‫! ا‬
! ‫ ز‬w2
A
‫اس‬2J‫" ! أ‬I ‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫( أو ر‬Name)
(Direct SNA) ‫ م ة‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression)
! " % " ‫! إام‬/ 9T‫و‬
‫ن‬2/9 ‫! ان‬/ 9‫ إ ري و‬2‫ وه‬، ,‫ أو "ل دا‬2‫! ا‬
! ‫لز‬H _ B
"I ‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫( أو ر‬Name) %‫( او إ‬Null) †T
Direct ) ‫ م ة‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression) ‫اس‬2J‫! أ‬
! " % " ‫! إام‬/ 9T‫( و‬SNA
‫! ان‬/ 9‫ إ ري و‬2‫ وه‬، M " ‫ أول‬2I eI ! ‫ ز‬2‫ وه‬e‫ ز ! ا‬,9‫ا‬
‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫( أو ر‬Name) %‫( او إ‬Null) †T ‫ن‬2/9
‫ م ة‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression) ‫اس‬2J‫" ! أ‬I
! " % " ‫! إام‬/ 9T‫( و‬Direct SNA)
394
C
,V‫ ا@;ا‬, :‫ وا‬، %‫ه‬2I %9 !9.‫ "د ا " ! ا‬J0‫ أو ا"د ا‬2‫ ا‬6
D
(Name) %‫( او إ‬Null) †T ‫ن‬2/9 ‫! ان‬/ 9‫ إ ري و‬2‫ وه‬، ,9 UT %" ‫ا ا‬.U
Parenthesized ) ‫اس‬2J‫" ! أ‬I ‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫أو ر‬
‫! إام‬/ 9T‫( و‬Direct SNA) ‫ م ة‬N ,9‫ د‬,`' ‫( أو‬Expression
! " % "
†T ‫ن‬2/9
‫! ان‬/ 9‫ و‬0 ,V‫ & ا@;ا‬J‫ إ ري و‬2‫ وه‬، ,f;0‫ى ا‬2
E
! "I ‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫( أو ر‬Name) %‫( او إ‬Null)
Direct ) ‫ م ة‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression) ‫اس‬2J‫أ‬
! " % " ‫! إام‬/ 9T‫( و‬SNA
‫ ص اد‬:‫ م وإ‬N‫ ! ا‬%U-‫ ‹ ! ا " ! وإا‬TERMINATE S :‫م ا‬9
3 ‫ ا‬S‫ ء و& اآ‬[email protected]‫ا‬
The TERMINATE Block:
TERMINATE
A
M "‫ ا‬P6
‫! ان‬/ 9‫ إ ري و‬2‫ وه‬0 & ,V‫ ا@;ا‬, :‫ ء وا‬[email protected]‫ ص اد ا‬:‫ار إ‬:
‫( أو‬PosInteger) S-2 a ' %J‫( أو ر‬Name) %‫( او إ‬Null) †T ‫ن‬2/9
‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression) ‫اس‬2J‫" ! أ‬I
(SNA*Parameter) %" ,9‫ د‬,`'
Example 1:
GENERATE 1
395
A
TERMINATE 1
GPSS 3; ‫ذج‬2 , `' 3; ‫ ا‬M‫أد‬
Create Simulation %X Command ‫ ا ر‬,?‫ ا‬, ? :‫! ا‬
396
]; a ' GPSS ,Y ‫ي‬2Y‫ ا‬S‫إذا آ ن اآ‬
! & ' ! f9T !/‫ي و‬2Y‫ ا‬S‫ اآ‬,6 ! a ' ] ‫ أن ا‬3"I Ready , ‫آ‬
! ] ‫اء ا‬-‫ إ‬MJ (,:7 ‫ ' & ا‬aV‫ ووا‬w 3 ‫" ا ] ا‬C) ,:7 ‫ ا‬,6 ‫ا‬
%X Window wYf ,?‫ ا‬, ? :‫ ! ا‬U M
3‫ وا‬S‫ا‬2:‫ة ا‬.; ,J‫ ا‬Mf;0‫ا‬
3 ‫ آ‬Blocks Window ‫ ر‬U ‫ و‬Simulation Window ‫إ ر‬
S‫ا‬2:‫ة ا‬.; UN;
397
START %X Command ,?‫ ا‬, ? :‫ ر ! ا‬g‫آ ة وذ‬
‫ي ا‬H ‫ن‬h‫ا‬
‫ار‬2 ‫ة ا‬.; UN;
398
TERMINATE S:‫ ا‬M /9 6 ‫آ ة‬
‫اء ا‬-‫ إ‬3"9 ‫ا‬.‫ ء وه‬[email protected]‫ "اد ا‬100 , :‫أد ا‬
9 M " 3?‫ا‬2O^ M/O 29 ‫ي‬.‫ وا‬GENERATE S : %‫ه‬2I %I M " 100 ‫ ء‬U‫إ‬
3; `I ‫آ ة وى‬
‫ى ا‬HI OK wYf .TERMINATE 3U9‫ م و‬N‫ ا‬3;
9:‫ ا‬UN9‫ م و‬N M " 100 ‫ ء ور‬U ‫آ ة‬
‫ ا‬3UI‫ و‬g‫ ذ‬%9 _‫ آ‬S‫ا‬2:‫ة ا‬.; .gI N6 ‫ ودون‬9:‫ة ا‬.; g.‫ وآ‬S‫ا‬2:‫ة ا‬.; “6T
2 ‫ل‬#
399
‫ا@ ار أو‬eI ‫ج‬. 9 ‫ي‬.‫ ا‬ADVANCE S J ,; V g‫ وذ‬J ‫ر ا [ ل ا‬27 ‫ف‬2
‫ أو‬,UI ‫ أو ز ! إ" ل‬, ! ‫ن ز‬2/I J ," ‫ `ة‬M " ‫ م‬N‫ء ! ا‬G- 3; ‫ث‬2/ ‫ا‬
U‫ م و‬N‫ ا‬3; ( ‫ء‬GH ‫ء‬G- ! ‫ ل‬:@‫ ز ! ا‬M[ I , ‫ ور ;ة ز‬w:; ‫ م أو‬N‫ ا‬3; ‫ن‬G
3 ‫ ا‬S‫اآ‬
The ADVANCE Block:
ADVANCE
A,B
:‫ ا" ل‬P6
‫( أو‬Name) %‫ن إ‬2/9 ‫! ان‬/ 9‫ و‬,9‫ور‬V 3‫ وه‬، ! G‫ ا‬w2 3; ‫ دة‬9G‫ا‬
A
Parenthesized ) ‫اس‬2J‫" ! أ‬I ‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫ر‬
%" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Expression
(SNA*Parameter)
‫ إ ري‬2‫ وه‬، ,‫ اا‬Y ‫ن‬2/; ,‫ إام دا‬, 6 3; ‫ ! او‬G‫ ل ا‬H _ B
‫وف‬6 ‫( او‬Number) %J‫( أو ر‬Name) %‫( او إ‬Null) †T ‫ن‬2/9 ‫! ان‬/ 9‫و‬
,9‫ د‬,`' ‫( أو‬Parenthesized Expression) ‫اس‬2J‫" ! أ‬I ‫( أو‬String)
(SNA*Parameter) %" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N
Example 2:
GENERATE 1
ADVANCE
TERMINATE
5
1
‫ ا ] ا‬3; ‫ا‬.‫ ه‬M
400
‫‪%X‬‬
‫و‪ , -I %I‬ا ‪2‬ذج‬
‫‪.; T‬ة ا‪2:‬ا‪ S‬و ‪-‬اء ا‬
‫آ ة ‪]9 START 100 RV2‬‬
‫‪401‬‬
.ADVANCE S :‫! ا‬9e 2‫زا‬T 5 %U ‫ م‬N ‫ و‬M " 105 2I %I &‫“ أ‬6T
.gI N6 ‫ ا "! ودون‬M/O‫أدرس ا‬
402
3 ‫ل‬#
! g‫ وذ‬ADVANCE S : ! " ‫ إام ا‬UN P
‫ر ا [ ل ا‬27 ‫ف‬2
ADVANCE S : ,[ ‫ ا‬,U‫ ا‬MY‫ أو أ‬g ‫ أو ا‬%‫ أ‬3"I‫ و‬SEIZE ! :‫ ا‬9C
S : ,[ ‫ ا‬,U‫ك أو أ;غ أو ^ در ا‬I‫ أ‬3"9 ‫ي‬.‫ وا‬RELEASE ‫ و‬S :‫وا‬
:3 ‫ ا‬S‫ اآ‬%U‫ و‬ADVANCE
The SEIZE Block:
SEIZE
A
:M "‫ ا‬P6
‫( أو‬Name)
%‫ن إ‬2/9 ‫! ان‬/ 9‫وري و‬V 2‫ وه‬Facility ,U‫ ا‬%‫ او إ‬%J‫ر‬
A
Parenthesized ) ‫اس‬2J‫" ! أ‬I ‫( أو‬PosInteger) S-2 a ' %J‫ر‬
%" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Expression
(SNA*Parameter)
The RELEASE Block:
RELEASE A
:M "‫ ا‬P6
‫( أو‬Name) %‫ن إ‬2/9 ‫! ان‬/ 9‫وري و‬V 2‫ وه‬Facility ,U‫ ا‬%‫ او إ‬%J‫ر‬
Parenthesized ) ‫اس‬2J‫" ! أ‬I ‫( أو‬PosInteger) S-2 a ' %J‫ر‬
%" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Expression
(SNA*Parameter)
403
A
‫! إام‬/ 9T‫ و‬Uf" R ,-‫او‬G 3IeI RELEASE ‫ و‬SEIZE ‫“ أن‬6T :#‫; ه‬r#
‫ آ‬ADVANCE ‫ أي‬,U‫ ا‬M[ 9 ‫ي‬.‫ ا‬S :‫ ا‬SEIZE I ‫ ان‬SH9 &‫ آ ا‬h‫ه دون ا‬6‫أ‬
ADVANCE ‫ أي‬,U‫ ا‬M[ 9 ‫ي‬.‫ ا‬S :‫ ا‬RI ‫ أن‬SH9 RELEASE ‫ان‬
Example 3:
GENERATE 1
SEIZE
ADVANCE
RELEASE
TERMINATE
Server
5
Server
1
,; [email protected]‫ ا‬S‫ا‬2:‫ ا‬M
S‫ا‬2:‫ة ا‬.; UN‫ ا ] و‬%-
404
]9‫ و‬START 100 ‫آ ة آ‬
405
‫ي ا‬H
6 GENERATE
S :‫ ا‬,7‫ا‬2 !92 ‫ل ا " ! ا‬2‫ د‬R SEIZE S :‫“ أن ا‬6T
S :‫ ا‬9 %6‫ا‬GI S
& 9 M " ‫ ! أي‬ADVANCE S :‫ إ;اغ ا‬%9
‫ة‬.; 3; GENERATE S J ! ‫ إ ا ر‬60‫ر ا‬2 7‫ ا‬, “6T) GENERATE
S :‫“ ان ا‬6T f9‫ ر( ا‬[email protected]‫ ا‬3; M " 400 & -29 GENERATE S :‫ آ أن ا‬S‫ا‬2:‫ا‬
.,U‫م م ا‬2:9 6‫ وا‬M " & -29 SEIZE
‫ رن‬J‫ و‬, ‫ ا‬, :‫ ! ا‬Y'‫ أ‬%: ADVANCE S :‫ ا‬3; A M "‫ ا‬, J ! ^ :4
.]? ‫ا‬
406
4 ‫ل‬#
‫? ت‬
6‫ إ‬R H ,2‫ ا‬3‫ ; ه‬، ,U ‫ ر‬N‫ إ‬w ‫ر أو‬2 C ‫ن‬2/I ‫ ا [ ل ا‬3; “6
MH ‫أ‬9 ‫ي‬.‫ و ا‬QUEUE ‫! ه‬-‫او‬G ! J -29 ‫ض‬Y‫ا ا‬.U ‫ر؟‬2 7‫ا ا‬.‫! ه‬
MHI 3U9 ‫ي‬.‫ و ا‬DEPART S :‫ ر وا‬[email protected]‫ر ا‬2 C ‫ إ‬M " ‫ل‬2‫? ت د‬
[email protected]‫ا‬
3 ‫ ا‬S‫ اآ‬U‫ ر و‬[email protected]‫ر ا‬2 C ! M " ‫? ت وج‬
[email protected]‫ا‬
The QUEUE Block:
QUEUE
A,B
:‫ ا" ل‬P6
%J‫( أو ر‬Name)
%‫ن إ‬2/9 ‫! ان‬/ 9‫وري و‬V 2‫ وه‬، ‫ر‬2 7‫ ا‬%‫ أو إ‬%J‫ر‬
A
‫( أو‬Parenthesized Expression) ‫اس‬2J‫" ! أ‬I ‫( أو‬PosInteger) S-2 a '
(SNA*Parameter) %" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`'
‫ إ ري‬2‫ وه‬1 ,V‫ & ا@;ا‬J‫ر و‬2 7‫ل ا‬2C U 9G9 3‫ات ا‬62‫د ا‬
B
(PosInteger) S-2 a ' %J‫( أو ر‬Name) %‫( او إ‬Null) †T ‫ن‬2/9 ‫! ان‬/ 9‫و‬
(SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression ) ‫اس‬2J‫" ! أ‬I ‫أو‬
(SNA*Parameter) %" ,9‫ د‬,`' ‫أو‬
The DEPART Block:
DEPART A,B
:‫ ا" ل‬P6
%J‫( أو ر‬Name)
%‫ن إ‬2/9 ‫! ان‬/ 9‫وري و‬V 2‫ وه‬، ‫ر‬2 7‫ ا‬%‫ أو إ‬%J‫ر‬
(Parenthesized Expression) ‫اس‬2J‫" ! أ‬I ‫( أو‬PosInteger) S-2 a '
(SNA*Parameter) %" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫أو‬
407
A
‫إ ري‬
2‫ وه‬1 ,V‫ & ا@;ا‬J‫ر و‬2 7‫ل ا‬2C U ‹:9 3‫ات ا‬62‫د ا‬
B
S-2 a ' %J‫( أو ر‬Name) %‫( او إ‬Null) †T ‫ن‬2/9 ‫! ان‬/ 9‫و‬
,`' ‫( أو‬Parenthesized Expression ) ‫اس‬2J‫" ! أ‬I ‫( أو‬PosInteger)
(SNA*Parameter) %" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫د‬
‫! إام‬/ 9T‫ و‬Uf" R ,-‫او‬G 3IeI DEPART ‫ و‬QUEUE ‫“ أن‬6T :#‫; ه‬r#
SEIZE ‫ أي‬,U‫ إم ا‬M[ 9 ‫ي‬.‫ ا‬S :‫ ا‬QUEUE I ‫ ان‬SH9 &‫ا‬
‫ آ‬h‫ه دون ا‬6‫أ‬
_J29 3‫ ا‬,7:‫ د ا‬9 DEPART S :‫ ا‬RV2 ,:: ‫ ا‬3; ،&"I ‫ أن‬SH9 DEPART ‫آ ان‬
! ‫ب‬27 ‫ ا‬U"J2 "9‫ و‬QUEUE S :‫ل ا‬2‫ د‬,N ! ‫ ر‬[email protected]‫ ز ! ا‬MHI U;
.‫ م‬N‫ذج أو ا‬2 ‫ا‬
‫ر‬2 7‫ ت ! ا‬2" R - ! / 9 ‫ ] ا‬927I 3 ‫ا‬
‫ة‬.; ‫ آ‬U M
‫ و‬,U‫ة ا‬.; I ‫ة‬9- ‫ة‬.; ‫م‬: ‫ف‬2 !/‫ي ا ] و‬H‫ و‬%-
I S‫ا‬2:‫ا‬
UN;
408
‫‪ “6T‬ا& ‪ UN9T‬أي † ;‪.; 3‬ة ا‪ MJ ,U‬إ‪-‬اء ا‬
‫;]‬
‫ ;‪.‬ة ا‪2:‬ا‪:S‬‬
‫ ;‪.‬ة ا‪U‬ت‪:‬‬
‫ ;‪.‬ة ا‪:9:‬‬
‫‪409‬‬
‫آ ة ;"‪ ،‬ا‪h‬ن ر ‪START 100‬‬
‫‪ “6T‬أن ا‪2 7‬ر ‪ M/OI‬ا‪ QUEUE S :‬وا‪ WU‬ا‬
‫آ ة وا‪2 7‬ر ‪2 9‬ي ‪400‬‬
‫" ‪ “6T M‬ان ;" ‪ ,‬ا‪ ,U‬ه‪ 0.998 3‬وه‪- , 3‬ا و‪ ˆ/"I‬ي إ‪ YO‬ل ا‪ ,U‬آ‬
‫أن ا‪2 7‬ر و'‪ &2C M‬ا‪ J0‬إ ‪ .M " 402‬أ‪ N‬إ ا‪ 9:‬و ;‪ 3I.‬ا‪2:‬ا‪S‬‬
‫وا‪U‬ت و ‪ ،gI N6 MH‬أ‪-‬ي ‪ HI‬رب ا ‪2‬ذج وذ‪S J %" Y g‬‬
‫‪ ADVANCE‬و‪ “6T‬ذا ‪ 9‬ث‪.‬‬
‫‪410‬‬
‫‪#‬ل ‪5‬‬
‫‪27‬ر ا [ ل ا د ل ‪2O‬ا?‪ ,‬ا‪ N‬م وذ‪ M"H g‬أز ‪,‬‬
‫! ا‪ RI 2‬ا‪2‬ز‪R9‬‬
‫) (‬
‫ا وي ! ‪ 3‬و ‪ 7‬أو ‪ U 3,7‬و‪I 3; U G 9‬آ‪ GPSS S‬آ ‪5 P6 5 ± 2 3‬‬
‫‪ w2‬ز !‬
‫! ا‪ 2‬و ‪ H _ 2‬ل ز !‬
‫! ا‪ 2‬و‪ S J S/9‬ا‪ 2‬آ ‪3‬‬
‫‪5,2‬‬
‫أ‪ M"H f9‬ز ! ا‪2O e‬ا?‪ R9 3‬ا‪2‬ز‪ R9‬ا‬
‫‪GENERATE‬‬
‫ وي ‪4 ± 1‬‬
‫‪4,1‬‬
‫و‪ a 9‬ا‪S :‬‬
‫‪ADVANCE‬‬
‫‪H‬ي ه‪.‬ا ا"‪ M9‬ا ] ا ‬
‫‪ %-‬ا ] و‪2 UN‬ا;‪ .‬ا‪2:‬ا‪ S‬وا‪U‬ت آ ‪:‬م ;‪.‬ة ‪9-‬ة ه‪.; 3‬ة ا‪27‬ا ‬
‫و‬
‫‪ U M‬آ ‪ 6‬ا‪2‬ا;‪ .‬ا ‪,:‬‬
‫و‪H‬ي ا‬
‫آ ة ;]‬
‫ ;‪.‬ة ا‪2:‬ا‪:S‬‬
‫‪411‬‬
‫ ;‪.‬ة ا‪U‬ت‪:‬‬
‫ ;‪.‬ة ا‪27‬ا ‪:‬‬
‫ ;‪.‬ة ا‪:9:‬‬
‫‪9 :4‬ك ‪ `I S 7‬ا ?]‪.‬‬
‫‪412‬‬
6 ‫ل‬#
0 g‫ ذ‬%9‫ م و‬N‫ '` ت ا‬60 ‫اري‬/I R9‫ز‬2I ‫ول‬- ‫ن‬2/ P
‫ر ا [ ل ا‬27
The TABLE Command:
NAME
TABLE
A,B,C,D
%‫ن إ‬2/9 ‫ أن‬SH9‫ و‬5‫د‬2-‫وري و‬V‫ول و‬H %‫ او إ‬, NAME P6
:M ‫ا‬2"‫ا‬
‫وري‬V
2‫ وه‬U‫و‬- ‫اد‬9 3‫ ا ت ا‬%: G ‫ أو ر‬%‫ إ‬2‫ول وه‬H‫ ا‬,H6
A
! "I ‫( أو‬String) ‫وف‬6 ‫( او‬Number) %J‫( أو ر‬Name) %‫ن إ‬2/9 ‫! ان‬/ 9‫و‬
(SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression) ‫اس‬2J‫أ‬
%J‫ن ر‬2/9 ‫ ان‬SH9‫وري و‬V 2‫و وه‬T‫ ا‬,b` 0‫ا ا‬
B
%J‫ن ر‬2/9 ‫ ان‬SH9‫وري و‬V 2‫ ت وه‬b`‫ ا‬%H6
C
S-2 a ' %J‫ن ر‬2/9 ‫ ان‬SH9‫وري و‬V 2‫—ت وه‬b`‫د ا‬
D
U‫و‬-‫ و‬, ‫ ا ت از‬R H "; ‫م‬2:9 ‫ي‬.‫ ا‬TABULATE S :‫ ا‬TABLE 0‫ ا‬R 3Ie9
S :‫ ا‬. U" H ,J & ˆ‫ول و‬H‫! ا‬92/I‫ و‬M/ ,`‫ آ‬w:; 37"9 TABLE 0‫ ا‬P6
S‫ & اآ‬TABULATE
The TABULATE Block:
TABULATE
A,B
:‫ ا" ل‬P6
a ' %J‫( أو ر‬Name) %‫ن إ‬2/9 ‫! ان‬/ 9‫وري و‬V 2‫ & وه‬J‫ول أو ر‬H‫ ا‬%‫إ‬
,`' ‫( أو‬Parenthesized Expression ) ‫اس‬2J‫" ! أ‬I ‫( أو‬PosInteger) S-2
413
A
(SNA*Parameter) %" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫د‬
‫( أو‬Number) %J‫( أو ر‬Name) %‫( او إ‬Null) †T ‫ن‬2/9 ‫! ان‬/ 9‫زن و‬2‫ ا‬M B
‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬Parenthesized Expression )‫اس‬2J‫" ! أ‬I
(SNA*Parameter) %" ,9‫ د‬,`'
2‫ وه‬Transit Time ‫ ل‬:@‫ أو ز ! ا‬M1 ‫ م‬N‫ ا‬3; ‫ث‬2/ ‫ ! ا‬G ‫اري‬/‫ ا‬R9‫ز‬2‫ن ا‬h‫ ا‬-2
M " M/ , J U -2I ‫ م‬N ,9‫ د‬,`'
U M
‫ول و‬H‫ة ا‬.; I ‫ة‬9- ‫ة‬.; ‫م‬: ‫ف‬2 w:; ] ‫ا ا‬.‫اء ه‬[email protected] ‫ ا " د‬R
.;‫ا‬2‫ ا‬,:‫آ‬
‫! إ ره‬/ ‫اول ا‬H‫ ء ا‬e , ? J ‫ ره‬3; g7"I ‫ة‬.; ‫ ا‬5.‫ى ان ه‬
414
‫‪ “6T‬ا& ‪- -29‬ول وا‪ w:; 6‬ه‪ TTime 2‬وه‪ 2‬ا‪.‬ي ‪ %9‬إ ر‪ UN; "C 5‬ا ;‪.‬ة‬
‫‪ “6T‬ا‪.; U‬ة ر‪%‬‬
‫‪H‬ي ا‬
‫آ ة ‪]; START 500 R‬‬
‫ ;‪.‬ة ا‪2:‬ا‪:S‬‬
‫‪415‬‬
‫ ;‪.‬ة ا‪U‬ت‪:‬‬
‫ ;‪.‬ة ا‪27‬ا ‪:‬‬
‫ ;‪.‬ة ا‪H‬اول‪:‬‬
‫‪ “6T‬ا& ] رج ‪/I‬اري ‪ ! G‬ا ور ‪ N‬م‪.‬‬
‫ا‪9:‬‬
‫‪416‬‬
FACILITY
DELAY
SERVER
0
ENTRIES
500
UTIL.
AVE. TIME AVAIL. OWNER PEND INTER RETRY
0.798
3.991
1
0
0
QUEUE
RETRY
LINE
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
TABLE
CUM.%
TTIME
MEAN
STD.DEV.
4.231
0.772
1
0
500
366
0.048
RANGE
0.239
0
0
AVE.(-0)
0.892
RETRY FREQUENCY
0
3.000
-
4.000
202
4.000
-
5.000
243
5.000
-
6.000
45
6.000
-
7.000
9
7.000
-
8.000
1
40.40
89.00
98.00
99.80
100.00
.]? ‫` ا‬I S 7 ‫ك‬9 :!9 I
417
7 ‫ل‬#
&‫ر و‬2 7‫ ا‬, ‫ز‬0 ‫اري‬/‫ ا‬R9‫ز‬2‫ول ا‬H9 ‫ي‬.‫ وا‬QTABLE 0‫ا ا [ ل ا‬.‫ ه‬3; ‫م‬: ‫ف‬2
S‫اآ‬
The QTABLE Command:
NAME
QTABLE
A,B,C,D
%‫ن إ‬2/9 ‫ أن‬SH9‫ و‬5‫د‬2-‫وري و‬V‫ول و‬H %‫ او إ‬, NAME P6
:M ‫ا‬2"‫ا‬
a ' %J‫( أو ر‬Name) %‫ن إ‬2/9 ‫! ان‬/ 9‫وري و‬V 2‫ر وه‬2 7‫ ا‬%‫إ‬
A
(PosInteger)
%J‫ن ر‬2/9 ‫ ان‬SH9‫وري و‬V 2‫و وه‬T‫ ا‬,b` 0‫ا ا‬
B
%J‫ن ر‬2/9 ‫ ان‬SH9‫وري و‬V 2‫ ت وه‬b`‫ ا‬%H6
C
S-2 a ' %J‫ن ر‬2/9 ‫ ان‬SH9‫وري و‬V 2‫—ت وه‬b`‫د ا‬
D
‫ [ ا‬3; 0‫ا ا‬.‫ب ه‬H ‫ف‬2
TTime
QTime
TABLE
QTABLE
GENERATE
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TABULATE
TERMINATE
M1,1,1,10
Line,1,1,10
5,2
Line
Server
Line
4,1
Server
TTime
1
3 ‫ر آ‬2 7‫ول ا‬- ‫ة‬.; N‫ا‬
418
‫‪.; ! %X‬ة ا ‪2‬ار‬
‫‪ “6T‬ان ه‪ 5.‬ا ;‪.‬ة ‪ 7"I‬إ ‪ , /‬إ ر أي ‪-‬ول و‬
‫‪ UNI‬ا ;‪.‬ة‬
‫أد‪ M‬ه‪.‬ا ا ] وأ‪ 5-‬ـ ‪START 500‬‬
‫‪419‬‬
‫ ر ‪Qtime‬‬
‫ر‬2 7‫ول ا‬- UN9‫ ا [ ل ا و‬3; ‫ آ‬3‫ى ه‬T‫ ت ا‬-‫ ا ا‬R -
9:‫وا‬
FACILITY
DELAY
SERVER
0
ENTRIES
500
UTIL.
AVE. TIME AVAIL. OWNER PEND INTER RETRY
0.798
3.991
1
0
0
QUEUE
RETRY
LINE
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
TABLE
CUM.%
TTIME
MEAN
STD.DEV.
4.231
0.772
1
0
500
366
0.048
RANGE
0.239
0
0
AVE.(-0)
0.892
RETRY FREQUENCY
0
3.000
-
4.000
202
4.000
-
5.000
243
5.000
-
6.000
45
6.000
-
7.000
9
7.000
-
8.000
1
_
-
1.000
454
1.000
-
2.000
35
40.40
89.00
98.00
99.80
100.00
QTIME
0.239
0.524
0
90.80
97.80
420
2.000
-
3.000
10
3.000
-
4.000
1
99.80
100.00
.]? ‫` ا‬I S 7 ‫ك‬9 :!9 I
421
8 ‫ل‬#
‫ول‬- 3; P ‫ ا‬,:9C ‫"ف‬9 ‫ي‬.‫ وا‬FUNCTION 0‫ا ا [ ل ا‬.‫ ه‬3; ‫ف "ض‬2
S‫ اآ‬U‫ول و‬- M/ 7" 3 R9‫ز‬2I ! ,9 " ‫م‬I‫و‬
The FUNCTION Command:
NAME
FUNCTION
A,B
‫ ا" ل‬P6
S-2 a ' %J‫( أو ر‬Name) %‫ن إ‬2/9 ‫! ان‬/ 9‫ و‬,9‫ور‬V 3‫ وه‬,‫ اا‬,H6
A
Parenthesized Expression ) ‫اس‬2J‫" ! أ‬I‫( أو‬String) ‹ ‫( أو‬PosInteger)
(SNA*Parameter) %" ,9‫ د‬,`' ‫( أو‬SNA) ‫ م‬N ,9‫ د‬,`' ‫( أو‬
2‫ وه‬,‫ اا‬3; ‫ر "د أزواج ا ت‬2`‫ ا‬R9 (6‫ف وا‬6) ,‫ع اا‬2
B
‫وري‬V
:‫اع اوال‬2‫أ‬
‫ع‬2 ! ,‫"ف دا‬9‫( و‬Continuous)
C
R7: ‫ع‬2 ! ,‫"ف دا‬9‫( و‬Discrete)
D
,`'‫ و‬,‫"ف دا‬9 (Discrete Attribute)
E
, ? J ‫ع‬2 ! ,‫( دا‬List)
L
‫ '` ت‬, ? J ‫ع‬2 ! ,‫( دا‬List Attribue)
M
.‫[ ل‬
U ‫ق‬7‫ع ا‬2 M‫ح آ‬O ‫ف‬2‫و‬
Single Channel Queue
)‫ اا‬9‫ ر ا‬C
U M `9 3?‫ا‬2O M/O R;‫ ا‬,7: ‫ ?! إ‬G‫ ا‬M 9 .6‫ وا‬S
ˆ` U ‫ل‬2'‫! و‬
& Y' , : M
, ‫ز‬0‫ ا‬5.‫ ? وه‬J‫ د‬8 ‫ و‬1 ! Interarrival times ‫ل‬2'‫! و‬
, ‫أز‬
:3 ‫ول ا‬H‫ ا‬3; ‫ ل آ‬[email protected]‫ا‬
:‫ل‬2'2‫! ا‬
Time between
422
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Arrivals
(Minutes)
Cumulative
Probability
Probability
1
0.125
0.125
2
0.125
0.250
3
0.125
0.375
4
0.125
0.500
5
0.125
0.625
6
0.125
0.750
7
0.125
0.875
8
0.125
1.000
:3 ‫ول ا‬H‫ ا‬3; ‫ت آ‬T 6 ? J‫ د‬6 ‫ و‬1 !
423
‫اوح‬I Sevice times , ‫ ا‬, ‫أز‬
:, ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
Cumulative
(Minutes)
Probability
Probability
1
0.10
0.10
2
0.20
0.30
3
0.30
0.60
4
0.25
0.85
5
0.10
0.95
6
0.05
1.00
. 2 ‫ ز‬500 , ‫ل و‬2'‫آ ة و‬
,‫ دا‬M/ ‫ل‬2'2‫! ا‬
IAT
‫ م‬N‫ ا‬M I ‫ب‬27 ‫ا‬
, ‫ أز‬R9‫ز‬2I ‫ول‬- Rf ‫ف‬2
FUNCTION RN1,D8
0.125,1/0.25,2/0.375,3/0.5,4/0.625,5/0.75,6/0.875,7/1.0,8
:“6T
IAT 2‫ ه‬,‫ اا‬%‫( إ‬1
‫ا‬2 16 ‫ي‬2 9 GPSS ‫“ ان‬6T) GPSS 3; ‫ول‬0‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬2 2‫ ه‬,‫ اا‬,H6 (2
(RN16 6‫ و‬RN1 ! ,?‫ا‬2O"‫ م ا‬J‫ر‬q
‫ أزواج ! ا ت‬8 ‫ي‬2 9‫ و‬R7: ,‫ع اا‬2 (3
M/O‫ ا‬SII‫ و‬7‫ اول ا‬3; ‫ك ;اغ‬I ‫ و ون‬M ` 7 3; ‫زواج‬0‫ ا‬MI (4
Y ‫ ا‬, J 3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ دا‬, J F(x) P6 F(x1),x1/F(x2),x2/…/F(xn),xn
X=x 3?‫ا‬2O"‫ا‬
,‫ دا‬M/ , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬- Rf M[ STime FUNCTION RN1,D6
0.1,1/0.3,2/0.6,3/0.85,4/0.95,5/1.0,6
424
‫ر ا ] ا‬27‫و‬
TTime
TABLE
M1,1,1,10
QTime QTABLE
Line,1,1,10
IAT
FUNCTION
RN1,D8
0.125,1/0.25,2/0.375,3/0.5,4/0.625,5/0.75,6/0.875,7/1.0,8
STime
FUNCTION
RN1,D6
0.1,1/0.3,2/0.6,3/0.85,4/0.95,5/1.0,6
GENERATE
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TABULATE
TERMINATE
FN$IAT
Line
Server
Line
FN$STime
Server
TTime
1
‫ل‬2'‫! و‬
GENERATE
, ‫ أز‬2I 3; !‫“ آ_ ا اا‬6T
FN$IAT
S J 3; , ‫ ا‬, ‫ز‬0 †O‫ ;" `ˆ ا‬g.‫ وآ‬FN$ ,‫ اا‬G 5 :‫ و‬IAT ,‫ اا‬%‫ إ‬.‫ا‬
‫ ة‬500 &9H‫ ا ] و‬M ADVANCE
:]? ‫وا‬
S‫ا‬2:‫ة ا‬.; ‫ت‬U‫ة ا‬.; 425
‫ا‬27‫ة ا‬.; ‫ر‬2 7‫ول ا‬- ‫ة‬.; 9:‫ا‬
FACILITY
DELAY
SERVER
0
ENTRIES
501
UTIL.
AVE. TIME AVAIL. OWNER PEND INTER RETRY
0.749
3.232
1
501
0
QUEUE
RETRY
LINE
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
TABLE
CUM.%
TTIME
MEAN
STD.DEV.
5.438
3.513
6
1
501
229
0.509
RANGE
2.196
0
0
AVE.(-0)
4.044
RETRY FREQUENCY
0
_
-
1.000
30
1.000
-
2.000
48
2.000
-
3.000
76
3.000
-
4.000
85
4.000
-
5.000
68
6.00
15.60
30.80
47.80
61.40
426
‫‪52‬‬
‫‪6.000‬‬
‫‪-‬‬
‫‪5.000‬‬
‫‪43‬‬
‫‪7.000‬‬
‫‪-‬‬
‫‪6.000‬‬
‫‪30‬‬
‫‪8.000‬‬
‫‪-‬‬
‫‪7.000‬‬
‫‪13‬‬
‫‪9.000‬‬
‫‪-‬‬
‫‪8.000‬‬
‫‪-‬‬
‫‪9.000‬‬
‫‪284‬‬
‫‪1.000‬‬
‫‪-‬‬
‫_‬
‫‪51‬‬
‫‪2.000‬‬
‫‪-‬‬
‫‪1.000‬‬
‫‪46‬‬
‫‪3.000‬‬
‫‪-‬‬
‫‪2.000‬‬
‫‪37‬‬
‫‪4.000‬‬
‫‪-‬‬
‫‪3.000‬‬
‫‪24‬‬
‫‪5.000‬‬
‫‪-‬‬
‫‪4.000‬‬
‫‪17‬‬
‫‪6.000‬‬
‫‪-‬‬
‫‪5.000‬‬
‫‪9‬‬
‫‪7.000‬‬
‫‪-‬‬
‫‪6.000‬‬
‫‪6‬‬
‫‪8.000‬‬
‫‪-‬‬
‫‪7.000‬‬
‫‪8‬‬
‫‪9.000‬‬
‫‪-‬‬
‫‪8.000‬‬
‫‪-‬‬
‫‪9.000‬‬
‫‪71.80‬‬
‫‪80.40‬‬
‫‪86.40‬‬
‫‪89.00‬‬
‫_‬
‫‪55‬‬
‫‪3.227‬‬
‫‪0‬‬
‫‪2.200‬‬
‫‪100.00‬‬
‫‪QTIME‬‬
‫‪56.80‬‬
‫‪67.00‬‬
‫‪76.20‬‬
‫‪83.60‬‬
‫‪88.40‬‬
‫‪91.80‬‬
‫‪93.60‬‬
‫‪94.80‬‬
‫‪96.40‬‬
‫‪18‬‬
‫_‬
‫‪100.00‬‬
‫‪:!9 I‬‬
‫‪9‬ك ‪ S 7‬إاج ‪ ˆ9 :‬ا‪0‬داء ! ا ‪ -‬ت‬
‫‪427‬‬
9 ‫ل‬#
^ M/O ( S J ‫ إ‬S J ! ‫ ل‬:@‫ وا‬S"O‫ ا‬,`‫ف "ض آ‬2 ‫ا ا [ ل‬.‫ ه‬3;
S J ‫ ل إ‬:@‫ ا‬wO‫ ا‬M " S9 ‫ي‬.‫ وا‬TRANSFER S :‫ف "ض ا‬2 ،M
S‫ و& اآ‬," ‫ وط‬W I 3 ‫ ا‬S :‫ ا‬R9T (
The TRANSFER Block:
TRANSFER
A,B,C,D
‫ ا" ل‬P6
‫ او‬BOTH ‫ن‬2/9 ‫ ان‬SH9‫ إ ري و‬2‫ وه‬:6T &` ‫ف‬2‫ ل و‬:@‫ ا‬S J ‫ر‬2C
A
a ' ‫ او د‬Name %‫ أو إ‬fraction ‫ او آ‬SBR ‫ او‬P ‫ او‬FN ‫ او‬PICK ‫ او‬ALL
,9‫ د‬,`' ‫ او‬ParenthesizedExpression ‫اس‬2J‫" ! أ‬I ‫ او‬PosInteger S-2
SNA*Parameter %" ,9‫ د‬,`' ‫ او‬SNA ‫ م‬N
‫ن‬2/9 ‫ ان‬SH9‫ إ ري و‬2‫ وه‬P ‫ر‬27‫ أو ا‬,‫ دا‬3; ‫ دة‬9G‫ار ا‬: ‫ ن أو‬/ ‫ أو‬S J %J‫ر‬
B
‫اس‬2J‫" ! أ‬I ‫ او‬PosInteger S-2 a ' ‫ او د‬Name %‫ او إ‬Null ‫إ‬
%" ,9‫ د‬,`' ‫ او‬SNA ‫ م‬N ,9‫ د‬,`' ‫ او‬ParenthesizedExpression
SNA*Parameter
‫ن‬2/9 ‫ ان‬SH9‫ إ ري و‬2‫ وه‬P ‫ر‬27‫ أو ا‬,‫ دا‬3; ‫ دة‬9G‫ار ا‬: ‫ ن أو‬/ ‫ أو‬S J %J‫ر‬
C
‫اس‬2J‫" ! أ‬I ‫ او‬PosInteger S-2 a ' ‫ او د‬Name %‫ او إ‬Null ‫إ‬
%" ,9‫ د‬,`' ‫ او‬SNA ‫ م‬N ,9‫ د‬,`' ‫ او‬ParenthesizedExpression
SNA*Parameter
‫ن‬2/9 ‫ ان‬SH9‫ إ ري و‬2‫ وه‬1 ,V‫ & ا@;ا‬J‫ و‬ALL ‫ر‬27 ‫ ن‬/ ‫ أو‬S J %J‫ر‬
D
‫اس‬2J‫" ! أ‬I ‫ او‬PosInteger S-2 a ' ‫ او د‬Name %‫ او إ‬Null ‫إ‬
%" ,9‫ د‬,`' ‫ او‬SNA ‫ م‬N ,9‫ د‬,`' ‫ او‬ParenthesizedExpression
SNA*Parameter
TRANSFER S :‫ار ا‬2C‫أ‬
g‫ وذ‬B M " ‫د‬
S J ‫وط إ‬O ‫ ل ^ ا‬:@‫! ! ا‬/ 9‫و‬
M[ A M "‫^` ل ا‬
428
3CO‫ر ^ ا‬27‫ا‬
TRANSFER
,NewPlace
‫ر‬2C 3; M "9 S :‫ا ا‬.‫ ;ن ه‬3 ‫ ^ أ‬A M " ‫ن ا‬2/9 ‫ي‬/‫ر ا‬27‫ا‬
[ ; /‫ا‬
TRANSFER 0.75,,NewPlace
! 75% 3; S‫ه‬.9 S :‫ا ا‬.‫ ه‬M9 ‫ي‬.‫ ا‬wO‫ ا‬M " ‫;ن ا‬
NewPlace G %" ‫ ا‬S :‫ت إ ا‬T ‫ا‬
wO‫ ا‬M " ‫ ;ن ا‬BOTH , /‫ ا‬2‫ ه‬A M " ‫ن ا‬2/9 BOTH ‫ر‬2C
% ‫ ;ن‬B M " ‫ ا‬3; 5G ‫ ر‬-29 ‫ي‬.‫ ا‬S :‫ل إ ا‬2‫ ول ا‬9
M " ‫ ا‬3; 5G ‫ ر‬-29 ‫ي‬.‫ ا‬S :‫ل إ ا‬2‫ ول ا‬9 g‫ ذ‬R79
! !/ 9 6 ! :‫! ا‬9.‫ ه‬R ,‫و‬
‫" ا‬9 g‫ ذ‬R79 % ‫ ;ن‬C
M9 U2‫! د‬/ 9 ! :‫ن آ ! ا‬2‫ آ‬, 6 3;‫ه و‬6‫ل ا‬2‫د‬
M[ B M "‫ ا‬3; 5G ‫ي ر‬.‫ ا‬S :‫ا‬
TRANSFER BOTH,FirstPlace,SecondPlace
FirstPlace G ‫ ا‬S :‫ل إ ا‬2‫ ا‬wO‫ ا‬M " ‫ ا‬M"H9 ‫ا‬.‫وه‬
‫ ;ن‬SecondPlace G ‫ ا‬S :‫ل إ ا‬2‫ ول ا‬9 !/ 9 % ‫;ن‬
&/ I , 6 3;‫ا و‬./‫ول وه‬0‫ ا‬S : ‫ل‬2 ,‫و‬
‫" ا‬9 !/ 9 %
FirstPlace G ‫ ا‬S : ,f;0‫ن ا‬2/I %U ‫ي‬0 ‫ل‬2
‫ ل‬:‫ إ‬, / @ S‫ا‬2:‫ إ ر د آ ! ا‬%9 ‫ر‬27‫ا ا‬.‫ ه‬3;
ALL ‫ر‬2C
‫ (ه‬g.‫ وآ‬G S‫ا‬2:‫ ا‬5.‫ أول ه‬G 9‫ و‬U‫ إ‬wO‫ ا‬M " ‫ا‬
‫ن‬2/I‫ل إ& و‬2 S‫ا‬2:‫ ا‬5.‫ ه‬6‫ أ‬a 9 6 U ‫ ل‬:@‫ ا‬%9‫و‬
[ ; S‫ا‬2: 3" ‫ ا‬SI‫ ا‬S6 ,f;0‫ا‬
TRANSFER ALL,FirstPlace,LastPlace,2
‹ `9 &2‫ر د‬G"I ‫ ;ن‬FirstPlace G ‫ ا‬S :‫ إ ر ا‬%9
6 ‫ا‬./‫( وه‬D M "‫ ن ا‬/ 3; 2 “6T) ! : &9 ‫ي‬.‫ ا‬S :‫ا‬
‫ل‬2‫ ا‬, / ‫ و " ; ‹ إ‬LastPlace G G ‫ ا‬S :‫ ا‬M ‫ا‬./‫ول وه‬0‫ ا‬S :‫ ! ا‬,‫و‬
‫" د ا` ‹ وا‬9 T ‫ا& أم‬
‫ ل‬:‫ إ‬, / @ S‫ا‬2:‫ إ ر د آ ! ا‬%9 ‫ر‬27‫ا ا‬.‫ ه‬3;
‫ (ه‬g.‫ وآ‬G S‫ا‬2:‫ ا‬5.‫ أول ه‬G 9‫ و‬U‫ ا‬wO‫ ا‬M " ‫ا‬
S‫ا‬2:‫ ا‬5.‫ ه‬6‫ أ‬a 9 6 3?‫ا‬2O M/O U ‫ ا@ ر‬%9‫و‬
429
PICK ‫ر‬2C
[ ; ?‫ا‬2O 5‫ إ ر‬%I S J ‫ول‬0 ,f;0‫ن ا‬2/I‫ل إ& و‬2
TRANSFER PICK,FirstPlace,LastPlace
S :‫ وا‬FirstPlace G ‫ ا‬S :‫ا? ! ا‬2O S J ‫ إ ر‬%9
g. a 9 S J ‫ل اول‬2‫ د‬%9‫ و‬LastPlace G ‫ا‬
‫ د‬I ,‫ دا‬%:I ! ‫ ر‬9 S J ‫ ل إ‬:@‫ ا‬%9 ‫ر‬27‫ا ا‬.‫ ه‬3;
FN ,‫ر اا‬2C
[ ; C M " ‫ د‬9 ‫ دة إ ري‬9‫ار ز‬: ,; V‫ وإ‬B M "
TRANSFER FN,Function1,5
&‫ إ‬M:9 ‫ي‬.‫ ا‬S :‫ ا‬9 5 U‫ ف إ‬f9‫ و‬Function1 ,‫ر اا‬:I
R H &"J2 ‫ د‬9 S J ‫ إ‬wO‫ ا‬M " ‫ ا‬M:9 ‫ر‬27‫ا ا‬.‫ ه‬3;
P %" ‫ر ا‬2C
‫ إ‬M:9 C ‫ د‬9 % ‫ وإذا‬C M " ‫ ا دة‬, :‫ وا‬%" , J
%" ‫ ا‬, : ‫ ا د‬RJ2 ‫ا‬
, ‫ ا‬,6 ‫ ا‬3; ‫ر‬27‫ا ا‬.U ‫ق‬7T ‫ف‬2
3`‫ر ا ] ا‬2C
, ‫ ا‬,6 ‫ ا‬3; ‫ر‬27‫ا ا‬.U ‫ق‬7T ‫ف‬2
! ‫ا‬G‫ر ا‬2C
3 ‫ ا [ ل ا‬3; TRANSFER S :‫ف م ا‬2
430
. ‫ ا‬#)$/ B ‫أ) و‬
.‫ر‬2 C _' ‫د اآ[ ! ر او‬2-‫آ ة و‬
‫ ا‬,:9C ‫ ض‬2‫ا ا [ ل ه‬.‫ض ! ه‬Y‫ا‬
‫ رات‬S7‫ ا‬M'2I‫ و‬.0 ! ‫ ت د‬7‫ ا‬,I ‫م‬2:9 ‫ رات‬,"9 , %"7
:, ‫ل ا‬2'2‫! ا‬
, ‫ از‬R9‫ز‬2I S6 %"7 ‫ ا رات إ ا‬M I .%"7 ,'‫ا‬2‫ا‬
:‫ل‬2'2‫! ا‬
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Time between
Arrivals
(Minutes)
Cumulative
Probability
Probability
1
0.25
0.25
2
0.40
0.65
3
0.20
0.85
4
0.15
1.00
S^‫ ا‬,f`9 g.‫ )و‬/ ! ‫رة وة‬J [‫ اآ‬6‫ ا‬،/ 3 [‫ وا‬6‫ ا‬%‫ه‬6‫ ا‬9 ! ‫ا د‬
3‫ ه‬/ ‫ و‬6‫ ! ا‬M/ , ‫ ا‬, ‫ از‬R9‫ز‬2I ،!? G‫ ا‬, 3; ‫ ?!( آ ا& اع‬G‫ا‬
:3‫ا‬2‫ا‬
: 60 , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
(Minutes)
Cumulative
Probability
Probability
2
0.30
0.30
3
0.28
0.58
4
0.25
0.83
5
0.17
1.00
:/ , ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
(Minutes)
Cumulative
Probability
Probability
3
0.35
0.35
4
0.25
0.60
431
5
0.20
0.80
6
0.20
1.00
.&?‫ أدا‬,;" ‫ م‬N‫آ ة ا‬
AHMD & ‫ و‬60 , ‫ وز ! ا‬IAT U ‫ل و‬2'2‫! ا‬
‫ب‬27 ‫ا‬
, ‫ن دوال أز‬2/ ‫ف‬2
BKR & ‫ و‬/‫و‬
IAT
FUNCTION RN1,D4
0.25,1/0.65,2/0.85,3/1.0,4
AHMD
FUNCTION RN1,D4
0.3,2/0.58,3/0.83,4/1.0,5
BKR FUNCTION RN1,D4
0.35,3/0.6,4/0.8,5/1.0,6
] ‫ن ا‬2/9‫و‬
IAT
FUNCTION
0.25,1/0.65,2/0.85,3/1.0,4
AHMD FUNCTION
0.3,2/0.58,3/0.83,4/1.0,5
BKR
FUNCTION
0.35,3/0.6,4/0.8,5/1.0,6
TTime
TABLE M1,1,1,10
QTime QTABLE Line,1,1,10
RN1,D4
RN1,D4
RN1,D4
GENERATE
QUEUE Line
TRANSFER
FN$IAT
SEIZE
DEPART
ADVANCE
RELEASE
TRANSFER
AHMAD
Line
FN$AHMD
AHMAD
,FIN
BOTH,,BAKUR
BAKUR SEIZE
DEPART
BAKR
Line
432
FIN
ADVANCE
RELEASE
TABULATE
TERMINATE
FN$BKR
BAKR
TTime
1
, [‫ وا‬60 ,f;0‫ ا‬37" 3/ BOTH ‫ر‬2C 3; ‫و ا ه‬0‫ ا‬TRANSFER “6T
‫" د‬I ‫ ! ان‬6‫ أ‬,7‫ا‬2 & %I ‫ي‬.‫ن ا‬2 G‫ ا‬R 3/ 3CO‫ر ^ ا‬27‫ ا‬3; ‫ا ه‬
‫ي‬2Y‫آ& ا‬I , ' ! ‫آ‬e‫ & وا‬-I " ‫ و‬GPSS 3; ] ‫ا ا‬.‫ ه‬M‫ أد‬./ ,7‫ا‬2 & S‫ا‬2:‫ة ا‬.; Uƒ‫ أ‬3:7 ‫وا‬
‫ زر‬wYf g‫ وذ‬9‫و‬9 ‫آ ة‬
‫ى ا‬H TRANSFER S‫ا‬2:‫ ا‬M ‫ ه‬O /
‫ هة‬O ! / ‫ا‬.‫ ه‬.S‫ا‬2:‫ة ا‬.; ! ,?‫ ا‬, ? :‫ ا‬3; ‫د‬2-2 ‫ وا‬Step & I ‫ب‬2/ ‫وا‬
3 ‫“ ا‬6T .‫ة‬27 ‫ة‬27 ‫آ ة‬
‫ا‬
-1
433
‫‬
‫‪ M " 2I Step 7YV‬ا‪GENERATE S :‬‬
‫‪-2‬‬
‫ا‪ &HI‬ا " ‪ M‬إ ا‪2 7‬ر ا ‪O‬ك د !‬
‫‪-3‬‬
‫أن آ‪ ! M‬أ‪ 6‬و ‪ 3 /‬و‬
‫أن ا‪; 60 ,f;0‬ن ا " ‪ 9 M‬ك إ ا‪2 7‬ر ا‪.‬ي‬
‫‪A9‬دي ‪ z‬ك ‪ 6e‬و ‪ %9‬ا " ‪ M‬ا‪ 6‬‬
‫‪-4‬‬
‫‪434‬‬
‫وذ‪ Y g‬درة ا‪2 7‬ر )‪ “6T‬ان ا‪2 a SEIZE S :‬ل ا " ‪ M‬و‪.U‬ا ;ن ة ‪3; &X2/‬‬
‫ا‪2 7‬ر ‪( 0‬‬
‫‪-5‬‬
‫‪9‬أ أ‪ , 6‬ا " ‪M‬‬
‫‪-6‬‬
‫‪435‬‬
GENERATE S :‫ ا‬,7‫ا‬2 ‫ م‬N‫ إ ا‬9- M " M9
-7
‫ك‬O ‫ر ا‬2 7‫ ا‬M9
-8
436
‫ان ا‪2YO 6‬ل ;‪ , 3‬ا‪2 G‬ن ا‪0‬ول ;ن ‪ M:9 TRANSFER S J‬ا‪2 G‬ن ا[ ‪ 3‬إ‬
‫‪ SEIZE S J‬ا "‪ BAKUR G %‬وذ‪9 3/ g‬أ ‪.& /‬‬
‫وه‪./‬ا ‪ I‬ا‬
‫آ ة ‪) U9 U 6‬أآ ‪ M‬ا‬
‫آ ة او‪.( /I 2I‬‬
‫ ;‪.‬ة ا‪2:‬ا‪:S‬‬
‫ ;‪.‬ة ا‪U‬ت‪:‬‬
‫ ;‪.‬ة ا‪27‬ا ‪:‬‬
‫‪437‬‬
:‫ر‬2 7‫ول ا‬- ‫ة‬.; :‫ م‬N‫ ا‬3; ‫ث‬2/ ‫ول ز ! ا‬- ‫ة‬.; :9:‫ا‬
FACILITY
DELAY
AHMAD
0
BAKR
0
ENTRIES
UTIL.
AVE. TIME AVAIL. OWNER PEND INTER RETRY
299
0.860
3.344
1
0
0
0
0
202
0.727
4.183
1
501
0
0
0
438
QUEUE
RETRY
LINE
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
TABLE
CUM.%
TTIME
MEAN
STD.DEV.
4.508
1.951
4
0
501
343
0.352
RANGE
0.816
AVE.(-0)
2.589
RETRY FREQUENCY
0
1.000
-
2.000
58
2.000
-
3.000
112
3.000
-
4.000
114
4.000
-
5.000
101
5.000
-
6.000
53
6.000
-
7.000
20
7.000
-
8.000
17
8.000
-
9.000
14
9.000
-
_
-
1.000
403
1.000
-
2.000
33
2.000
-
3.000
25
3.000
-
4.000
20
4.000
-
5.000
8
5.000
-
6.000
3
6.000
-
7.000
5
7.000
-
8.000
2
8.000
-
9.000
1
9.000
-
11.60
34.00
56.80
77.00
87.60
91.60
95.00
97.80
100.00
QTIME
0.816
_
11
1.591
0
80.44
87.03
92.02
96.01
97.60
98.20
99.20
99.60
99.80
_
1
100.00
:, ‫داء ا‬0‫ˆ ا‬9 : H 9:‫! ا‬
59.8% ‫ن أي‬2 ‫ ز‬500 ! ‫ن‬2 ‫ ز‬299 = 6‫ ا‬%U !9.‫د ا‬
40.4% ‫ن أي‬2 ‫ ز‬202 = / %U !9.‫د ا‬
86% = 6‫ ا‬, ";
72.7% = / , ";
439
‫‪ w2‬ز ! ا ‪ 3.344 = 6T ,‬د‪,:J‬‬
‫‪ w2‬ز ! ا ‪ 4.183 = / ,‬د‪,:J‬‬
‫أ‪2C %N‬ل ‪2 7‬ر = ‪ 4‬ز ?!‬
‫د ا‪ !? G‬ا‪N9 % !9.‬و = ‪ 343‬ز ‪2‬ن‬
‫إ‪ 6‬ل ان ا‪2 G‬ن ‪31.4% = (500/343) – 1 = N9‬‬
‫‪2C w2‬ل ا‪2 7‬ر = ‪ 0.352‬ز ‪2‬ن‬
‫‪ w2‬ز ! ا@‪ N‬ر ;‪ 3‬ا‪2 7‬ر = ‪ 0.816‬د‪,:J‬‬
‫‪ w2‬ز ! ا@‪ N‬ر ;‪ 3‬ا‪2 7‬ر ! إ‪ 2.589 = "; N‬د‪,:J‬‬
‫‪ w2‬ز ! ا ‪2/‬ث ;‪ 3‬ا‪ N‬م = ‪ 4.508‬د‪,:J‬‬
‫! ‪-‬ول ز ! ا@‪ N‬ر ;‪ 3‬ا‪2 7‬ر ‪ H‬ان ه ك‬
‫‪ 403‬ز ‪2‬ن ا‪N‬و ;‪ 3‬ا‪2 7‬ر ! ‪ 0‬و ‪ 1‬د‪? J‬‬
‫و ‪ 33‬ز ‪2‬ن ! ‪ 1‬و ‪ 2‬د‪? J‬‬
‫و ‪ 25‬ز ‪2‬ن ! ‪ 2‬و ‪ 3‬د‪? J‬‬
‫و ‪ 20‬ز ‪2‬ن ! ‪ 3‬و ‪ 4‬د‪? J‬‬
‫وه‪./‬ا‬
‫و `ˆ ا‪- `I !/ 9 ,:97‬ول ز ! ا ‪2/‬ث ;‪ 3‬ا‪ N‬م‪.‬‬
‫‪440‬‬
10 ‫ل‬#
‫ و‬RETURN ‫ و‬PREEMPT S‫ا‬2:‫ وا‬RMULT ‫ و‬EQU !9 0‫م ا‬: ‫ف‬2 ‫ا ا [ ل‬.‫ ه‬3;
PRIORITY
The EQU Command:
NAME
EQU
X
, :‫ ا‬.eI 3/ ‫ ة‬, J NAME P6 %‫ه إ إ‬9‫( و‬,9-) ‫ر رة‬:9 0‫ا ا‬.‫ه‬
‫وري‬V 2‫ي وه‬- "I X %‫ن إ‬2/9 ‫ أن‬S 9‫وري و‬V 2‫ وه‬,9H‫رة " رة ا‬: ‫ا‬
‫ي‬- "I ‫ن‬2/9 ‫ أن‬SH9‫و‬
:‫[ ل‬
Price EQU 10
‫ ا ] ;ن‬3; Price %@‫ ا‬-29 !9‫ا أ‬./‫ وه‬10 , :‫& ا‬7"9‫ و‬Price %@‫"ف ا‬9 ‫ا‬.‫وه‬
10 , :‫& ا‬7" GPSS
The RMULT Command:
RMULT
A,B,C,D,E,F,G
GPSS 3; ,"‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ات ا‬2 ‫اة‬2 , J 37"9 0‫ا ا‬.‫ه‬
‫ا" ل‬
‫† أو‬T ‫ن‬2/9 ‫! ان‬/ 9‫ إ ري و‬2‫ وه‬RN1 ‫ول‬0‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬2 ‫اة‬2
A
S-2 a ' ‫د‬
‫† أو‬T ‫ن‬2/9 ‫! ان‬/ 9‫ إ ري و‬2‫ وه‬RN2 3 [‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬2 ‫اة‬2
B
S-2 a ' ‫د‬
‫† أو‬T ‫ن‬2/9 ‫! ان‬/ 9‫ إ ري و‬2‫ وه‬RN3 P [‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬2 ‫اة‬2
S-2 a ' ‫د‬
441
C
‫‪D‬‬
‫‪2‬اة ‪ 2‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬اا ‪ RN4 R‬وه‪ 2‬إ ري و‪ !/ 9‬ان ‪2/9‬ن ‪ †T‬أو‬
‫د ' ‪S-2 a‬‬
‫‪E‬‬
‫‪2‬اة ‪ 2‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا ˆ ‪ RN5‬وه‪ 2‬إ ري و‪ !/ 9‬ان ‪2/9‬ن ‪ †T‬أو‬
‫د ' ‪S-2 a‬‬
‫‪F‬‬
‫‪2‬اة ‪ 2‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا دس ‪ RN6‬وه‪ 2‬إ ري و‪ !/ 9‬ان ‪2/9‬ن ‪ †T‬أو‬
‫د ' ‪S-2 a‬‬
‫‪G‬‬
‫‪2‬اة ‪ 2‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا ‪ RN7 R‬وه‪ 2‬إ ري و‪ !/ 9‬ان ‪2/9‬ن ‪ †T‬أو‬
‫د ' ‪S-2 a‬‬
‫‪The PREEMPT Block:‬‬
‫‪A,B,C,D,E‬‬
‫‪PREEMPT‬‬
‫‪ H9‬ا " ‪ M‬ا‪.‬ي ‪ ( M " JA U? ,UI MYO9‬أ & أ;‪,f‬‬
‫ا" ل‬
‫‪A‬‬
‫ر‪ %J‬أو إ‪ %‬ا‪ ,U‬وه‪V 2‬وري و‪ SH9‬ان ‪2/9‬ن إ‪ %‬أو د ' ‪S-2 a‬‬
‫‪B‬‬
‫‪2C‬ر ا‪ ,f;0‬و‪ PR U G 9‬أو ‪2C‬ر ا ‪ ,"C :‬إذا ا^`‪ W‬ا‪ ,f;0‬وه‪ 2‬إ ري‬
‫و‪ SH9‬ان ‪2/9‬ن ‪ PR‬أو ‪Null †T‬‬
‫‪C‬‬
‫إ‪ %‬او ر‪ %J‬ا‪ S :‬ا‪.‬ي ‪ M:9‬إ& ا " ‪ M‬ا ‪G‬اح ! ا‪ ,U‬وه‪ 2‬إ ري و‪SH9‬‬
‫أن ‪2/9‬ن ‪ †T‬او إ‪ %‬او د ' ‪ S-2 a‬او ‪ ! "I‬أ‪2J‬اس او '`‪ ,‬د‪,9‬‬
‫‪ N‬م أو '`‪ ,‬د‪%" ,9‬‬
‫‪D‬‬
‫ر‪ %J‬ا "‪ %‬وه‪ 2‬ا "‪ %‬ا‪.‬ي ‪ &; RV29‬ا‪ ! G‬ا‪ M " R? f‬ا ‪G‬اح‬
‫‪E‬‬
‫‪2C‬ر ا@ " د ‪ RE‬و‪ "9‬ا " ‪ ! M‬ه‪ 5.‬ا‪ q ,U‬وذ‪ g‬ر ‪,9 ,U U‬‬
‫‪ SH9‬ان ‪ 7"9‬ر ‪G‬ه ;‪ 3‬ا "‪ C %‬وه ‪2/9‬ن ا "‪V C %‬وري‬
‫‪The RETURN Block:‬‬
‫‪A‬‬
‫‪442‬‬
‫‪RETURN‬‬
‫و‪ "9‬ا " ‪ M‬ا ‪G‬اح ‪2‬ا‪2C 3; PREEMPT ,7‬ر ‪ PR‬إ ا‪ ,U‬ا‪ 3‬آ ن ‪ UYO9‬ة‬
‫اى " إ‪ U‬ء ‪ ,‬ا " ‪ M‬ا‪.‬ي & ا;‪ ,f‬أ‬
‫ا" ‪M‬‬
‫‪A‬‬
‫ر‪ %J‬أو إ‪ %‬ا‪ ,U‬وه‪V 2‬وري و‪ SH9‬أن ‪2/9‬ن إ‪ %‬او د ' ‪ S-2 a‬او‬
‫‪ ! "I‬أ‪2J‬اس او '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪%" ,9‬‬
‫‪The PRIORITY Block:‬‬
‫‪PRIORITY‬‬
‫‪A,B‬‬
‫‪ 9‬د او ‪ 37"9‬أ;‪ M " ,f‬ا‪.wO‬‬
‫ا" ل‪:‬‬
‫‪A‬‬
‫‪ , J‬ا‪ ,f;0‬ا‪9H‬ة وه‪V 3‬ور‪ ,9‬و‪ SH9‬ان ‪2/9‬ن إ إ‪ %‬أو د ' ‪ a‬أو ‹‬
‫أو ‪ ! "I‬أ‪2J‬اس أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪%" ,9‬‬
‫‪B‬‬
‫ ر ا‪.‬اآة ا ‪ ,JA‬و‪ Rf9‬ا " ‪ M‬ا‪ _ wO‬ا " ! ا‪2 ˆ` %U !9.‬ى‬
‫ا‪ ,f;0‬وه‪ 2‬إ ري و‪ SH9‬ان ‪2/9‬ن ‪ BU‬او ‪†T‬‬
‫[ ل‪:‬‬
‫‪10‬‬
‫‪PRIORITY‬‬
‫ه‪.‬ا ا‪2 37"9 S :‬ى أ;‪ M9 M " M/ 10 ,f‬إ&‪.‬‬
‫آة ور‬
‫ ‬
‫ن‬
‫"! م ور إح اة ن إح وا ‬
‫ا ور ‪) Overhaul‬ة ار ا('&ة و اة ا‪#$%‬‬
‫و‪0‬م ‪ /%‬ت ‪ .1 *+ ,&-‬ا ا ور )ة ار ‪ 4‬أ‬
‫آ ‪ - 40±8‬و"!‪&7‬ق ‪8 - 10±1‬آ(‪ .‬ا‪ 8‬ت‬
‫ا"&‪+ &7 = ,‬ز او ‪1; ,‬ات ‪&:‬ي ‪+‬ر و آ ‪90±10‬‬
‫د;‪ 0‬و"!‪&7‬ق ‪ 15±5‬د;‪ .0‬أة ا‪ #$%‬ا!* @!ج إح‬
‫و د آ ‪ - 5±1‬و"!‪&7‬ق ‪ 120±30‬د;‪0‬‬
‫‪443‬‬
‫ ا ا ور‬# A!‫* ا‬+ B+)‫ ا‬#$%‫ أة ا‬.$!8
.‫)ة ار‬
.‫ م‬50 ‫ ( ار ( ة‬E‫آ‬
.#$%‫ ا‬G *+ &GH!‫ وا‬A!‫ ا‬,+ ‫د‬
-1
-2
:] ‫ا‬
Rseed
EQU
39941
RMULT
Rseed
Overhaul
QTABLE
Overhaul,10,10,20
Spot
QTABLE
Spot,10,10,20
Service
QTABLE
Service,10,10,20
Alljobs
QTABLE
Alljobs,10,10,20
GENERATE
2400,480,,,1
QUEUE
Overhaul
QUEUE
Alljobs
SEIZE
Maintenance
DEPART
Overhaul
DEPART
Alljobs
ADVANCE
600,60
RELEASE
Maintenance
TERMINATE
GENERATE
90,10,,,3
QUEUE
Spot
QUEUE
Alljobs
PREEMPT
Maintenance,PR
DEPART
Spot
DEPART
Alljobs
ADVANCE
15,5
RETURN
Maintenance
TERMINATE
444
GENERATE
300,60,,,2
QUEUE
Service
QUEUE
Alljobs
PREEMPT
Maintenance,PR
DEPART
Service
DEPART
Alljobs
ADVANCE
120,30
RETURN
Maintenance
TERMINATE
GENERATE
480
TERMINATE
1
:]? ‫ا‬
S‫ا‬2:‫ة ا‬.; ‫ت‬U‫ة ا‬.; 445
‫ ;‪.‬ة ا‪27‬ا ‬
‫ ;‪.‬ة ‪-‬ول ‪2 C‬ر ‪ R -‬ا‪_? ƒ2‬‬
‫ ;‪.‬ة ‪2 C‬ر ‪2 C‬ر ا ‪ ,‬اور‪,9‬‬
‫‪446‬‬
!? G‫ة ا‬GU-‫ أ‬a I ‫ر‬2 C ‫ة‬.; ,"9‫ر ا ت ا‬2 C ‫ة‬.; 9:‫ا‬
FACILITY
DELAY
MAINTENANCE
0
QUEUE
RETRY
OVERHAUL
0
ENTRIES
353
UTIL.
AVE. TIME AVAIL. OWNER PEND INTER RETRY
0.796
54.138
1
401
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
1
0
9
0
447
0.032
86.413
0
0
AVE.(-0)
86.413
SPOT
0
SERVICE
0
ALLJOBS
0
1
0
265
265
0.000
0.000
0.000
2
0
79
67
0.033
10.019
65.960
2
0
353
332
0.065
4.445
74.726
TABLE
CUM.%
OVERHAUL
MEAN
86.413
STD.DEV.
RANGE
RETRY FREQUENCY
60.070
0
_
-
10.000
1
10.000
-
20.000
2
20.000
-
30.000
0
30.000
-
40.000
0
40.000
-
50.000
0
50.000
-
60.000
0
60.000
-
70.000
0
70.000
-
80.000
0
80.000
-
90.000
0
90.000
-
100.000
0
100.000
-
110.000
2
110.000
-
120.000
2
120.000
-
130.000
0
130.000
-
140.000
1
140.000
-
150.000
0
150.000
-
160.000
0
160.000
-
170.000
1
_
-
10.000
_
-
10.000
73
10.000
-
20.000
3
20.000
-
30.000
0
30.000
-
40.000
0
40.000
-
50.000
0
50.000
-
60.000
1
60.000
-
70.000
0
70.000
-
80.000
0
80.000
-
90.000
0
11.11
33.33
33.33
33.33
33.33
33.33
33.33
33.33
33.33
33.33
55.56
77.78
77.78
88.89
88.89
88.89
100.00
SPOT
100.00
SERVICE
0.000
10.019
0.000
0
59.251
265
0
92.41
96.20
96.20
96.20
96.20
97.47
97.47
97.47
97.47
448
90.000
-
100.000
0
100.000
-
110.000
0
110.000
-
120.000
0
120.000
-
130.000
0
130.000
-
140.000
0
140.000
-
150.000
0
150.000
-
160.000
1
160.000
-
170.000
0
170.000
-
180.000
0
180.000
-
190.000
0
190.000
-
97.47
97.47
97.47
97.47
97.47
97.47
98.73
98.73
98.73
98.73
100.00
ALLJOBS
4.445
_
1
32.459
0
_
-
10.000
339
10.000
-
20.000
5
20.000
-
30.000
0
30.000
-
40.000
0
40.000
-
50.000
0
50.000
-
60.000
1
60.000
-
70.000
0
70.000
-
80.000
0
80.000
-
90.000
0
90.000
-
100.000
0
100.000
-
110.000
2
110.000
-
120.000
2
120.000
-
130.000
0
130.000
-
140.000
1
140.000
-
150.000
0
150.000
-
160.000
1
160.000
-
170.000
1
170.000
-
180.000
0
180.000
-
190.000
0
190.000
-
96.03
97.45
97.45
97.45
97.45
97.73
97.73
97.73
97.73
97.73
98.30
98.87
98.87
99.15
99.15
99.43
99.72
99.72
99.72
100.00
449
_
1
‫‪9 :!9 I‬ك ‪ S 7‬إاج و‪ `I‬ا ?]‪.‬‬
‫‪450‬‬
‫‪#‬ل ‪:11‬‬
‫ا‪ Facility ,U‬ه‪ 3‬أي ‪2‬رد ;‪ 3‬ا‪ N‬م ‪ MYOI‬أو ‪I‬م " ‪ M‬وا‪ 3; w:; 6‬أي و‪WJ‬‬
‫و‪ ;9‬أي " ‪2/9 ( M‬ن ‪ M[ . T2YO‬آ‪ 3‬ا ‪ 3; ,J‬دآ ن ‪6‬ق وا‪.6‬‬
‫وا ‪G‬ن ‪ Storage‬ه‪ 2‬أي ‪2‬رد ;‪ 3‬ا‪ N‬م ‪ S29‬أآ[ ! " ‪ 3; M‬و‪ WJ‬وا‪ 6‬و& "‪,‬‬
‫"‪ ,‬و‪ ;9‬ا " ! ‪ MYOI‬آ ‪ : M[ .&" M‬ا@‪ N‬ر ;‪ 3‬دآ ن ‪.,J‬‬
‫) ‪ R7 :,N6‬ان ‪G N‬ن ا& د ! ا‪U‬ت ا‪.( " M "I 3‬‬
‫ أن ‪ J‬آ`‪ ,‬إ‪ Y‬ل وإء ا‪2 ,U‬ا‪ ,7‬ا‪2:‬ا‪ SEIZE S‬و ‪, 6 3; RELEASE‬‬
‫ا ‪G‬ن ج إ أ "‪ &" _9‬و‪2 ! J‬ل واوج ! ا ‪G‬ن‪.‬‬
‫ا‪"9 STORAGE 0‬ف او ‪ 9‬د "‪G ,‬ن و& اآ‪S‬‬
‫‪The STORAGE Command:‬‬
‫‪A‬‬
‫‪STORAGE‬‬
‫‪NAME‬‬
‫‪ [email protected] NAME P6‬ء إ‪G %‬ن وه‪V 3‬ور‪ ,9‬و‪ SH9‬ان ‪2/9‬ن إ‪%‬‬
‫ا" ل‬
‫‪A‬‬
‫ا"‪ ,‬ا‪G ,/‬ن وه‪V 3‬ور‪ ,9‬و‪ SH9‬ان ‪2/9‬ن د ' ‪S-2 a‬‬
‫ا‪ ENTER ! :‬و ‪ 9 LEAVE‬ن ‪G‬او‪ YO !-‬أو إء و‪6‬ة ! و‪6‬ات ا ‪G‬ن‬
‫و‪ %U‬اآ ت‬
‫‪The ENTER Block:‬‬
‫‪A,B‬‬
‫‪ 3; S9‬أ‪ .‬أو إ‪ N‬ر د‬
‫‪ENTER‬‬
‫د ! و‪6‬ات ا ‪G‬ن‪.‬‬
‫ا" ل‪:‬‬
‫‪A‬‬
‫ر‪ %J‬أو إ‪ %‬ا ‪G‬ن وه‪V 2‬وري و‪ SH9‬أن ‪2/9‬ن إ إ‪ %‬إو ر‪S-2 a ' %J‬‬
‫أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪451‬‬
‫ون‬G ‫ ا‬," ! U' :‫ إ‬%9 3‫ ره وا‬Y‫ب إ‬27 ‫ن ا‬G ‫ات ا‬6‫د و‬
B
a ' ‫ أو د‬%‫† أو إ‬T ‫ن‬2/I J‫ و‬,9‫ إ ر‬3‫ وه‬1 ,V‫ ا@;ا‬U J‫و‬
.%" ,9‫ د‬,`' ‫ م او‬N ,9‫! او '`& د‬2J ! "I ‫ او‬S-2
The LEAVE Block:
LEAVE
A,B
%I 3‫ات ا‬62‫ر د ا‬: ‫ن‬G ‫ ا‬," R;‫ن ور‬G ‫ات ا‬6‫ إء د ! و‬3; S9
. U?‫إ‬
:‫ا" ل‬
S-2 a ' %J‫ إو ر‬%‫ن إ إ‬2/9 ‫ أن‬SH9‫وري و‬V 2‫ن وه‬G ‫ ا‬%‫ أو إ‬%J‫ر‬
A
.%" ,9‫ د‬,`' ‫ م أو‬N ,9‫ د‬,`' ‫! أو‬2J ! "I ‫أو‬
‫ون‬G ‫ ا‬," ! U' :‫ إ‬%9 3‫ ره وا‬Y‫ب إ‬27 ‫ن ا‬G ‫ات ا‬6‫د و‬
B
a ' ‫ أو د‬%‫† أو إ‬T ‫ن‬2/I J‫ و‬,9‫ إ ر‬3‫ وه‬1 ,V‫ ا@;ا‬U J‫و‬
.%" ,9‫ د‬,`' ‫ م او‬N ,9‫! او '`& د‬2J ! "I ‫ او‬S-2
#‫د‬$ )‫ اا‬9‫ ر ا‬C
Single Channel Queue with two
servers
M `9 3?‫ا‬2O M/O R;‫ ا‬,7: ‫ ?! إ‬G‫ ا‬M 9 .6‫ر وا‬2 C‫! و‬
U ‫ل‬2'‫! و‬
& Y' , : M
, ‫ز‬0‫ ا‬5.‫ ? وه‬J‫ د‬8 ‫ و‬1 ! Interarrival times ‫ل‬2'‫! و‬
, ‫ أز‬U
:3 ‫ول ا‬H‫ ا‬3; ‫ ل آ‬[email protected]‫`ˆ ا‬
:‫ل‬2'2‫! ا‬
Time between
Arrivals
(Minutes)
Cumulative
Probability
Probability
1
0.125
0.125
2
0.125
0.250
3
0.125
0.375
452
, ‫ أز‬R9‫ز‬2I ‫ول‬-
4
0.125
0.500
5
0.125
0.625
6
0.125
0.750
7
0.125
0.875
8
0.125
1.000
3; ‫ت آ‬T 6 ! ‫ ! ا د‬M/ ? J‫ د‬6 ‫ و‬1 !
‫اوح‬I Sevice times , ‫ ا‬, ‫أز‬
:3 ‫ول ا‬H‫ا‬
:, ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬-
Service Time
(Minutes)
Cumulative
Probability
Probability
1
0.10
0.10
2
0.20
0.30
3
0.30
0.60
4
0.25
0.85
5
0.10
0.95
6
0.05
1.00
. 2 ‫ ز‬500 , ‫ل و‬2'‫آ ة و‬
‫ م‬N‫ ا‬M I ‫ب‬27 ‫ا‬
:3 ‫ آ‬8 ‫ [ ل‬3; ] ‫ر ا‬27
TTime
TABLE
M1,1,1,10
QTime QTABLE
Line,1,1,10
IAT
FUNCTION
RN1,D8
0.125,1/0.25,2/0.375,3/0.5,4/0.625,5/0.75,6/0.875,7/1.0,8
STime
FUNCTION
RN1,D6
0.1,1/0.3,2/0.6,3/0.85,4/0.95,5/1.0,6
Server
STORAGE
2
GENERATE
QUEUE
ENTER
DEPART
FN$IAT
Line
Server
Line
453
ADVANCE
LEAVE
TABULATE
TERMINATE
FN$STime
Server
TTime
1
3 ‫ آ آ‬U M
‫ة ا زن و‬.; 3‫ة ه‬9- ‫ة‬.; ‫م‬:
‫ة ا زن‬.; UN;
‫ ة‬500 &9H‫ ا ] و‬M
:]? ‫ا‬
454
‫ ;‪.‬ة ا‪2:‬ا‪:S‬‬
‫ ;‪.‬ة ا زن‪:‬‬
‫ ;‪.‬ة ا‪27‬ا ‪:‬‬
‫ ;‪.‬ة ‪-‬اول ا‪2 7‬ر‪:‬‬
‫ ;‪.‬ة ‪-‬ول ز ! ا ‪2/‬ث ;‪ 3‬ا‪ N‬م‪:‬‬
‫‪455‬‬
:9:‫وا‬
QUEUE
RETRY
LINE
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
STORAGE
DELAY
SERVER
CAP. REM. MIN. MAX.
TABLE
CUM.%
TTIME
MEAN
STD.DEV.
3.176
1.336
2
2
0
2
500
0
487
0.007
ENTRIES AVL.
2
500
1
AVE.(-0)
0.034
1.308
AVE.C. UTIL. RETRY
0.689
RANGE
0.345
0
0
RETRY FREQUENCY
0
_
-
1.000
57
1.000
-
2.000
106
2.000
-
3.000
133
3.000
-
4.000
127
4.000
-
5.000
51
5.000
-
6.000
25
6.000
-
7.000
1
_
-
1.000
496
1.000
-
2.000
4
11.40
32.60
59.20
84.60
94.80
99.80
100.00
QTIME
0.034
0.221
0
99.20
100.00
.8 ‫ ا ?] و ?] [ ل‬5.‫ رن ! ه‬J :!9 I
456
12 ‫ل‬#
.‫آ ة‬
‫ ا‬3; ‫ات‬Y ‫"ف‬I 3‫وا ا‬0‫م " ا‬: ‫ف‬2 ‫ا ا [ ل‬.‫ ه‬3;
The BVARIABLE Command:
NAME
BVARIABLE
X
.Boolean 3:7 Y ‫"ف‬9
.%‫ن إ‬2/9 ‫ ان‬SH9‫وري و‬V 2‫ وه‬Y ‫ ا‬%‫ او إ‬G ‫"ف ر‬I NAME P6
."I ‫ن‬2/9 ‫ أن‬SH9‫وري و‬V 2‫ي وه‬- "I X
‫[ل‬
AC
BVARIABLE (BV$A’AND’BV$C)
, :‫" ا‬9‫اس و‬2J0‫ ! ا‬,:7 ‫ ا‬,H‫` ‹ ا‬9 0‫ا ا‬.‫ه‬
BV$A1C = 1 “TRUE” IF BV$A = “TRUE” AND BV$C = “TRUE”
= 0 “FALSE” OTHERWISE
The FVARIABLE Command:
NAME
FVARIABLE
X
.Floating Point 3::6 ‫ي‬- Y ‫"ف‬9‫و‬
.%‫ن إ‬2/9 ‫ ان‬SH9‫وري و‬V 2‫ وه‬Y ‫ ا‬%‫ او إ‬G ‫"ف ر‬I NAME P6
."I ‫ن‬2/9 ‫ أن‬SH9‫وري و‬V 2‫ي وه‬- "I X
‫[ل‬
VarX
FVARIABLE 5*LOG(Q$Line)
37"9 0‫ا ا‬.‫ه‬
FV$VarX = 5*LOG(Q$Line)
.Line ‫ر‬2 7‫ى ا‬2
The VARIABLE Command:
457
Q$Line P6
NAME
VARIABLE
X
.‫ي دي‬- Y ‫"ف‬9‫و‬
.%‫ن إ‬2/9 ‫ ان‬SH9‫وري و‬V 2‫ وه‬Y ‫ ا‬%‫ او إ‬G ‫"ف ر‬I NAME P6
."I ‫ن‬2/9 ‫ أن‬SH9‫وري و‬V 2‫ي وه‬- "I X
‫[ل‬
VarX
VARIABLE 5*LOG(Q$Line)
37"9 0‫ا ا‬.‫ه‬
V$VarX = 5*LOG(Q$Line)
.Line ‫ر‬2 7‫ى ا‬2
458
Q$Line P6
‫‪#‬ل ‪13‬‬
‫;‪ 3‬ه‪.‬ا ا [ ل ‪:‬م ا‪2:‬ا‪ ASSIGN S‬و ‪ SAVEVALUE‬و ‪ TEST‬ا‪ %U !9.‬ااآ‪ S‬ا ‪:,‬‬
‫‪The ASSIGN Block:‬‬
‫‪A,B,C‬‬
‫‪ASSIGN‬‬
‫و‪9‬م @‪ 7‬ء أو ‪ %" , J M9"I‬ا " ‪ M‬ا‪) wO‬أي ا " ‪ M‬ا‪.‬ي ‪ M9‬ا‪.(S :‬‬
‫ا" ل‪:‬‬
‫‪A‬‬
‫ر‪ %" %J‬ا " ‪ M‬ا‪ wO‬وه‪V 2‬وري و‪ SH9‬أن ‪2/9‬ن إ أو د ' ‪S-2 a‬‬
‫أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪ %" ,9‬و‪ RI‬ـ ‪ +‬أو – أو‬
‫‪.†T‬‬
‫‪B‬‬
‫‪ , J‬وه‪V 3‬ور‪ ,9‬و‪ SH9‬أن ‪2/9‬ن إ أو د أو ‹ أو ‪ !2J ! "I‬أو '`‪,‬‬
‫د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪C‬‬
‫ر‪ %J‬دا‪ ,‬وه‪ 2‬إ ري و‪ SH9‬أن ‪2/9‬ن ‪ †T‬أو إ أو د ' ‪ S-2 a‬أو ‪"I‬‬
‫! ‪ !2J‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪The SAVEVALUE Block:‬‬
‫‪A,B‬‬
‫‪"9‬ف و‪, J" , J ! Y9‬‬
‫‪SAVEVALUE‬‬
‫`‪ ",ƒ2‬وه‪.‬ا ا‪9 S :‬م @‪-‬اء ت ‪% " ,9-‬‬
‫و ‪Y‬ات ا‪ N‬م‪.‬‬
‫ا" ل‪:‬‬
‫‪A‬‬
‫إ‪ %‬أو ر‪ %J‬ا‪ , :‬ا `‪ ,ƒ2‬وه‪V 2‬وري و‪ RI J‬ـ ‪ +‬أو ‪ R H -‬او ‪C‬ح ‪%J‬‬
‫اى ‪ , :‬ا ‪ ,‬و‪ SH9‬أن ‪2/9‬ن إ أو د ' ‪ S-2 a‬أو ‪!2J ! "I‬‬
‫أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪B‬‬
‫ا‪ , :‬ا ‪27‬ب ‪ U9GI‬أو إ‪ U; V‬أو ‪ U6C‬وه‪V 3‬ور‪ ,9‬و‪ SH9‬أن ‪2/9‬ن إ‬
‫أو د أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪459‬‬
‫‪The TEST Block:‬‬
‫‪A,B,C‬‬
‫‪2:9‬م ه‪.‬ا ا‪ : S :‬ر‪ ^ ،! J ,‬‬
‫‪TEST O‬‬
‫‪2/I‬ن '` ت د‪ N ,9‬م‪ ،‬و‪ : 79‬أو‬
‫ا‪ ,UH‬ا‪ M:9 3‬إ‪ U‬ا " ‪ M‬ا‪ 5.U ,H wO‬ا ‪ :‬ر‪.,‬‬
‫ا" ل‪:‬‬
‫‪O‬‬
‫ ‪ 3:7 M‬أو ‪ ,J‬ا" ‪2/9 3/ B M " A M‬ن ا@ ر ' ‪ a‬وه‪2‬‬
‫‪V‬وري و‪ SH9‬أن ‪2/9‬ن ‪ 9) E‬وي( أو ‪) G‬اآ !( أو ‪) L‬ا‪ (! MJ‬أو ‪) GE‬اآ‬
‫! أو ‪ 9‬وي( أو ‪) LE‬ا‪ ! MJ‬أو ‪ 9‬وي( أو ‪ 9T) NE‬وي(‪.‬‬
‫‪A‬‬
‫‪ , J‬ا@ ر )ا‪ , :‬ا ة( وه‪V 3‬ور‪ ,9‬و‪ SH9‬أن ‪2/9‬ن إ‪ %‬أو د أو ‹‬
‫أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪B‬‬
‫‪ , J‬ا@ د )ا‪ , :‬ا‪ :I 3‬رن ‪ , J U‬ا@ ر( وه‪V 3‬ور‪ ,9‬و‪ SH9‬أن ‪2/9‬ن‬
‫إ‪ %‬أو د أو ‹ أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫‪C‬‬
‫ر‪ %J‬أو إ‪ S J %‬ا ‪ :‬وه‪ 2‬إ ري و‪ SH9‬أن ‪2/9‬ن إ‪ %‬أو د ' ‪ S-2 a‬أو‬
‫‪ †T‬أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م أو '`‪ ,‬د‪.%" ,9‬‬
‫و‪2‬ف "ض إا ‪ 3; %U‬ا [ ل ا ‪:3‬‬
‫‪ ! /BJ#‬ا‪:9‬‬
‫ه‪ N 3; ,9:I ,/O 5.‬م ا ‪G‬ون و‪O "I‬اء و ‪ R? ._ ' R‬ا‬
‫ا‪2‬ا‪6‬ة ـ ‪ 150‬ه‪ ,‬و‪ U"9‬ـ ‪ 200‬ه‪ ،,‬ا‬
‫" ‪ 10‬ه‪ ,‬‬
‫`‪ ,‬ا‪2‬ا‪6‬ة‪O9 .‬ي ا ?‪ R‬ا‬
‫_ ‪O9‬ي ا‬
‫_ ا ‪ ,9 U ,:‬ا‪2‬م ‪ I‬ع ‬
‫`‪,‬‬
‫‪J R‬ا‪ˆC‬‬
‫_ ! ا ‪2‬زع ;‪G6 3‬م ‪2/I‬ن ! ‪10‬‬
‫' _ )أي ‪ &/ 9‬اء ‪ 10‬او ‪ 20‬او ‪ 30‬وه‪./‬ا‪ 3; ,` ' ...‬آ‪ M‬ة(‪ .‬ا‪ S7‬ا‬
‫_‬
‫‪2 "9‬ع ا‪ 0‬ر ;‪ 3‬ذ‪ g‬ا‪2‬م ;‪ U‬ك ‪29‬م أ ر ‪ -‬و‪29‬م أ ر ‪ w2‬و‪29‬م أ ر‬
‫‪T 6 _"V‬ت ا‪2‬ا‪ 0.35 3‬و ‪ 0.45‬و ‪2I 0.20‬ز‪ R9‬ا‪ S7‬ا‬
‫‪2 S6‬ع أ‪ 0‬ر ه‪ 3; 2‬ا‪H‬ول ا ‪:3‬‬
‫‪460‬‬
‫_ ‪29 M/‬م‬
Demand Probability Distribution
__________________________
Demand
Good
Fair
Poor
40
0.03
0.10
0.44
50
0.05
0.18
0.22
60
0.15
0.40
0.16
70
0.20
0.20
0.12
80
0.35
0.08
0.06
90
0.15
0.04
0.00
100
0.07
0.00
0.00
._
‫ ا‬R? U9O9 3‫_ ا‬
‫ "د ا‬M[ 0‫ ا"د ا‬9 I ‫ب‬27 ‫ا‬
:,J"‫ ! ا‬S 9 ‫ي‬.‫ وا‬3 2‫ ا‬a ‫ و د ا‬29 100 ‫ م ة‬N‫ ا‬3‫ف آ‬2
 Revenue   Cost of  Lost profit from  Salvage from sale 
Profit = 
−
−
+

From Sales  newspapers   excess demand   of scrap papers 
:‫أي‬
‫ آ ع‬.: ‫ ا‬+ S7‫ دة ا‬9‫ ! ز‬R? f‫ ا‬a ‫_ – ا‬
‫ – "ا‬R‫ ا‬3; ' = a ‫ا‬
ˆC‫ا‬:
:‫ ان‬H ,/O ‫! ح ا‬
, ‫_ ا‬
‫اة‬O ‫_ ا‬
(‫اة‬O ‫_ ا‬
‫ * د ا‬150 = _
‫" ا‬
‫ * )د ا‬50 = S7‫ دة ا‬9‫ ! ز‬R? f‫ ا‬a ‫ا‬
‫ – د ا‬, 27 ‫_ ا‬
‫اة‬O ‫_ ا‬
‫( ان‬, 27 ‫_ ا‬
‫ * د ا‬200 = R‫ ا‬3; '
‫ اآ ! د ا‬, 27 ‫_ ا‬
‫اة – د ا‬O ‫_ ا‬
., 27 ‫_ ا‬
‫ * ) د ا‬10 = ˆC‫ا‬: ‫ آ ع‬.: ‫ا‬
‫اة اآ ! د ا‬O ‫_ ا‬
‫آة‬
%X 29 _
‫ اء د "! ! ا‬, 3I SH9 ‫آ ة‬
_
‫ د ا‬3‫ )وه‬, ‫ ا‬،3 2‫ ا‬a ‫ ا‬9 I‫و‬
461
‫ن د ا‬2/I ‫ان‬
‫ن د ا‬2/I
,/O ‫ ا‬5.‫ ه‬M 29 100 ‫_ ة‬
‫ ا‬S7‫ا‬
‫ ه اآ‬a ‫ن ا‬2/9 3‫اة ا‬O ‫_ ا‬
‫ د ا‬M
6 YI 5.‫اة( ه‬O ‫ا‬
.!/ 9
:‫ ر‬0‫م ا‬29 ‫ع‬2 R9‫ز‬2 , ‫اول ا‬H‫ا‬
Cumulative
Type of Newsday
Probability
Probability
Good
0.35
0.35
Fair
0.45
0.80
Poor
0.20
1.00
3 ‫ آ‬GPSS 3; ,[ ‫ي‬.‫وا‬
NDay FUNCTION RN1,D3
0.35,GOOD/0.8,FAIR/1.0,POOR
:‫ ر‬0‫م ا‬29 ‫ع‬2 S6 _
‫ ا‬S7‫ ا‬R9‫ز‬2 3 ‫ول ا‬H‫وا‬
Cumulative Probability
_____________________
Demand
Good
Fair
Poor
40
0.03
0.10
0.44
50
0.08
0.28
0.66
60
0.23
0.68
0.82
70
0.43
0.88
0.94
80
0.78
0.96
1.00
90
0.93
1.00
1.00
100
1.00
1.00
1.00
3 ‫ آ‬GPSS 3; ,[ ‫ي‬.‫وا‬
GOOD FUNCTION RN1,D7
0.03,40/0.08,50/0.23,60/0.43,70/0.78,80/0.93,90/1.0,100
FAIR FUNCTION RN1,D6
0.1,40/0.28,50/0.68,60/0.88,70/0.96,80/1.0,90
POOR FUNCTION RN1,D5
0.44,40/0.66,50/0.82,60/0.94,70/1.0,8
462
:] ‫وا‬
Npaper
EQU
30
NewsDay FUNCTION
RN1,D3
0.35,GOOD/0.8,FAIR/1.0,POOR
GOODF
FUNCTION
RN1,D7
0.03,40/0.08,50/0.23,60/0.43,70/0.78,80/0.93,90/1.0,100
FAIRF
FUNCTION
RN1,D6
0.1,40/0.28,50/0.68,60/0.88,70/0.96,80/1.0,90
POORF
FUNCTION
RN1,D5
0.44,40/0.66,50/0.82,60/0.94,70/1.0,8
GENERATE
TRANSFER
1
FN,NewsDay
GOOD
ASSIGN
TRANSFER
1,FN$GOODF
,Clcprft
FAIR
ASSIGN
TRANSFER
1,FN$FAIRF
,Clcprft
POOR
ASSIGN
1,FN$POORF
Clcprft
SAVEVALUE PapersToBuy,(Npaper)
TEST GE
(Npaper-P1),0,LostP
SAVEVALUE TotalProfit+,(2.0#P1-1.5#Npaper+0.1#(Npaper-P1))
TRANSFER
,FINS
LostP
Npaper))
SAVEVALUE
TotalProfit+,(2.0#Npaper-1.5#Npaper-0.5#(P1-
FINS
SAVEVALUE
TERMINATE
START
AverageProfit,(X$TotalProfit/100)
1
100
:] ‫ ت ا‬N6
3; S7‫ "! ا‬3/ 3‫ر اا‬27‫ ا‬3; TRANSFER S :‫ ا‬R W ‫ ا‬NewsDay ,‫ اا‬-1
.‫ ر‬0‫م ا‬29 ‫ت‬T 6 ! , 6 ‫أي‬
TRANSFER
FN,NewsDay
, J (‫م‬2‫ ا‬M[ 9 ‫ي‬.‫ )وا‬wO‫ ا‬M " ‫ ا‬3; (P1) 1 %" ‫ ء ا‬[email protected] ‫ ام‬ASSIGN S :‫ ا‬-2
.‫ ري‬0‫م ا‬2‫ع ا‬2 "9 3?‫ا‬2O"‫ ا‬S7
463
‫‪ -3‬ا‪2:‬ا‪ SAVEVALUE S‬ا[‪ ,X‬ام ا‪0‬ول `“ ا‪ S7‬ا‪ 3 2‬وا[ ‪ (! J) 3‬ب‬
‫و‪ “`6‬ا‪0‬ر ح ا‪ 9 ) ,/‬ل( و ا[ ‪ P‬ب و‪ w2 “`6‬ا ‪29 (100) ,b a‬م‪.‬‬
‫‪ -4‬ا‪ J TEST S :‬م ‪ 9‬ا ‪ ,Y‬ا ‪ ,‬ب ا ‪.a‬‬
‫‪ M‬ا ] و‪2 ،& -‬ف ‪:‬م ;‪.‬ة ا‪ %:‬ا `‪ ,ƒ2‬وا‪ 3‬‬
‫ا‪2‬ا;‪ .‬ا ‪,:‬‬
‫;‪ UN‬ا ;‪.‬ة‬
‫‪464‬‬
‫‪ U M‬آ ‪ 6‬‬
3/ ,ƒ2` ‫ ا‬%:‫ ا‬%J H 0 g‫ ا ] وذ‬3; V RV‫ و‬START 100 0‫“ ا‬6T
.‫م‬29 100 ‫ ى‬a ‫ ا‬w2 -2I
Y‫ و‬Npaper Y M/O 29 _
‫ ا‬R? U9O9 3‫_ ا‬
‫“ أ أد د ا‬6T
.EQU 0‫ ا‬9C ! ‫ ا@ رات‬M‫ & @ ر آ‬J
‫م‬29 100 ‫ ة‬29 ,` ' 30 ‫اء‬O ‫أ‬
,` ' 40
,` ' 50
,` ' 60
465
‫‪,` ' 70‬‬
‫‪,` ' 80‬‬
‫‪,` ' 90‬‬
‫و‹ ا ?] ;‪- 3‬ول‬
‫د ا‬
‫_ ا ‪O‬اة ‪ 29‬‬
‫‪ w2‬ا ‪ a‬ـ ‪29 100‬م ) ‪ 9‬ل(‬
‫‪30‬‬
‫‪-2.10‬‬
‫‪466‬‬
7.90
40
15.02
50
18.78
60
15.34
70
7.34
80
-4.50
90
‫ وط ء‬:I ‫ أن‬a ‫ ر‬w2 ‫ أ‬: 9 &; 29 ,` ' 60 ‫اء‬O &‫“ أ‬69
.YIT , X ‫ذج‬2 ‫ا‬
14 ‫ل‬#
U‫ ا `“ و‬%:‫ات و‬Y ,‫ أو‬, J 37"9 ‫ي‬.‫ وا‬INITIAL 0‫م ا‬: ‫ف‬2 ‫ا ا [ ل‬.‫ ه‬3;
:3 ‫ ا‬S‫اآ‬
The INITIAL Command:
INITIAL
A,B
:‫ا" ل‬
M/O‫ن ا‬2/9 ‫ أن‬SH9‫وري و‬V 2‫ وه‬X ‫أ ف‬9‫& و‬U‫ ا اد إ‬Y ‫ا‬
A
.X$Name ‫ أو‬XPosInteger
‫† أو د أو‬T ‫ن‬2/9 ‫! أن‬/ 9‫ و‬.1 ,V‫ ا@;ا‬U J‫ و‬,9‫ إ ر‬3‫ ا ة وه‬, :‫ا‬
B
.%‫‹ أو إ‬
:>$‫ ا‬A /BJ#
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬R9 !" ] 3 2‫اء ا‬O‫ ا‬SC
Daily Demand
0
1
2
467
3
4
Probability
0.33
0.25
0.20
0.12
0.10
SC %9 ‫ات‬6‫ و‬6 ‫ وي‬9 ‫ ! او‬MJ‫ ا& ا‬-‫ م ;ذا و‬9‫ ا‬," M‫ا ا ] آ‬.‫ون ! ه‬G ‫` ‹ ا‬9
" : I ‫ )أي‬,f92"I ‫ ت‬C .AIT‫د و‬2-2 ‫ون ا‬G ‫را‬: : I ,C ‫ أي‬.‫ات‬6‫ و‬10
S7‫ ا‬RV‫! و‬6 ! ‫ع‬27: ‫ ! ا‬G‫ ا‬2‫ )وه‬Lead Time ‫م‬:‫ ز ! ا‬.(9- ‫ون‬G ‫ل‬2'‫و‬
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬R9 (&2'‫ و‬6
Lead Time (Days)
1
2
3
Probability
0.3
0.5
0.2
" ‫ون‬G ‫ ا‬R; ‫ ت‬C -2IT‫ة و‬6‫ و‬12 3?‫ون اا‬G ‫ع إذا آ ن ا‬20‫ا ! اول ا‬
,‫ و‬,C : I 3; ‹: U; ‫ث‬6 3‫ م ا‬90‫ ا‬, ‫د‬6 . ‫ م‬N‫ا ا‬.U ‫ع‬2‫ أ‬52 3‫; آ‬
. 2‫اء ا‬O , 27 ‫ات ا‬62‫ د ا‬w2 ‫ و‬: I %‫ و‬WC 3‫ات ا‬62‫ا‬
:M ‫ا‬
:, ‫ن اوال ا‬2/
:3 2‫ ا‬S7‫ ا‬,9 " ,‫دا‬
DailyDemand
FUNCTION RN1,D5
0.33,0/0.58,1/0.78,2/0.9,3/1.0,4
:‫م‬:‫ ز ! ا‬,9 " ,‫دا‬
LeadTime
FUNCTION RN1,D3
0.3,1/0.8,2/1.0,3
:] ‫ن ا‬2/9‫و‬
DailyDemand
FUNCTION
0.33,0/0.58,1/0.78,2/0.9,3/1.0,4
LeadTime
FUNCTION
0.3,1/0.8,2/1.0,3
Inventory
Sales
RN1,D5
RN1,D3
INITIAL
INITIAL
INITIAL
TABLE
TABLE
X$EOQ,10
X$Point,6
X$Stock,12
X$Stock,0,5,10
P$Demand,1,2,10
468
Again
GENERATE
TEST L
ADVANCE
SAVEVALUE
TRANSFER
,,,1
X$Stock,X$Point
FN$LeadTime
Stock+,X$EOQ
,Again
GENERATE
ASSIGN
TABULATE
TEST GE
SAVEVALUE
SAVEVALUE
TABULATE
TERMINATE
1
Demand,FN$DailyDemand
Inventory
X$Stock,P$Demand
Stock-,P$Demand
Sold,P$Demand
Sales
1
.‫ات‬Y ,‫ أو‬%J I 3‫ ا‬INITIAL ‫وا‬0‫ ا‬,2 H “6T
,ƒ2` ‫ ا‬%:‫ة ا‬.; Uƒ‫ أ‬%X & -I‫ا ا ] و‬.‫ ه‬M‫أد‬
] ‫ ا‬-‫ أ‬INITIAL ‫وا‬0‫ ا‬,7‫ا‬2 U ‫ ات‬3‫ ا‬%: ‫ أت‬,ƒ2` ‫ ا‬%:‫“ أن ا‬6T
START 52
:]? ‫ا‬
:,ƒ2` ‫ ا‬%:‫ة ا‬.; :9:‫وا‬
TABLE
CUM.%
INVENTORY
MEAN
STD.DEV.
9.519
3.358
RANGE
RETRY FREQUENCY
0
0.000
-
5.000
7
5.000
-
10.000
21
13.46
53.85
469
100.00
SALES
1.327
10.000
-
15.000
_
-
1.000
32
1.000
-
3.000
17
3.000
-
5.000
3
1.150
24
0
61.54
94.23
100.00
SAVEVALUE
EOQ
POINT
STOCK
SOLD
RETRY
0
1
1
0
VALUE
10.000
6.000
3.000
4.000
.]? ‫` ا‬I‫ب و‬27 ‫ إاج ا‬S 7 ‫ك‬9 :!9 I
470
‫‪#‬ل ‪15‬‬
‫;‪ 3‬ه‪.‬ا ا [ ل ‪2‬ف ‪:‬م ا‪ GATE S :‬وا‪.‬ي ‪ M " Y9‬إ دا أو ر‬
‫و; ‹ ‪ , 6‬آ ?!‪ .‬و& اآ‪S‬‬
‫‪The GATE Block:‬‬
‫‪A,B‬‬
‫‪GATE O‬‬
‫ا" ل‪:‬‬
‫‪O‬‬
‫ ‪ 3C M‬وه‪ 2‬ا‪O‬ط ا ‪27‬ب ! ا‪ !? /‬ان ‪ .&:: 9‬وه‪V 2‬وري و‪ SH9‬ان‬
‫‪2/9‬ن أ‪ 6‬ا ‪FNV, FV, I, LS, LR, M, NI, NM, NU, SE, SF, SNE,SNF, :3‬‬
‫‪ SNV, SV, U‬و‪2‬ف ‪O‬ح ج إ& ;‪ 3‬ا [ ل‪.‬‬
‫‪A‬‬
‫إ‪ %‬ا‪ !? /‬أو ر‪ & J‬ا‪.‬ي ‪ ,2 P6 9‬ا‪ 3; V 7"I !? /‬ا" ‪ M‬ا‪3CO‬‬
‫وه‪V 2‬وري و‪ SH9‬ان ‪2/9‬ن إ‪ %‬أو د ' ‪ S-2 a‬أو ‪ !2J ! "I‬أو‬
‫'`‪ ,‬د‪ N ,9‬م او '`‪ ,‬د‪%" ,9‬‬
‫‪B‬‬
‫ر‪ %J‬او ر ‪ G‬ا‪ S :‬ا‪.‬ي ‪ &H9‬إ& ا " ‪ MO; M‬ا‪O‬ط وه‪ 2‬إ ري و‪ SH9‬أن‬
‫‪2/9‬ن ‪ †T‬أو إ‪ %‬أو د ' ‪ S-2 a‬أو ‪ !2J ! "I‬أو '`‪ ,‬د‪ N ,9‬م‬
‫او '`‪ ,‬د‪%" ,9‬‬
‫ا" ‪:O M‬‬
‫‪FNV‬‬
‫ا‪ ,U‬ا "‪ 3; V ,‬ا" ‪ SH9 A M‬ان ‪2/I‬ن ;‪;2 ^ , 6 3‬ة ‪ H‬ح‬
‫ا‪O‬ط‪.‬‬
‫‪FV‬‬
‫ا‪ ,U‬ا "‪ 3; V ,‬ا" ‪ SH9 A M‬ان ‪2/I‬ن ;‪;2 , 6 3‬ة ‪ H‬ح ا‪O‬ط‪.‬‬
‫‪NU‬‬
‫ا‪ ,U‬ا "‪ 3; V ,‬ا" ‪ SH9 A M‬ان ‪2/I‬ن ;‪ , 6 3‬م إام ‪ H‬ح‬
‫ا‪O‬ط‪.‬‬
‫‪SE‬‬
‫ا ‪G‬ن ا "! ‪ 3; V‬ا" ‪ SH9 A M‬ان ‪2/9‬ن ;‪ ; , 6 3‬رغ ‪ H‬ح ا‪O‬ط أي‬
‫أن ‪ R -‬و‪6‬ات ا ‪G‬ن ‪2/I‬ن ‪.,‬‬
‫‪471‬‬
‫ط أي‬O‫ ح ا‬H †
, 6 3; ‫ن‬2/9 ‫ ان‬SH9 A M "‫ ا‬3; V !" ‫ن ا‬G ‫ا‬
SF
.,2YO ‫ن‬2/I ‫ن‬G ‫ات ا‬6‫ و‬R - ‫أن‬
‫ط‬O‫ ح ا‬H ‫ ^ ; رغ‬, 6 3; ‫ن‬2/9 ‫ ان‬SH9 A M "‫ ا‬3; V !" ‫ن ا‬G ‫ا‬
SNE
., ^ ‫ن‬2/I ‫ن‬G ‫ة ! ا‬6‫ة وا‬6‫ و‬MJ0‫أي أن ا‬
‫ ح‬H †
^ , 6 3; ‫ن‬2/9 ‫ ان‬SH9 A M "‫ ا‬3; V !" ‫ن ا‬G ‫ا‬
SNF
. U ‫! إا‬/ 9 ‫ن‬G ‫ة ! ا‬6‫ة وا‬6‫ و‬MJ0‫ط أي أن ا‬O‫ا‬
‫ ح‬H ;2 ^ , 6 3; ‫ن‬2/9 ‫ ان‬SH9 A M "‫ ا‬3; V !" ‫ن ا‬G ‫ا‬
SNV
.‫ط‬O‫ا‬
.‫ط‬O‫ ح ا‬H ;2 , 6 3; ‫ن‬2/9 ‫ ان‬SH9 A M "‫ ا‬3; V !" ‫ن ا‬G ‫ا‬
SV
.‫ط‬O‫ ح ا‬H ‫ إام‬, 6 3; ‫ن‬2/I ‫ ان‬SH9 A M "‫ ا‬3; V ," ‫ ا‬,U‫ا‬
U
I"% J‫م ه‬L ‫@آة‬
M‫ آ‬M I ‫ ! ا رج‬3IeI 3‫ ت ا‬/ ‫ ا‬.!7 ! ‫ن‬2/9 w _I ‫ م ه‬N
.,:J‫د‬
5±1
‫ " ور‬S7‫" ا‬9 S 7‫ ;ن ا‬T2YO w‫ إذا آ ن ا‬.,:J‫د‬
S 7‫ ا‬,JY9 ‫ي‬.‫ ! ازم ا‬G‫ ا‬R9‫ز‬2I ,‫و‬- ‫ب‬27 ‫ ا‬.,:J‫د‬
‫؟‬, /
200
3±1
2 ±1
, / ‫ق ا‬YI
‫ب @آ ل‬27 ‫ ا‬WJ2‫ل ا‬2C %‫ آ‬., - , / ‫@آ ل‬
:] ‫ا‬
Lines
STORAGE
TimeInsYS TABLE
M1,.5,1,20
TryAgain
Busy
2
GENERATE
2,1
GATE SNF
Lines,Busy
ENTER
Lines
ADVANCE
3,1
LEAVE
Lines
TABULATE
TimeInSys
TERMINATE
1
ADVANCE
5,1
472
TRANSFER
,TryAgain
SH9 A M "‫ ا‬3; V !" ‫ن ا‬G ‫ أي ا‬SNF 3CO‫ ا‬M "‫ ا‬R GATE ‫“ إام‬6T
!/ 9 _I U‫ط ا‬27 ! 6‫ وا‬w MJ0‫ط أي أن ا‬O‫ ح ا‬H †
^ , 6 3; ‫ن‬2/9 ‫ان‬
. U ‫إا‬
473
:]? ‫ا‬
S‫ا‬2:‫ة ا‬.; ‫ة ا زن‬.; ‫اول‬H‫ة ا‬.; 9:‫ا‬
LABEL
LOC
1
BLOCK TYPE
GENERATE
ENTRY COUNT CURRENT COUNT RETRY
204
0
0
474
TRYAGAIN
BUSY
2
3
4
5
6
7
8
9
GATE
ENTER
ADVANCE
LEAVE
TABULATE
TERMINATE
ADVANCE
TRANSFER
295
200
200
200
200
200
95
91
STORAGE
DELAY
LINES
CAP. REM. MIN. MAX.
TABLE
CUM.%
TIMEINSYS
MEAN
STD.DEV.
5.040
4.550
2
2
0
0
0
0
0
0
0
4
0
ENTRIES AVL.
2
200
1
0
0
0
0
0
0
0
0
AVE.C. UTIL. RETRY
1.428
RANGE
0.714
0
0
RETRY FREQUENCY
0
1.500
-
2.500
38
2.500
-
3.500
73
3.500
-
4.500
40
4.500
-
5.500
0
5.500
-
6.500
0
6.500
-
7.500
7
7.500
-
8.500
15
8.500
-
9.500
9
9.500
-
10.500
0
10.500
-
11.500
3
11.500
-
12.500
1
12.500
-
13.500
2
13.500
-
14.500
1
14.500
-
15.500
2
15.500
-
16.500
0
16.500
-
17.500
0
17.500
-
18.500
3
18.500
-
19.00
55.50
75.50
75.50
75.50
79.00
86.50
91.00
91.00
92.50
93.00
94.00
94.50
95.50
95.50
95.50
97.00
_
6
100.00
.]? ‫` ا‬I‫ إاج و‬S 7 ‫ك‬9 :!9 I
475
16 ‫ل‬#
:‫ ا ل‬- B ‫آ‬
! ‫ر أن‬:I ,: ‫ ا‬UI ! .‫ ! ا ل‬Y ‫ي‬HI ‫ت ا زل‬T2 ‫ ا‬6‫ أ‬I
‫ر أن‬:I U‫ آ ا‬.‫ ل‬-‫ ! ا‬20% ‫ ! ا ء و‬%U 80% M/O9 ‫ ! _ ا ب‬UC 9
‫ ل‬-‫ ! ا‬40% w:; !/‫ ” ! ا ل و‬U? 7 ! :9 UC 9 3I•‫ ! ا ء ا‬70%
R9 ‫& ا ء‬7"9 ‫ي‬.‫ر أن ا ” ا‬:I ,: ‫ ا‬UI ! f9‫ أ‬.g‫ن ذ‬2"`9 U2C 9 !9.‫ا‬
10 ‫ و‬7 ! ‫ وي‬R9‫ز‬2I f9‫ ا‬R9 ‫ ل‬- g‫ ل ذ‬9‫ ر‬22‫ و‬18 ! ‫ وي‬R9‫ز‬2I
w2 ‫ر‬:; ‫ ل‬[email protected]‫ `ˆ ا‬29 TG 15 ‫ إ‬10 ! 37YI ,2 ‫ أن ا‬W ‫ إذا‬. ‫ ل‬9‫ر‬
.‫ل‬2I ‫ م‬9‫ أ‬100 ‫ "د‬3 2‫ ا‬U‫د‬
:M ‫ا‬
,‫ م اا‬,2 ‫ ا‬SC 9 ! ,9 " WhoAnswer
FUNCTION
RN1,D2
0.8,Female/1.0,Male
‫ أ[ ل‬U7"I M‫ ه‬,9 " FDonate
FUNCTION
RN1,D2
0.7,FYes/1.0,FNo
‫ ل‬M-‫ ر‬U7"9 M‫ ه‬,9 " MDonate
FUNCTION
RN1,D2
0.4,MYes/1.0,MNo
[0‫;"& ا‬I ‫ي‬.‫ ا ” ا‬,9 " FGive
VARIABLE
[email protected]+18
M-‫;"& ا‬9 ‫ي‬.‫ ا ” ا‬,9 " MGive
VARIABLE
[email protected]+7
] ‫ن ا‬2/9‫و‬
WhoAnswer
0.8,Female/1.0,Male
FDonate
0.7,FYes/1.0,FNo
MDonate
0.4,MYes/1.0,MNo
FGive
MGive
FUNCTION
RN1,D2
FUNCTION
RN1,D2
FUNCTION
RN1,D2
VARIABLE
VARIABLE
[email protected]+18
[email protected]+7
476
Female
FYes
FNo
Male
MYes
MNo
Fin1
Fin2
GENERATE
SAVEVALUE
TRANSFER
TRANSFER
ASSIGN
TRANSFER
TRANSFER
TRANSFER
ASSIGN
TRANSFER
TRANSFER
SAVEVALUE
TERMINATE
1
NumberOfHouses+,1
FN,WhoAnswer
FN,FDonate
Donation,V$FGive
,Fin1
,Fin2
FN,MDonate
Donation,V$MGive
,Fin1
,Fin2
Total+,P$Donation
GENERATE
SAVEVALUE
TERMINATE
12.5,2.5
NumberOfDays+,1
1
:]? ‫ا‬
S‫ا‬2:‫ة ا‬.; ,ƒ2` ‫ ا‬%:‫ة ا‬.; 9:‫ة ا‬.; LABEL
RETRY
LOC
BLOCK TYPE
1
GENERATE
477
ENTRY COUNT CURRENT COUNT
1232
0
0
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
FEMALE
FYES
FNO
MALE
MYES
MNO
FIN1
FIN2
SAVEVALUE
NUMBEROFHOUSES
TOTAL
NUMBEROFDAYS
SAVEVALUE
TRANSFER
TRANSFER
ASSIGN
TRANSFER
TRANSFER
TRANSFER
ASSIGN
TRANSFER
TRANSFER
SAVEVALUE
TERMINATE
GENERATE
SAVEVALUE
TERMINATE
RETRY
0
0
0
1232
1232
991
695
695
296
241
100
100
141
795
1232
100
100
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
VALUE
1232.000
14826.000
100.000
:H ]? ‫! ا‬
148.26 2‫ ه‬3
2‫ ا‬U‫ د‬w2 ‫ ل أي‬9‫ ر‬14826 ,2 ‫ ا‬W" - ‫م‬29 100 3; -1
.( ‫ ل‬9‫ ر‬148.5 ,9N‫ ا‬, :‫ ل ) ا‬9‫ر‬
.80.044% , ‫ أي‬1232 ! 991 !-‫ أ‬3Ih‫ د ا ء ا‬-2
70.13% , ‫ أي‬,2 !";‫ د‬695 !U 991 !-‫ أ‬3Ih‫ د ا ء ا‬-3
478
17 ‫ل‬#
:-/D‫)) ا‬4 /BJ#
‫ "د‬3 [email protected]‫ أ‬R9‫ز‬2‫ ا‬. 29 ‫"ه‬9 3‫ ا‬G‫ أ‬,`^‫ د أر‬w2 9 I !9‫ ا ز‬6‫ أ‬99
:‫ول‬H 7"9 29 !? G‫ا‬
Number of Customers/Day
8
10
12
14
Probability
0.35
0.30
0.25
0.10
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬S6 ,`^‫ر‬0‫ي د ! ا‬O9 ‫ن‬2 ‫ ز‬M‫آ‬
Number of Loafs/Customer
4
8
12
16
Probability
0.4
0.3
0.2
0.1
. 29 ‫"ه ا ز‬9 3‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫د‬6
‫م‬29 M‫ ?! آ‬G‫ د ا‬,9 " ,‫ن دا‬2/
NCustmr
FUNCTION RN1,D4
0.35,8/0.65,10/0.9,12/1.0,14
‫ن‬2 ‫ ز‬M/ ,`^‫ر‬0‫ د ا‬,9 " ,‫ن دا‬2/
NLoaf FUNCTION RN1,D4
0.4,4/0.7,8/0.9,12/1.0,16
] ‫ا‬
NCustmr
FUNCTION
0.35,8/0.65,10/0.9,12/1.0,14
NLoaf
FUNCTION
0.4,4/0.7,8/0.9,12/1.0,16
RN1,D4
RN1,D4
GENERATE
ASSIGN 1+,FN$NLoaf
ASSIGN 2,1
SAVEVALUE
SAVEVALUE
TERMINATE
1
TotalCustomers+,P2
TotalLoafs+,P1
479
GENERATE
ASSIGN 1,1
SAVEVALUE
TERMINATE
1,FN$NCustmr
TotalDays+,P1
1
M ‫ا‬
(‫ن‬2 ‫ ز‬10.2 9N) ‫ن‬2 ‫ ز‬10.17 = 100/1017 = !? G‫ د ا‬w2
‫ ر^_ أو‬81.6 3‫ ه‬,9N‫ ا‬, :‫ ) ا‬._^‫ ر‬82.28 = 100/8228 = ,`^‫ر‬0‫ د ا‬w2
.(_^‫ ر‬82 9:I
480
18 ‫ل‬#
3; 3T‫ ا‬R9‫ز‬2‫ وا‬3"7‫ ا‬R9‫ز‬2‫ ا‬M[ ,9N ‫" ت‬9‫ز‬2I ‫ إام‬,`‫م آ‬: ‫ا ا [ ل‬.‫ ه‬3;
.‫آ ة‬
3‫ ا‬R9‫ز‬2I U ‫ل‬2'‫! و‬
‫ا‬
, ‫ز‬e M ‫ ?! إ ا‬G‫ ا‬M 9 ،! & M "9 ,J6 ‫دآ ن‬
bJ‫ د‬8 w2 3"C R9‫ز‬2I S6 ‫ن‬2 G‫ ا‬, ‫م‬2:9 ‫ول‬0‫ ا‬M "‫ ا‬،? J‫ د‬7 w2
? J‫ د‬10 w2 3"C f9‫ ز ! & ا‬3 [‫ ا‬M "‫ ? وا‬J‫ د‬3 ‫وإ اف " ري‬
.,:J‫ د‬2 ‫وإ اف " ري‬
., ‫داء ا‬0‫ˆ ا‬9 : -‫ن وأو‬2 ‫ ز‬100 , %I 6 ‫ م‬N‫ا ا‬.‫آ ة ه‬
3 ‫ ? آ‬J‫ د‬7 w2 3‫ ا‬R9‫ز‬2I U ‫ل‬2'‫! و‬
GENERATE
‫ب‬27 ‫ا‬
, ‫ز‬e !? G‫ ا‬29
(Exponential(1,0,7))
‫ وه أ‬,?‫ا‬2O"‫اد ا‬0‫ ا‬2 ‫ل‬9 ‫ول‬0‫ ا‬%J‫ ا‬Exponential(1,0,7) M‫“ د‬6T
3T‫ ا‬R9‫ز‬2 RJ2 ‫ ا‬%" 3 [‫ ا‬%J‫( ا‬RN1 ‫ )أي‬1 %J‫ ر‬2 ‫ا‬
1
f ( x) = e
−
( x−β )
λ
λ
, λ > 0, E ( X ) = λ + β , V ( X ) = λ 2
. λ = 7 ‫ وه‬Scale ‫ س‬:‫ ا‬%" P [‫ ا‬%J‫ا‬
β =0
‫وه‬
3 ‫ آ‬29 ‫ول‬0‫ ا‬M " , ‫ز ! ا‬
ADVANCE
(Normal(1,8,3))
1 %J‫ ر‬2 ‫ وه أ ا‬,?‫ا‬2O"‫اد ا‬0‫ ا‬2 ‫ل‬9 ‫ول‬0‫ ا‬%J‫ا‬
Normal(1,8,3) M‫د‬
‫“ أ م ا@ اف‬6T) ‫ ا@ اف ا " ري‬P [‫ ا‬%J‫ وا‬w2 ‫ ا‬3 [‫ ا‬%J‫( ا‬RN1 ‫)أي‬
.(!9 ‫ا " ري وˆ ا‬
3 [‫ ا‬M " M[ ‫و‬
ADVANCE (Normal(1,10,2))
] ‫ن ا‬2/9‫و‬
Barb1
GENERATE
QUEUE
TRANSFER
SEIZE
DEPART
ADVANCE
(Exponential(1,0,7))
Line
BOTH,Barb1,Barb2
Barber1
Line
(Normal(1,8,3))
481
Barb2
Fin
RELEASE
TRANSFER
SEIZE
DEPART
ADVANCE
RELEASE
TERMINATE
Barber1
,Fin
Barber2
Line
(Normal(1,10,2))
Barber2
1
]? ‫ا‬
S‫ا‬2:‫ة ا‬.; ‫ت‬U‫ة ا‬.; ‫ا‬27‫ة ا‬.; 9:‫ا‬
LABEL
BARB1
BARB2
FIN
LOC
1
2
3
4
5
6
7
8
9
10
11
12
13
BLOCK TYPE
GENERATE
QUEUE
TRANSFER
SEIZE
DEPART
ADVANCE
RELEASE
TRANSFER
SEIZE
DEPART
ADVANCE
RELEASE
TERMINATE
ENTRY COUNT CURRENT COUNT RETRY
100
0
0
100
0
0
100
0
0
60
0
0
60
0
0
60
0
0
60
0
0
60
0
0
40
0
0
40
0
0
40
0
0
40
0
0
100
0
0
482
FACILITY
DELAY
BARBER1
0
BARBER2
0
QUEUE
RETRY
LINE
0
ENTRIES
UTIL.
AVE. TIME AVAIL. OWNER PEND INTER RETRY
60
0.679
7.945
1
0
0
0
0
40
0.598
10.490
1
0
0
0
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
6
0
100
50
0.540
3.793
AVE.(-0)
7.585
.‫ب‬27 ‫` ا‬I‫ إاج و‬S 7 ‫ك‬9 :!9 I
483
19 ‫ل‬#
15 ± 10 M‫ة آ‬6‫"ل وا‬
‫ة‬H ‫ اءات‬,H ‫ آة‬,9 3; ‫ ك رات إ" ف‬I
U ‫ق ا@" ف‬Y9‫ إ" ف( و‬, 3IT ‫ )أو‬, ‫ن آ ذ‬2/I ‫! ااءات‬
15% .? J‫د‬
, 6 &‫ _ ا‬9 ‫ول‬0‫ع ا‬2‫ ا‬،!2 ! ‫ة‬6‫ن وا‬2/I‫ دة و‬- ‫ ااءات‬,: .,:J‫ د‬12
‫ ااءات‬,:
‫ أ‬U ‫ @آ‬,:J‫ د‬25
‫ود ! رات‬
± 5 ‫ق‬YI‫ دة و‬H‫ت ا‬T
‫! ا‬
15% M/O9‫ و‬,-6
^ ‫ د‬-29 &‫ ;ض ا‬. U ‫ @آ‬,:J‫ د‬20
, ‫ م‬N‫ ا‬3‫ آ‬6 .,N ‫! اي‬
±2
± 10 .eI
U;
‫ اء‬,I 3; ‫ن‬2/9 ‫! ان‬/ 9 U ‫ا@" ف وان اي د‬
.‫ اء‬500
:] ‫ا‬
; Ambulance dispatch: Exersise 4.4
; Discrete-Event System Simulation,
; Banks,j et al
; Version 2
GENERATE
QUEUE
TRANSFER
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TRANSFER
NFALARM TRANSFER
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TRANSFER
SERIOUS QUEUE
SERIOUSQ
SEIZE
DEPART
ADVANCE
RELEASE
OUT
DEPART
TERMINATE
15,10
ALLQ
0.85,,NFALARM
FALARMQ
FALARMS
FALARMQ
12,2
FALARMS
,OUT
0.15,,SERIOUS
NORMALQ
NORMALS
NORMALQ
20,10
NORMALS
,OUT
SERIOUSS
SERIOUSQ
25,5
SERIOUSS
ALLQ
1
]? ‫ا‬
S‫ا‬2:‫ة ا‬.; 484
‫ت‬U‫ة ا‬.; ‫ا‬27‫ة ا‬.; 9:‫ا‬
LABEL
NFALARM
LOC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
BLOCK TYPE
GENERATE
QUEUE
TRANSFER
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TRANSFER
TRANSFER
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TRANSFER
ENTRY COUNT CURRENT COUNT RETRY
501
0
0
501
0
0
501
0
0
76
0
0
76
0
0
76
0
0
76
0
0
76
0
0
76
0
0
425
0
0
359
0
0
359
0
0
359
0
0
359
1
0
358
0
0
358
0
0
485
SERIOUS
OUT
FACILITY
DELAY
NORMALS
0
SERIOUSS
0
FALARMS
0
QUEUE
RETRY
ALLQ
0
NORMALQ
0
SERIOUSQ
0
FALARMQ
0
17
18
19
20
21
22
23
ENTRIES
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
DEPART
TERMINATE
UTIL.
66
66
66
66
66
500
500
0
0
0
0
0
0
0
0
0
0
0
0
0
0
AVE. TIME AVAIL. OWNER PEND INTER RETRY
359
0.952
20.068
1
501
0
0
0
66
0.222
25.475
1
0
0
0
0
76
0.121
12.087
1
0
0
0
0
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
AVE.(-0)
11
1
501
0
4.207
63.538
63.538
8
0
359
26
2.879
60.678
65.416
2
0
66
52
0.030
3.435
16.193
1
0
76
71
0.002
0.237
3.595
.]? ‫ب ! ا‬27 ‫` ا‬I‫ إاج و‬S 7 ‫ك‬9 :!9 I
486
20 ‫ل‬#
‫ا‬.‫ ه‬37‫ ا‬.3 ‫ ا‬,‫ ء ر‬h‫ˆ ا‬H ‫ ع‬-‫ر إ‬2f ‫ر‬2 T‫آ او ء ا‬. ‫ ء‬h‫ ا‬6‫ع أ‬27I
H , X 5
± 2 ‫ع‬27
.‫ ع‬[email protected] 5‫آ‬. 30
‫ق ا‬Y9 . ‫ أ‬3‫ و‬100 ‫ ت‬2` , ? J ,‫ع ! إدارة ا ر‬27 ‫ا‬
± 5 ‫ و‬%J‫ ا‬S7 , X 7 ± 2
‫ق‬Y9 ‫ و‬3 ‫ ا‬0‫ ا‬3‫ و‬%J‫ر‬
‫ ع‬7‫! أ‬9.‫ر ا‬2 T‫ د او ء ا‬%/; .‫آة‬. 0‫ ا‬3‫ع و‬27 ‫ ا‬H9 ‫ ان‬35% ‫ ل‬6‫ه ك إ‬
‫؟‬g‫ق ذ‬Y9 WJ2‫ ! ا‬%‫ وآ‬w:; ‫ة‬6‫ ة وا‬,X‫د‬
‫ ول ا‬9 &‫ ا س ا‬%U" ‫ا ث‬
] ‫ا‬
; Parent Volunteer : Exersise 7.4
; Discrete-Event System Simulation,
; Banks,j et al
; Version 1
TTIME
NCALL
TABLE
GENERATE
ADVANCE 5,2
ADVANCE 7,2
TRANSFER
ADVANCE 30,5
ASSIGN 1,1
TABULATE
SAVEVALUE
TERMINATE
M1,10,10,20
1,,,100
;FIND NUMBER
;DIAL NUMBER
0.65,,NCALL
;PLACE CALL
TTIME
TOT +,M1
1
]? ‫ا‬
S‫ا‬2:‫ة ا‬.; ,ƒ2` ‫ ا‬%:‫ة ا‬.; ‫اول‬H‫ة ا‬.; 487
9:‫ا‬
LABEL
NOCALL
TABLE
CUM.%
TTIME
LOC
1
2
3
4
5
6
7
8
9
BLOCK TYPE
GENERATE
ADVANCE
ADVANCE
TRANSFER
ADVANCE
ASSIGN
TABULATE
SAVEVALUE
TERMINATE
MEAN
STD.DEV.
22.492
ENTRY COUNT CURRENT COUNT RETRY
100
0
0
100
0
0
100
0
0
100
0
0
36
0
0
36
0
0
100
0
0
100
0
0
100
0
0
RANGE
RETRY FREQUENCY
14.492
0
_
-
10.000
10
10.000
-
20.000
54
20.000
-
30.000
0
30.000
-
40.000
11
40.000
-
50.000
25
10.00
64.00
64.00
75.00
100.00
SAVEVALUE
TOT
RETRY
0
VALUE
2249.236
.]? ‫` ا‬I‫ إاج و‬S 7 ‫ك‬9 :!9 I
488
: GPSS ‫ اآة‬#> ‫)ام‬$'_ ‫= واآة‬31‫ا‬
‫ أو‬General Purpose Simulation System ‫آ ة‬
‫آ ة أي‬
‫ ا‬, G6 ‫ف م‬2 M `‫ا ا‬.‫ ه‬3;
Blocks S‫ا‬2J‫ و‬Commands ‫" أوا‬I ‫آ ة‬
, G6 3‫ وه‬GPSS
.‫ م‬N
: GPSS ‫أوا‬
• BVARIABLE
Boolean ‫ع‬1‫ ا‬# &7! #$‫&ف آ‬,
• CLEAR
Transaction ,!(‫ ا‬# O !‫ و‬$ 8‫ ادات ا‬,‫& ا‬
• CONDUCT
%&: ‫&ي‬:
• CONTINUE
J; ,% &(!" ,: ، ‫( ا(@آة‬P
• EQU
‫& ا("! م‬7!( (; *R,
• EXIT
GPSS ‫* " او دورة‬1
• FUNCTION
‫ دا‬#$‫&ف آ‬,
• FVARIABLE
(" &7!) Fvariable ‫ ع‬# #$‫&ف آ‬,
489
• HALT
Queued Commands U1!‫&ة ا‬L!1(‫ ا(@آة و(@* آ ا)وا& ا‬J;
• INCLUDE
‫ي‬V ‫ (ذج‬J X&!‫&أ و‬0
• INITIAL
Matrix *+ #$‫ أو آ‬Savevalue Z (; ‫ أو‬Logicswitch *0R1 ‫ر @ل‬R ‫"! او‬
Entity
• INTEGRATE
User Variable ‫& ا("! م‬7! *+ 1‫ ز‬0![ $0 P
• MATRIX
*+ #$‫&ف آ‬,
• QTABLE
(‫ر‬%\ ‫ ) ول‬Qtable ‫ ع‬# #$‫&ف آ‬,
• REPORT
‫ري‬+ &&0 ]R ‫&& أو "! م‬0!‫ ا‬J( (-‫^ إ‬B
• RESET
‫ت ا(@آة‬$ ‫& إ‬
• RMULT
$‫[ا‬,‫ _ اد ا‬E‫ ا`و‬,4"‫^ اة ا( ات ا‬B
• SHOW
490
Expression ‫رات‬4,‫ ا‬display ‫&ض‬, ‫ و‬evaluate ‫ ر‬0
• START
‫ أ ا(@آة‬4‫ و‬Termination Count ‫ء‬8‫ اد ا‬, (; *R,
• STEP
]‫ا‬0‫ ا‬# ‫ د @ د‬%&:!% ‫ة‬R % ‫ة‬RG ‫&ي ا(@آة‬:
• STOP
]0‫ل ا‬G‫ إ!(دا * @و`ت د‬J; ‫^ &ط‬B
• STORAGE
Storage Entity ‫ ن‬#$‫&ف آ‬,
• TABLE
Table Entity ‫ ول‬#$‫&ف آ‬,
• VARIABLE
Variable Entity &47! #$‫&ف آ‬,
GPSS ‫رات ا‬
The GPSS Block Statements
ADOPT
Assembly Set ^(:!‫( ا‬: &7
ADVANCE
Future Events Chain 40!"(‫( ا) اث ا‬$; * Transaction ,! ^B
ALTER
491
Group (: *+ #,!(‫ ل ا‬,‫& و‬4! ASSEMBLE
related Transactions #R4&(‫ ا‬#,!(‫* ا‬1‫& و‬L!1
ASSIGN
Transaction Parameter ,!(‫ ا‬X, ‫ ل‬,
BUFFER
Current Events Chain @‫( ا) اث ا‬$; *+ ,!(‫^ ا‬B
CLOSE
‫ت‬% ‫ل‬G‫* إد‬1
COUNT
Transaction Parameter ,!(‫ ا‬X, *+ ‫ت‬1$P‫ ا‬count ‫ اد‬, ^B
DEPART
Queue Entity ‫ر‬%\ #$‫ @!ت آ‬# O01
DISPLACE
,!( Next Sequential Block *!‫] ا(!"" ا‬0‫& ا‬7
ENTER
Storage Entity ‫ ن‬#$‫* آ‬+ ‫& و ات ن‬L!‫ او ا‬e!‫ا‬
EXAMINE
group (: B ‫ او‬E‫& إ!(ء ا‬4! EXECUTE
492
&Gf ]; R-‫ا‬% ‫د‬
‫[ط‬1% ‫م‬0
FAVAIL
"available" " ‫&ة‬+! " E‫ إ‬Facility Entity " #$‫ آ‬status # &7
FUNAVAIL
"not available" " ‫&ة‬+! &h " E‫ إ‬Facility Entity " #$‫ آ‬status # &7
GATE
Transaction flow ,!(‫ ل إ"ب ا‬,‫ و‬#$‫& آ‬4! GATHER
related Transactions #R4&(‫ ا‬#,!(‫& ا‬L!1
GENERATE
Future Events Chain 40!"(‫( ا) اث ا‬$; *+ j,B‫ و‬Transaction ,! Create INDEX
Transaction Parameter ,! X, ‫ ل‬,
INTEGRATION
Off E‫ إ‬On # ‫ دا "! م‬P ‫@ل‬
JOIN
Numeric or Transaction Group ,! (: ‫( د او‬: *+ ‫ا‬B ^B
LEAVE
Storage Entity ‫ ن‬#$P storage units ‫!&ك او @&ر و ات ن‬
LINK
493
Userchain Entity ‫( "! م‬$; #$‫ آ‬E‫ ا‬,! ‫ او @&ك‬01
LOGIC
Logicswitch Entity *0R1 ‫ @ل‬#$‫ ل آ‬,
LOOP
& &h :!1‫ ا‬l‫& إذا آ‬Gf ]; *‫ ا‬0‫ و‬X, (; # O01
MARK
Transaction Parameter ,!(‫ ا‬X, *+ ‫م‬L1‫ ا‬- (; ^B
MATCH
‫!&ن‬0(‫ ا‬MATCH ]; *‫* ا إ‬P #R4&(‫ ا‬#,!(‫& ا‬L!1
MSAVEVALUE
Matrix Entity + #$‫& آ‬1, (; *R,
OPEN
‫ت‬% ‫ل‬G‫"! إد‬
PLUS
X, *+ :!1‫ ا‬[email protected]‫ و‬PLUS &%, ]"@ ‫ ر او‬0
PREEMPT
"!‫ ا‬P E *!" ‫ او‬A
PRIORITY
,! B+‫ ل ا‬,
QUEUE
494
‫ر‬%\ ‫ @!ت آن‬
READ
‫ت‬% J # *!‫& ا‬R"‫& ا‬[email protected]
RELEASE
Facility Entity "!‫ ا‬#$‫&ر آ‬
REMOVE
Numeric or Transaction Group ,! (: ‫( د او‬: # ‫ا‬B ‫ &ج‬
RETURN
Facility Entity "!‫ ا‬#$‫@&ر آ‬
SAVAIL
" &+! " E‫ ا( ن إ‬#$‫& آ‬h
SAVEVALUE
Savevalue #$P (; ^m
SCAN
X, *+ (0‫^ ا‬m‫ و‬#,! (: &4!G‫ا‬
SEEK
G ‫ت‬% *+ &R"‫& '& ا‬h
SEIZE
" #$‫& آ‬L!‫ أو ا‬e!‫ا‬
495
SELECT
!(‫ ا‬X, *+ ‫ ا( !ر‬#$P‫ ا‬X;‫^ ر‬m
SPLIT
I4& ! nG‫ا‬
SUNAVAIL
" &+! &h " E‫ ا( ن إ‬#$‫& آ‬h
TABULATE
‫ ول‬#$‫ د آ‬
TERMINATE
‫ء‬8‫ اد ا‬O0‫ وا‬,! *‫ا‬
TEST
,!(‫ و ل إ"ب ا‬arithmetic condition *%"@‫& ا[&ط ا‬4!G‫ا‬
TRACE
Active Transaction I[1‫ ا‬,!( Trace Indicator ]0, &' ^m
TRANSFER
‫] ا(@ د‬0‫ ا‬E‫ ا‬0‫&ك او ا‬
UNLINK
‫( ا("! م‬$; #$‫ آ‬# ,!(‫ازل ا‬
UNTRACE
496
I[1‫ ا‬,!( ]0,!‫ '& ا‬nh‫ا‬
WRITE
‫ت‬4‫ ا‬J *‫ ;( ا‬-‫ار‬
GPSS ‫م ا"! ة‬$% ‫ا ت ا('د‬
System Numerical Attributes (SNA) available in GPSS:
• A1
@@ (; .I[1‫ ا‬,!( Assembly Set X‫( ا!&اآ‬:
• AC1
00 (; .CLEAR &Gf # E‫ ا(@آ‬l;‫ ا‬.0R(‫م ا‬L1‫ ا‬- (;
• BVEntnum
00 (; . Entnum E(" Boolean Variable Entity *% &7! #$‫ & آ‬0 :!
• C1
00 (; .RESET &Gf # E‫ ا(@آ‬l;‫ ا‬.4"1‫م ا‬L1‫ ا‬- (;
• CAEntnum
E(" ‫( "! م‬$; *+ #""!(‫ ا‬#,!(‫ ا‬1‫ د از‬, ‫ ا(زون‬I-!(‫ ا‬.‫( ا("! م‬$; ‫ @!ى‬I-!
00 (; .Entnum
• CCEntnum
. Entnum ‫( ا("! م ا("(ة‬$; E‫ إ‬#""(‫ ا‬#,!(‫ اد آ ا‬, .‫( "! م‬$0 *P‫ل ا‬G ‫ د ا‬
@@ (;
• CHEntnum
497
. Entnum ‫( ا("! م ا("(ة‬$; E‫ إ‬#""(‫ ا‬#@‫ ا‬#,!(‫ د ا‬. ‫( "! م‬$; ‫@!ت‬
@@ (;
• CMEntnum
. Entnum ‫( ا("! م ا("(ة‬$; E‫ إ‬#""(‫ ا‬#,!(‫ ا‬# ‫ د‬E‫ ا‬.‫( "! م‬$0 ‫ @!ى‬E‫ا‬
@@ (;
• CTEntnum
(; . Entnum ‫( ا("! م ا("(ة‬$; *+ ,! ‫ث‬P I-! .‫( "! م‬$; *+ ‫ث‬P(‫ ا‬#‫ ز‬I-!
00
• FEntnum
0 ^& `‫ وإ‬1 ^& Fentnum ، ‫ل‬7[ Entnum ‫ ا!" ا("(ة‬#$‫ إذا آن آ‬.7[ "
@@ (;
• FCEntnum
*("(‫ ا!" ا‬#$‫ آ‬PREEMPT ‫&غ‬+‫ او ا‬SEIZE e!‫ د ا(&ات ا!* ا‬."!‫ ا‬7 ‫ اد‬,
@@ (; .,!(% Entnum
• FIEntnum
1 ^& FIEntnum ، ‫&غ‬+‫ ا‬Entnum "!‫ ا‬#$‫ إذا آن آ‬.l,\; Entnum ‫ا!" ا("(ة‬
@@ (; . 0 ^& `‫وإ‬
• FNEntnum
00 (; . Entnum ‫ ا ا‬#$‫ آ‬X0 :! .‫دا‬
• FREntnum
1000 # ‫ء‬:‫ و(= آ‬.‫ل‬7[ Entnum "!‫ ا‬#$‫ آ‬+ ‫ي آن‬U‫ ا‬#‫ ا‬# ‫ء‬:‫ ا‬."!‫ ا‬,+
00 (; . (‫ )[( ء [&ي‬[email protected] &h ‫ن‬P ;‫ و‬،`(!‫ إ‬1000 ‫ و‬0 #% (; ^& ‫ا‬U‫ء و‬
• FTEntnum
498
00 (; .,!(% Entnum "!‫ ا‬#$‫ آ‬j+ e!‫ى ا‬U‫ ا‬#‫ ا‬I-! ."!‫ إ"ك ا‬#‫ ز‬I-!
• FVEntnum
(h‫ر‬+ ‫& )أي‬+ *+ Entnum "!‫ ا‬#$‫ إذا آن آ‬1 ^& FVEntnum .&+ *+ "
@@ (; .0 ^& `‫وإ‬
• GNEntum
@@ (; . Entnum ‫( د‬: B ‫ اد‬, ^& GNEntnum .‫( د‬: ‫ اد‬,
• GTEntnum
@@ (; . Entnum #,! (: B ‫ اد‬, ^& GTEntnum .#,! (: ‫ اد‬,
• LSEntnum
. 0 , `‫* " ه " وإ‬+ *0R1(‫ ا(@ل ا‬#$‫ إذا آن آ‬1 , LSEntnum .‫* ه‬0R1 ‫@ل‬
@@ (;
• MBEntnum
q j ‫ي‬U‫ وا‬Entnum ]; 1 ,! ‫ إذا و‬1 , MBEntnum .]; 1 Match n+
1 , MBEntnum .Active Transaction I[1‫ ا‬,!(‫ آ‬Assembly Set ^(:!‫( ا‬:
@@ (; . 0 `‫وإ‬
• MPParameter
00 (; . Parameter X,(‫ ا@ ; ;( ا‬0R(‫م ا‬L1‫ ا‬- (; .X, ،‫ل‬0!8‫ ا‬#‫ز‬
• MXEntnum(m,n)
Entnum *+(‫ ا‬#$P n ‫(د‬,‫ وا‬m &R"‫* ا‬+ (0‫*( ا‬R,) , .*+ Z (;
• M1
00 (; .,!( "Mark Time" :!‫ ا‬#‫ ; ز‬0R(‫م ا‬L1‫ ا‬- , M1 .*0!8‫ ا‬l;‫ا‬
499
• NEntnum
@ (; . Entnum ]0‫ ا‬G‫ي د‬U‫* ا‬P‫ ا‬#,!(‫د د ا‬, .]; ‫ل‬G‫ اد د‬,
• PParameter or *Parameter
(; .I[1‫ ا‬,!( Parameter X,(‫ ;( ا‬, *Parameter ‫ أو‬Pparameter .X,(‫;( ا‬
+& ‫ او‬00 ‫@@ او‬
• PR
@@ (; .I[ ,! B+‫ ;( ا‬.,! B+‫ا‬
• QEntnum
@@ (; . Entnum *@‫ر ا‬%R‫ ا‬#$‫ اد ;( @!ى آ‬, .*@‫ر ا‬%R‫@!ت ا‬
• QAEntnum
00 (; . Entnum ‫ر‬%R‫ ا‬#$‫* آ‬+ ‫ د‬, ‫* ا(زون‬1‫ ا‬I-!(‫ ا‬.‫ر‬%R‫ @!ي ا‬I-!
• QCEntnum
@@ (4; . Entnum ‫ر‬%\ #$‫ل إ* آ‬G ‫ ادات ا‬, ^( ^( .‫ر‬%R G‫* ا ا‬P‫ د ا‬,‫ا‬
• QMEntnum
@@ (; . Entnum ‫ر‬%R‫ ا‬#$P E;)‫ اد ا‬,!‫ ا‬.‫ر‬%R ‫ @!ى‬E;‫أ‬
• QTEntnum
@@ (; . Entnum ‫ر‬%R‫ ا‬#$P ‫ اد‬,! ‫* ا(زون‬1‫ ا‬I-!(‫ ا‬.‫ر‬%\ *+ ‫ث‬P(‫ ا‬#‫ ز‬I-!
• QXEntnum
#$P ‫ اد‬,! ‫* ا(زون‬1‫ ا‬I-!(‫ ا‬.%&‫ت ا‬G (‫ر ا‬4!‫ر ^ م إ‬%\ *+ ‫ث‬P(‫ ا‬#‫ ز‬I-!
00 (; .& ‫ث‬P 1‫ ا!* از‬#G‫ ^ م "ب ا ا‬Entnum ‫ر‬%R‫ا‬
• QZEntnum
500
(; .& ‫ث‬P 1‫ ا!* از‬Entnum ‫ر‬%R‫ ا‬#$P #G‫ د ا ا‬.‫ر‬%R #&‫ ا‬#G‫ اد ا ا‬,
@@
• REntnum
. Entnum ‫ ا( ن‬#$‫ إ* آ‬#G‫ ا ا‬#,!(% ‫(ل‬,!-r !(‫ @!ت ا( ن ا‬.‫ ا( ن‬,- I-!
@@ (;
• RNEntnum
Entnum $‫[ا‬,‫ ا`ر;م ا‬# 0-999 #% *$‫ [ا‬[email protected] X;‫ ر‬, RNEntnum .*$‫ [ا‬X;‫ر‬
@@ (; .
• SEntnum
#$‫ آ‬#G‫ ا ا‬#,!(% 7[(‫ ار @!ت ا( ن ا‬0 , SEntnum .‫ ا("! م‬# !‫ا‬
@@ (; . Entnum ‫ا( ن‬
• SAEntnum
#$‫ آ‬1 (,!"(‫ ا( ن ا‬," ‫* ا(زون‬1‫ ا‬I-!(‫ ا‬, SAEntnum .‫ ا("! م‬# !‫ ا‬I-!
00 (; . Entnum ‫ا( ن‬
• SCEntnum
@@ (; . Entnum ‫ ا( ن‬#$‫ آ‬# 7[(‫* ات ا( ن ا‬P‫ د ا‬,‫ ا‬.‫! ام ا( ن‬-‫ اد إ‬,
• SEEntnum
(; . 0 , `‫ وإ‬jP% &+! Entnum ‫ ا( ن‬#$‫ إذا آن آ‬1 , SEEntnum .‫رغ‬+ ‫ا( ن‬
@@
• SFEntnum
(; . 0 , `‫ وإ‬jP% s!( Entnum ‫ ا( ن‬#$‫ إذا آن آ‬1 , SFEntnum .s!( ‫ا( ن‬
@@
• SREntnum
501
. Entnum ‫ ا( ن‬#$‫* آ‬+ ‫ ا( ن ا("! م‬I-!(% =(! *P‫! ام ا‬-8‫ ا‬# &"‫ آ‬.‫ ا( ن‬,+
00 (; .&"‫ ;( آ‬UGH ;‫ & و‬0-1000 #% (; ,‫ ء و‬J‫ ا‬# ‫ء‬:‫ آ‬j1 &4,‫و‬
• SMEntnum
@@ (; . Entnum ‫ ا( ن‬#$‫* آ‬+ ‫(ل‬,!-8‫* ا‬+ ‫ ون‬E;‫أ‬
• STEntnum
00 (; . Entnum ‫ ا( ن‬#$‫* آ‬+ ‫ و ة‬P ‫ث‬P(‫ ا‬#‫ ز‬I-!
• SVEntnum
(; . 0 , `‫& وإ‬+ *+ Entnum #$P‫ إذا آن ا‬1 , SVEntnum .&+!‫* ا‬+ ‫ا( ن‬
@@
• TBEntnum
00 (; . Entnum ‫ ول‬:‫ ا‬#$‫* آ‬+ X0 ‫& ا(زون‬h I-!(‫ا‬
• TCEntnum
@@ (; . Entnum ‫ ول‬:‫ ا‬#$‫* آ‬+ ‫& زو‬7‫ ول ا‬:‫ ا‬X; ‫ اد‬,
• TDEntnum
00 (; . Entnum ‫ ول‬:‫ ا‬#$‫* آ‬+ ‫& زو‬7‫ ول ا‬:‫ ا‬X0 ‫ري‬,(‫@&اف ا‬8‫ا‬
• TG1
+ ‫ن‬P *!‫ ا‬TERMINATE ]‫ا‬0‫ ا‬R-‫ا‬% O;1! ‫ي‬U‫ ا‬,‫ ا‬, TG1 .‫ء‬8‫* اد ا‬+ *;4‫ا‬
(; . 0 !(; ‫ن‬P 1 ‫ إ!ء ا(@آة‬#4‫ و‬START ‫رة‬4,% !" *!‫ وه* ا‬، ] A X,(‫ا‬
@@
• VEntnum
00 (; . floating point ($,‫ ا‬R01‫* او ا‬%"@‫ ا‬Entnum &7!(‫ ا‬#$‫ آ‬X0 :!
502
• WEntnum
@@ (; . Entnum ]0‫ ا‬#$‫* آ‬+ #@‫ ا‬#,!(‫ د ا‬.*@‫] ا‬0‫ اد ا‬,
• XEntnum
+& ‫ او‬00 ‫ ;( @@ او‬. Entnum [email protected] (; #$P‫د ;( ا‬, . Savevalue [email protected] (;
• XN1
@@ (; .I[1‫ ا‬,!( ,!(‫ ا‬X;‫د ر‬, .I[1‫ ا‬,!(‫ ا‬X;‫ر‬
• Z1
@@ (; .7[!‫م ا‬L R-‫ا‬% ‫د‬, (; .‫اآ&ة ا@&ة‬U‫ا‬
:‫ت‬L ]0‫&ف ا‬, . 22 X;‫] ر‬0‫* ا‬+ #&L!1(‫ ا‬#,!(‫ د ا‬, (SNA ‫م‬L1 ‫ د‬,‫ ) ا‬W22 ‫ر‬
:*‫& " وه‬4,! ‫&ى‬G‫ل ا‬P‫ ا‬#P‫ و‬22 X;&‫ ا@ ه ا‬vU‫* ه‬+
• Wj
‫* ا(@آة‬+ ]0‫ ا‬X;‫ ر‬،] [email protected] ‫ د‬j w
• W$Name
*1,(‫] ا‬0‫ ه ;^ ا‬Name w
• W*j
‫&ة‬4 &h 1 vU‫ وه‬.*1,(‫] ا‬0‫ ا‬X;‫ي @ي ر‬U‫ ا‬I[1‫ ا‬,!(‫ ا‬X, X;‫ ر‬،] [email protected] ‫ د‬j w
indirect addressing
• W*Name
‫&ة‬4 &h 1 vU‫ وه‬.*1,(‫] ا‬0‫ ا‬X;‫ي @ي ر‬U‫ ا‬I[1‫ ا‬,!(‫ ا‬X, X-‫ ه إ‬Name w
503
• W*$Name
!0%" x+P .*1,(‫] ا‬0‫ ا‬X;‫ي @ي ر‬U‫ ا‬I[1‫ ا‬,!(‫ ا‬X, X-‫ ه إ‬Name w
• W*Parameter
W*$Name ‫ او‬W*Name ‫ او‬W*j # ‫! ام أي‬-‫ إ‬P‫ إ‬#4‫و‬
:GPSS '*!+"‫ ا‬Operators ‫ا("ل‬
^
.B ‫ة‬0 ‫ع‬+& A , A^B .‫^ )س‬+&‫ا‬
#
B *+ A ‫&ب‬B ‫ د‬,‫ ا‬:!1‫ ا‬, A # B .‫&ب‬m
/
B E A ("; :! , A / B .(";
\
B E A ‫"( ا@@ ـ‬0‫ ا‬:! , A \ B .Integer Division @@‫"( ا‬0‫ا‬
@
B E A ‫ ـ‬Modulo Division ("; *;% , A @ B .Integer Remainder [email protected]‫* ا‬04!(‫ا‬
B ‫ و‬A #% ‫ ا&ق‬, A - B .‫\&ح‬
+
B ‫ و‬A ‫(ع‬: , A + B .^(
>= ‘GE’
504
‫أآ‪ # &4‬أو "وي‪ 1 , A >= B .‬إذا آ‪ A l‬اآ‪ &4‬أو "وي د ‪ B‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪<= ‘LE‬‬
‫أ; ‪ #‬أو "وي‪ 1 , A <= B .‬إذا آ‪ A l‬أ; أو "وي د ‪ B‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪> ‘G‬‬
‫أآ‪ 1 , A > B .# &4‬إذا آ‪ A l‬أآ‪ &4‬د ‪ B #‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪< ‘L‬‬
‫أ; ‪ 1 , A < B .#‬إذا آ‪ A l‬أ; د ‪ B #‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪= ‘E‬‬
‫"وى‪ 1 , A = B .‬إذا آ‪" A l‬وى د ‪ B #‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪!= ‘NE‬‬
‫‪" q‬وى ـ ‪ 1 , A != B .‬إذا آ‪ ! A l‬د ‪ B #‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪& ‘AND‬‬
‫و ا(‪ 1 , A & B .0R1‬إذا و‪ I0+‬إذا آن آ ‪ A #‬و ‪ & &h B‬وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫’‪| ‘OR‬‬
‫أو ا(‪ 1 , A ‘OR’ B .0R1‬إذا آن ‪ A‬أو ‪ B‬أوآه( ‪& &h‬ي وإ` ‪ &h 0 ,‬ذ‪e‬‬
‫ ‪:L‬‬
‫ا‪1$P‬ت ا! ‪ ]:‬إ ‪ 4; declared‬أن (‪ #P‬إ‪ !-‬ا‪:‬‬
‫•‬
‫آ‪1$‬ت ا( ن ‪ ]:‬إ ‪4,%‬رة ‪STORAGE‬‬
‫•‬
‫ا(!‪&7‬ات ا@"‪ ]: %‬إ ‪4,%‬رة ‪VARIABLE‬‬
‫•‬
‫!‪&7‬ات ا‪ R01‬ا‪ ]: Floating point ($,‬إ ‪4,%‬رة ‪FVARIABLE‬‬
‫•‬
‫ا(!‪&7‬ات ا‪4‬و ‪ ]: Boolean‬إ ‪4,%‬رة ‪BVARIABLE‬‬
‫•‬
‫ا(‪+‬ت ‪ ]:‬إ ‪4,%‬رة ‪MATRIX‬‬
‫‪505‬‬
TABLE ‫رة‬4,% ‫] إ‬: ‫ اول‬:‫ا‬
•
QTABLE ‫رة‬4,% ‫] إ‬: Qtables ‫ر‬%R‫ اول ا‬
•
‫^ ا ا‬4! ‫رة‬4‫ و‬FUNCTION ‫رة‬4,% ‫] إ‬: ‫ا وال‬
•
MARK ‫ و‬ASSIGN ‫رات‬4,% ‫] إ‬: Transaction Parameters #,!(‫ ا‬X,
•
TRANSFER SUB ‫ و‬COUNT ‫ و‬SPLIT ‫ و‬SELECT ‫ و‬READ ‫و‬
:, ‫ ا‬,[ 0‫ ا‬3; GPSS ‫آ ة‬
506
‫ ا‬, G6 ‫ف "ض‬2
.‫ آة ا*)م‬-./# 0)# )12 ‫اآ‬34 ‫ك‬67 ‫آة‬# -1
:/BJ‫ض ا‬2
.‫اآ‬.‫اء ا‬O ‫ر‬2 C 3; ‫ا‬2`:9‫ و‬, X 7±7 M‫م آ‬J ‫ آة‬S" ‫اآ‬.I ‫ن ا ك‬2"HO ‫ ا‬M 9
., X 5±3 S" ‫ ا‬M‫ل ا دا‬2'2‫اآ وا‬.‫ق ز ! اء ا‬Y9
.S" ‫ ا‬M‫ ا دا‬RHO 300 ‫ل‬2 ‫ب‬27 ‫ ! ا‬G‫ ا‬9 ‫ذج‬2 ‫ب ء‬27 ‫ا‬
: GPSS u/ g#6‫ض ا‬2
; GPSS World Sample File - TURNSTIL.GPS, by Gerard F. Cummings
**************************************************************
*
*
*
Turnstile Model
*
*
Time is in seconds
*
**************************************************************
In_use EQU
5
;Mean time
Range
EQU
3
;Half range
GENERATE
7,7
;People arrive
QUEUE
Turn
;Enter queue
SEIZE
Turn
;Acquire turnstile
DEPART
Turn
;Depart the queue
ADVANCE
In_use,Range
;Use turnstile
RELEASE
Turn
;Leave turnstile
TERMINATE
1
;One spectator enters
**************************************************************
:‫ذج‬1‫ ا‬2 9H‫و‬
GENERATE
‫ل‬2'2 ( !"HO ‫ ) ه ا‬Transactions ! " ‫ ا‬S9 GENERATE Block S :‫ا‬
., X 7±7 M‫اآ آ‬.‫ ك ا‬
QUEUE
507
% !9.‫"! ا‬HO ‫ر ا‬2 C ! ‫? ت‬
6‫ إ‬R H9 DEPART S :‫ ا‬R QUEUE S :‫ا‬
,Y Queue Entity ‫ر‬2 7‫ آ ?! ا‬.‫اآ‬.‫وا ك ا‬N9 ‫ا‬2‫زا‬T‫ " و‬S" ‫ا ا‬29
Turn ‫ ه‬GPSS
SEIZE
M " ‫اآ ! ا‬.‫ ك ا‬2 ‫د‬H 6‫ وا‬N M "
S J ‫ل‬2‫ ! د‬M " ‫ اي‬R 3‫دي إ‬A9
&‫ل ا‬2‫ ا‬%9 SEIZE S :‫ا‬
‫ ك‬O‫ ل ا‬YO‫ إ‬3; S9 ‫ا‬.‫ وه‬.-‫ا إذا و‬
SEIZE
DEPART
S J M9 &; ‫اآ‬.‫ ك ا‬O ,[ ‫ ا‬Facility ,U‫ ا‬SEIZE MYO9 M " ‫د ان‬H
M O9T ‫ ر‬[email protected]‫“ ان ز ! ا‬6T Turn ‫ر‬2 7‫? ت ! آ ?! ا‬
6‫ إ‬R H g‫ وذ‬DEPART
.‫اآ‬.‫ق ك ا‬Y ‫ ! ا‬G‫ا‬
ADVANCE
,U‫ إام ا‬3; M " &JY9 ‫ي‬.‫آ ة ا‬
‫ل ز ! ا‬2C 3; %/ 9 ADVANCE S J
‫ @د ل‬, X 5±3 ‫اآ‬.‫ ك ا‬.e9 , ‫ ا‬5.‫ ه‬3;‫ و‬U UY %I J 3‫اآ( وا‬.‫) ك ا‬
, J YI ,2U g‫ وذ‬ADVANCE S J 3; , ‫ إ‬, J ‫“ ا أ‬6T .RHO ‫ا‬
. :6T ‫ آ ى‬Block operands S :‫ ا‬M RELEASE
5;2 ‫ن‬2/I P
( ‫اآ‬.‫ ) ك ا‬,U‫ إ;اغ ا‬3; M " S9 RELEASE S J
SEIZE S J 3; ‫ل‬2 g‫ ( وذ‬M " MYOI 3/
TERMINATE
.‫اآ‬.‫ ! ك ا‬5‫آ ة " ور‬
‫ ! ا‬M " ‫ ا‬,‫ إزا‬3‫ ه‬TERMINATE S J , U
:‫إ=اء اآة‬
‫ ! ا ] إ ر‬,?‫ة ا‬.; ‫ ا‬3; ،‫ " ري‬9:I 2I‫آ ة و‬
508
‫ي ا‬HI , ‫ات ا‬27‫ا‬
File / Open
‫ار إ ر‬2 ‫ر 'وق ا‬2Uƒ TURNSTIL
%X
Open
‫آ ة إ ر‬
‫اء ا‬[email protected]
Command / Create Simulation
‫ إ ر‬%X
Command / START
‫ ـ‬1 ‫ار ال‬2 ‫ 'وق ا‬3;
300
wYV‫ إ‬%X
OK
RHO 300 ‫ ور‬M[ 9 ‫ا‬.‫ وه‬TERMINATE S : M " 300 ‫آ ة ور‬
default ‫ي‬:‫ ا‬9:‫ _ ا‬3‫ إ‬9:I , / GPSS ‫م‬2:9 ‫آ ة‬
‫ ا‬3UI
‫ ء ا‬U‫ إ‬.‫اآ‬.‫ ك ا‬O
!/ 9 3‫ وا‬9‫ ر‬:‫ة ا‬.; 3; 3I‫ ذا‬M/O 9:‫ ا‬UN9‫ و‬Turnstil.1.1 3 ‫ ا‬report file
! Report ‫ إ ر‬%X ,?‫ة ا‬.; ‫ ! ا‬File / Open ‫ ر‬g‫ وذ‬WJ‫ اي و‬3; UI‫ ه‬O
. Files of type ‫'وق ا@ رات‬
U: %X clipboard d‫ ا‬,62 3‫ إ‬U SH9 U:‫ ص و‬M/O GPSS 9‫ ر‬:I S/I
word processor ‫ آ ت‬I ] ‫ اي‬3;
509
:g1‫ ا‬J1#
%J‫ ر‬RHO ‫ل ا‬2 ‫ ت‬, X 2134.023 ‫ ا " ري ي أن‬9:‫ ا‬3; End Time , J !
g‫ وذ‬J ,` ]? 37"9 ‫آ ة ة اي‬
S J ‫ ا‬9/I ) ‫اآ‬.‫ ! ل ك ا‬300
I ‫ق أو‬27IT DEPART ‫ و‬QUEUE S‫ا‬2J ‫“ ان‬6T (‫ هة‬N‫ ا‬,?‫ا‬2O"
! G‫ وˆ ا‬w:; ‫ر‬2 7‫ ا‬3; ‫ ر‬[email protected]‫ ز ! ا‬%U MH9 ! " ‫ ان ا‬3"9 ‫ا‬.‫ وه‬ADVANCE
‫ء‬GH‫ ا‬3‫ إ‬9:‫ ا‬3; N ‫ إذا‬Turn 3 ‫ ا‬Queue Entity ‫ر‬2 7‫ آ ?! ا‬3; 3/‫ا‬
!"HO ‫ د‬J‫ ي ان ا‬QUEUE Turn W I‫ و‬Queue Entity ‫ا ص ـ‬
. :6T ‫ اى‬M?‫ف ا‬2 . b ˆ ‫ا‬.‫ وه‬3 2‫ر ه‬2 7‫ ا‬3; !9N ‫ا‬
:‫ اآة‬0‫دا‬
‫ي و‬.‫ وا‬ending condition of the simulation ‫آ ة‬
‫ ا‬,9 U , 6 _O/
‫ م‬N ,9‫ إ " ا ` ت ا"د‬N SHOW 0‫ف م ا‬2 g. ‫ ا " ري‬9:‫ا‬
;2 U ‫ ا@ام وي أي‬,U U‫ ا‬P6 (SNA) System Numeric Attributes
., ‫ة ا‬.‫ ه‬3; ‫ إ ر‬، , ‫ م ا‬N‫ ا‬, 3‫ إ‬N T‫او‬
Command / SHOW
‫ة‬.; 3; status line , ‫ ا‬w 3 OK wYV‫ إ‬%X AC1 S‫ار أآ‬2 ‫ 'وق ا‬3;‫و‬
2134.023 3‫ ه‬, ‫ م ا‬N‫ ا‬, ‫ ى ان‬Model Window ‫ذج‬2 ‫ا‬
‫اء‬G-e‫ ك ) آ‬O‫ ل ا‬[email protected] 3/‫ ! ا‬G‫ء ! ا‬GH‫ ا‬37"I 3‫ وا‬utilization ‫اآ‬.‫ ك ا‬, ";
0‫ ر ا‬-2I (_‫! ا‬
Command / SHOW
689.67 , :‫ ا‬37"9 ‫ا‬.‫ ه‬OK ‫ إ ر‬%X
FR$Turn S‫ار أآ‬2 ‫ 'وق ا‬3;‫و‬
_‫اء ! ا‬G- ‫ آ‬37" 2‫ ( وه‬Fractional Busy Time)
‫اآ إ ر‬.‫ ك ا‬O !'‫ا‬2‫"! ا‬HO ‫ د د ا‬[email protected]
510
Command / SHOW
300 ‫ن‬2/ RJ2 2‫ وآ ه‬OK %X N1 S‫ار اآ‬2 ‫ 'وق ا‬3;‫و‬
‫ إ ر‬،‫ ت‬2‫ن ` ‹ " ا‬h‫ا‬
Window / Simulation Window / Facilities Window
T2YO ‫اآ آ ن‬.‫“ ان ك ا‬6 ( UI 92
M‫ة ي آ‬.; ‫ت ) آ ا‬U‫ة ا‬.; 3;
‫“ ان‬6T ( idle MC ) ‫ل‬2YO ^ ‫آ ة آ ن‬
‫ ا‬,9 U 3; &‫ وا‬WJ2‫ ! ا‬70% 3‫ا‬26
‫ اي‬U/ 9 T‫( و‬,7O ^ ‫ ر دي أي‬U2 ) ,2YO ^ ‫اآ‬.‫ ك ا‬O ,[ ‫ ا‬,U‫ا‬
M "
‫ إ ر‬،! " ‫ ا‬-29 !9‫ ا‬3 ‫ة‬N 3:
Window / Simulation Window / Blocks
Detailed View of the Blocks Window S‫ا‬2:‫ة ا‬.; M ` ‫ ا‬N ‫ ا‬7"9 ‫ا‬.‫وه‬
3‫ل إ‬2‫ ول ا‬9 ‫ا‬2I 301 %J‫ ر‬M " ‫ن ا‬0 g‫ وذ‬wO ‫ ;" ل او‬M " -29T ,‫“ ا‬6T
‫ ! ان‬/ I M ` ‫ ا‬N ‫ ا‬3; .‫ م‬N‫ ! ا‬N U‫ ا‬J 300 %J‫ ر‬M " ‫آ ة وان ا‬
3/‫! ا"د ا‬9 S‫ا‬2:‫ة ا‬.; ‫ ا‬N‫ ا‬.‫آ ة‬
‫ن‬h‫ ا‬.RJ2 2‫آ ة آ ه‬
‫ا‬
‫ ء ا‬X‫ ا‬S‫ا‬2: 3/‫ل ا‬2‫ ا‬d9‫ ر‬I ‫ ه‬O
‫ ا‬3; ‫ وا‬9 ! " ‫ ! ان ا‬: ‫ ! ا‬/ 9 2‫ وه‬S :‫ل ا‬2
.S‫ا‬2:‫ة ا‬.; ^‫ا‬
‫ة ا" رات‬.; f ‫ أ‬.‫ اى‬.;‫ا‬2 ‫ ! ل‬U‫ إ‬N ‫آ ة‬
‫اء ا‬-‫ف " إ‬2 ‫ن‬h‫ا‬
‫ إ ر‬Expressions Window ,9H‫ا‬
Window / Simulation Window / Expressions Window
S‫ اآ‬Label , 3;‫ و‬,9H‫ة ا" رات ا‬.; 3;
Number of people
!"HO ‫ هة د ا‬O !
/ ‫ا‬.‫ ه‬N3 S‫ اآ‬Expression field ‫ ا" رة‬, 3;‫و‬
;29 &‫ إذ ا‬,2U M/ ‫ ا ت‬R - ! !/ 9 &‫ ا‬GPSS ‫اص‬2 ! .‫اآ‬.‫ ك ا‬O !9‫ا ر‬
511
3 %X View 3 wYV‫ن أ‬h‫ ا‬.‫ ? ت‬/‫ ا‬, 6 _ I 3‫ ? وا‬:I Y 50 ! [‫اآ‬
Memorize
‫ا‬.‫آ ة ;ن ه‬
‫`“ ا‬
f9‫ ا‬. :6T U ‫! إا‬/ 9 3‫`“ ا" رات وا‬6 !
/ 9 ‫ا‬.‫وه‬
.‫ام ة اي‬z ‫ `“ ا" رات‬
‫ة ا" رات‬.; 3; .‫اآ‬.‫ ك ا‬O ‫ ر‬[email protected]‫ر ا‬2 C 3; ! ‫"! ا‬HO ‫ "د ا‬f9‫ ا‬N ‫د‬
S‫ اآ‬Label M:6 3;‫ و‬,9H‫ا‬
Q Content
, J _f ‫ واا‬Memorize ‫ و‬View wYV‫ إ‬%X Q$Turn S‫ ا" رة اآ‬, 3;‫و‬
S‫ اآ‬Label field G ‫ ا‬, 3`; ‫اآ‬.‫ ر ك ا‬[email protected]‫ ز ! ا‬w2 ‫ هة‬O ,[ X
%X Memorize ‫ و‬View 3 wYV‫ إ‬QT$Turn S‫ ا" رة اآ‬, 3;‫ و‬Avg Wait
OK
,?‫ ا‬, ? :‫ ر ! ا‬g‫ وذ‬, ‫? ت ا اآ‬
‫ 'وق‬3;‫و‬
[email protected]‫ن ! ا " ! و ` ا‬h‫‹ ا‬
Command / START 0‫ و إ ر ا‬OK %XCommand / Clear
25 RHO ‫ در ا‬Y9 36 ‫ي‬HI 3‫آ ة وه‬
‫ ه ا‬OI ‫ف‬2 OK %X‫ و‬25,NP ‫ ـ‬1 ‫ار ل‬2 ‫ا‬
,9H‫ة ا" ا‬.; M`J‫ ا‬T‫! او‬/‫اآ و‬.‫ ك ا‬M[ I 3‫ ا‬,U‫ ا‬SJ‫ ا‬.‫اآ‬.‫ ك ا‬
('‫ ا‬,2`: !/I % ‫ت ) إذا‬U‫ة ا‬.; 3‫ إ‬N‫و‬
Window / Simulation Window / Facilities Window
‫ت إ ر‬U‫ة ا‬.; “6‫ ة اى و‬25 U?‫ا‬- ‫آ ة‬
‫أ ا‬
Command / START
‫ت‬U‫ة ا‬.; M`J‫آ ة ا‬
‫ ء ا‬U‫ إ‬OK %X ! ‫ و‬25,NP ‫ ـ‬1 ‫ار ل‬2 ‫ 'وق ا‬3;‫و‬
Facilities Window
512
., X 5±3 ! T RHO ‫ ا‬, , X 7±4 ‫اآ‬.‫ ك ا‬.‫ ث اذا ا‬9 ‫ن ذا‬h‫ى ا‬
3; : ‫ ; ه‬3‫ ا‬%:‫ " ا ء ا‬Y Custom Command 0‫ف م ا‬2
‫ إ‬.‫ذج‬2 ‫ا‬
Command / Custom
‫ ` ح ا@د ل‬wYV‫ ا‬%X In_use EQU 7 ‫ول‬0‫ ا‬7‫ ا‬3; S‫ار اآ‬2 ‫ 'وق ا‬3;‫و‬
S‫ واآ‬3 ‫ ا‬7‫ ا‬3‫ ا‬M:;
Range EQU 4
U J 3‫ات ا‬Y‫آ ! ان ا‬e SHOW 0‫ إذا ارد إام ا‬/ 9 OK wYV‫ ا‬%X
3;‫ و‬Command / SHOW ‫ إ‬g‫ ذ‬%9 _‫ ي آ‬%:‫ ا‬6‫ ;" ; [ ا‬W 6 J
Status , ‫ ا‬7 3; 4 , :‫ ه ا‬O ‫ ان‬SH9 OK %X Range S‫ار أآ‬2 ‫'وق ا‬
. f9‫ أ‬Journal Window ‫ة‬9H‫ة ا‬.; 3;‫ و‬,?‫ة ا‬.; Line
%X Command / Clear ‫ إ ر‬ADVANCE Block 9H‫ ا‬S : ‫ث‬6 ‫ى ذا‬
، ‫أ‬
a
,‫و‬0‫وط ا‬O‫آ ة إ ا‬
‫ ا‬, 6 "‫ و‬,?
[email protected]‫ن ` ا"دادات ا‬h‫ ا‬OK
‫ ا‬6‫ا‬2‫ ! ا‬T 300 S‫ار اآ‬2 ‫ 'وق ا‬3;‫ و‬Command / START ‫إ ر‬
‫ة ا" رات‬.; a;‫ ا‬%X ‫آ ة‬
‫ ا‬3UI 6 N‫ إ‬OK %X
Window / Simulation Window / Expressions Window
Memorized Expressions box ‫آ‬.‫ 'وق ا‬3; ,X[‫ ا" رات ا‬M‫ف ي آ‬2
‫ل‬2C 3 J‫“ ان أ‬6T OK ‫ن إ‬h‫ رة ا‬M/ View 3 ‫ و‬Expression 3 wYV‫إ‬
3; AC ‫! ان ا‬9 ‫ا‬.‫ وه‬3‫ر ا‬2 7‫ ز ! ا‬w2 f9‫ ا‬،&: ! 3‫ن ا‬h‫ ا‬a'‫ر ا‬2 7
M ‫ " ا‬S9 J ‫ا‬.‫! ه‬/‫ب و‬27 ‫ ا‬WJ2‫ ا‬3; !"HO ‫ ا‬R - ‫ل‬2‫ د‬3‫دي ا‬A9 J , ‫ا‬
.!"HO ‫! ا‬
‫ة‬Xe ‫ ا‬%:‫ء ا‬
J‫ إ‬SH9 ‫ آ‬,; ‫ ا‬3‫ ا‬R-9T ]? ‫ ا‬5.‫ ت ان ا@ف ! ه‬X‫ إ‬SH9
SH9 ‫ آ‬RESET Command 0‫ ام ا‬g‫ وذ‬,? U‫? ت ا‬
[email protected]‫ ! ا‬,9‫وط اا‬O
3 6 3; ‫ر‬2 7‫ ز ! ا‬w2 ANOVA !9 I M ‫ م‬:‫ رب وا‬HI ‫اء ة‬[email protected] w7 ‫ان‬
.‫اآ‬.‫ ك ا‬O ,` ‫ ا‬, ‫ ا‬3 ‫ز‬
513
8
94‫آة ;م ه‬# -2
:/BJ‫ض ا‬2
M‫ آ‬M I ‫ ! ا رج‬3IeI 3‫ ت ا‬/ ‫ ا‬.!-‫! ر‬7 ! ‫ن‬2/9 w _I ‫ م ه‬N
‫ق‬YI .,:J‫ د‬5±1 ‫ " ور‬S7‫" ا‬9 S 7‫ ;ن ا‬T2YO w‫ إذا آ ن ا‬., X100±60
, / ‫ @آ ل‬S 7‫ ا‬,JY9 ‫ي‬.‫ ! ازم ا‬G‫ ا‬R9‫ز‬2I ,‫و‬- ‫ب‬27 ‫ ا‬.,:J‫ د‬3±1 , / ‫ا‬
‫؟‬, / 200 ‫ب @آ ل‬27 ‫ ا‬WJ2‫ل ا‬2C %‫ آ‬., - :g#6‫ض ا‬2
; GPSS World Sample File - TELEPHON.GPS, by Gerard F. Cummings
**************************************************************
*
*
*
*
*
Telephone System Model
*
*
*
**************************************************************
*
Simple Telephone Simulation
*
*
Time Unit is one minute
*
Sets
STORAGE
2
Transit
TABLE
M1,.5,1,20
;Transit times
GENERATE
1.667,1
;Calls arrive
GATE SNF
Sets,Occupied
;Try for a line
ENTER
Sets
;Connect call
ADVANCE
3,1
;Speak for 3+/-1 min
LEAVE
Sets
;Free a line
TABULATE
Transit
;Tabulate transit time
TERMINATE
1
;Remove a transaction
ADVANCE
5,1
;Wait 5 minutes
TRANSFER
,Again
;Try again
Again
Occupied
**************************************************************
514
: ‫ذج‬1‫ ا‬9H‫و‬
STORAGE
‫ن‬2` !7 M[ W"V‫ و‬2 ,‫ آ‬," ‫ و‬Storage Entity Sets ‫ن‬G ‫ آ ? ت ا‬,2 H
.3-‫ا ر‬
TABLE
‫ي‬.‫ ت وا‬/ ‫ ! ا‬G ‫اري‬/I Rf 37"9 P
‫ ف‬Table Transit 3 :@‫ول ا‬H‫ا‬
3; ! G‫ ـ " ا‬SNA ,9‫ ا"د‬, :‫ ;ن ا‬M " ‫ ء ا‬U‫ إ‬MJ ‫ ة‬., O‫ ا‬3 `I ‫"ض‬9
! &? U‫ إ‬36‫ و‬S7‫ ا‬3; &? ! S 7 ‫ق‬Y ‫ ا‬WJ2‫ ا‬M[ I 3‫ول وه‬HI M1 " ‫ م‬N‫ا‬
.‫ا ث‬
GENERATE
., X 100±60 M‫ آ‬29 , / M[ 9 M "
GATE
R - ‫ن‬2/I (‫ل‬2YO ) Occupied S J 3‫ ا‬M " ‫ ا‬M9 GATE Block S J
S C M[ I 3‫ وه‬,b
‫ن‬G ‫ آ ? ت ا‬,2 H ‫ن‬2/I
‫ ث‬9 ‫ا‬.‫ وه‬,2YO ‫ط‬27‫ا‬
.S7‫ إ دة ا‬MJ ‫ ر‬[email protected]‫ & ا‬SH9
ENTER
GATE ‫ ! ل‬9 M " ‫ ا@ام ;ن ا‬3; ‫ن‬G ‫ات ا‬6‫ ! و‬1 ‫ او‬0 W ‫إذا آ‬
‫ات‬6‫ و‬R - W ‫! اى ا إذا آ‬9GI ‫ة‬6‫م و‬I ‫ا‬.U ‫ و‬ENTER Block 3‫ وإ‬Block
‫ا ;ن ور اي‬.U ‫ و‬GATE Block ‫ ! ل‬M " ‫ ور اي‬a 9 !; ,2YO !9G‫ا‬
.‫ ح‬H U
9‫ ا‬%I , / M[ 9 ENTER Block ‫ ! ل‬M "
ADVANCE
515
M[ 9 ‫ي‬.‫ وا‬ADVANCE Block S J MI (, / ‫ ) ا‬M " ‫ ;ن ا‬5‫ ور‬, 6 3;
.‫آ ة‬
‫ ز ! ا‬9 36 S :‫ ا‬3; :9‫ و‬, X 180±60 ‫ق‬YI , /
LEAVE
!9G‫ ا‬,2 H ‫ات‬6‫ و‬6‫ ا‬M"H9 ‫ا‬.‫ ;ن ه‬LEAVE Block S J M " ‫ل‬2‫ د‬
.9- 3-‫ ر‬w ;2I M[ 9 ,‫ ( أي ا‬M " ‫;ة‬2
TABULATE
‫ ت‬/ ‫ ا‬, ‫ز‬0 ‫اري‬/‫ ا‬Rf ‫ ا‬3‫ ا‬, / ‫ل‬2C _f9 TABULATE Block S J
Table Transit 3; ," H ‫ا‬
TERMINATE
.S7‫آ ة " إآ ل ا‬
‫( ! ا‬, / ) M " M9G9 TERMINATE Block S J
ADVANCE
‫ ول‬6 J ‫ن‬2/9 Occupied , " %" ‫ وا‬ADVANCE Block 3‫ ا‬3Ie9 ‫ي‬.‫ ا‬M " ‫ا‬
Storage ‫ن‬G ‫ آ ? ت ا‬,2 H ! ( 3-‫ ر‬w ) !9GI ‫ة‬6‫ و‬3 ‫ل‬2
‫ ا‬3; MO;‫و‬
.‫ ة اى‬S7‫ ول ا‬9 ‫ ان‬MJ ,? fJ SH9 ‫ي‬.‫ ر ا‬[email protected]‫ ز ! ا‬M[ I 3‫ وه‬Entity Sets
TRANSFER
, " %" ‫ ا‬GATE Block
S J 3‫ ا‬M " M‫ آ‬M9 TRANSFER Block S J
‫ آ ? ت‬,2 H ! !9GI ‫ة‬6‫ و‬3 ‫ل‬2
‫ ا‬3; M " ‫ ول ا‬9 ‫ ه ك‬P6 Again
‫ أت‬3‫ ت ا‬/ ‫ا ا‬2[ 9 ! " ‫ء ا‬TA‫ ه‬., / ‫ ا‬SC "9 S 7‫ ( ان ا‬3" ‫ن‬G ‫ا‬
%" ‫ وا‬GATE Block S J ‫ل ;ن‬2YO !7‫ ! ا‬M‫ آ‬9- S C -‫ إذا و‬.%I %‫و‬
, "
%" ‫ ا‬ADVANCE Block S J 3; ‫ ر‬Nz &9 Again
, "
GATE S J ‫ ?ا‬.`:9 M " ‫ ;ن ا‬e‫ا ا‬.‫ " ه‬9:I ? J‫ د‬5 ‫ ة‬Occupied
eI U ‫ ث‬9‫ و‬GATE Block S J ! I , - ‫ ت ا‬7‫ ة اى ا‬,‫و‬
2 ," ‫ن‬G ‫ ? ت‬/‫ آ‬W-. _I U‫ط ا‬27 ‫“ ان د‬6h .‫آ ة‬
516
Block
‫ در ا‬YI %X , / ‫ ا‬M[ 9
!/ I % ‫ إذا‬.‫ط اى‬27 ,; V‫& إ‬9 ‫ي‬.‫ ا‬X0‫ ا‬3 ‫ رب‬HI ‫اء‬-‫ إ‬MU‫ن ! ا‬2/ :6T
S :‫ ا‬3; ‫آ ة‬
? J‫ د‬5 ‫وا ة‬N9 U‫! ا‬9? "‫ ! ا ور ;ن ا " ! ا‬, /
‫ ت‬/ ‫ د ا‬M[ 9 ‫ ود ا " ! ه‬Occupied , " %" ‫ ا‬ADVANCE Block
. UI‫ إ د‬NI 3‫ا‬
,‫و‬
‫ ت ا‬/ ‫ل ا‬2C ! , ` ‫ ت‬2" ]I ‫ف‬2 TABLE statement ‫ا" رة‬
‫اري‬/I Rf ‫! ! ء‬/ ; ! " ‫ ء ا‬U‫ إ‬MJ ‫ ة‬
M1 SNA ,‫و‬H ‫ا‬./‫وه‬
.%UI / ‫ @آ ل‬S C ,JY9 ‫ي‬.‫ ا‬WJ2‫ل ا‬2C ,`/
:‫إ=اء اآة‬
‫ار ا ر‬2 ‫ 'وق ا‬3;‫ و‬File / Open ‫ " ري إ ر‬9:I 2I‫آ ة و‬
Command / ‫آ ة ر‬
‫اء ا‬[email protected]
‫ ا‬SH9 ‫ا‬.‫ و " ه‬Open ‫ ا ر‬%XTELEPHON
Create Simulation
wYV‫ ا‬%X 200 ‫ ـ‬1 ‫ار ال‬2 ‫ 'وق ا‬3;‫ و‬Command / START ‫ إ ر‬%X
M[ 9 ‫ا‬.‫ وه‬TERMINATE Block S : M " 200 ‫آ ة " ور‬
‫ي‬:‫ ا‬9:‫ _ ا‬9:I , / GPSS ‫م‬2:9 ‫ف‬2 ‫آ ة‬
‫ ا‬3UOK
‫ ا‬,9 U ., / 200 ‫إآ ل‬
.9:‫ة ا‬.; 3; 3I‫ ذا‬M/O UN9 ‫ي‬.‫ وا‬Telephon.1.1
:g1‫ ا‬J1#
%J‫ ر‬, / ‫ ء ا‬[email protected] ‫ ت‬,:J‫ د‬359.16 ‫ ا " ري ي ان‬9:‫ ا‬3; End Time , J !
g‫ة ا ?] وذ‬.‫ ! ه‬,9J !/‫ و‬,` %J 37" ‫آ ة ات اي‬
‫" إ دة ا‬C200
‫ل ا`ة‬2C %‫ ! آ‬, ` ‫ ت‬2" 37"9 Transit 3 ‫ ا‬Table ‫ول‬H‫ ا‬3?‫ا‬2O"‫ ا‬Y
‫ ا‬,:J‫ د‬9.5 ! MJ‫ ا‬WJY‫ ت ا‬/ ‫ ا‬%N" ‫ ان‬%^ .& / ‫ @آ ل‬S 7‫ه ا‬.e9 3‫ا‬
.!? G‫ ء ا‬V‫ م ر‬SI J 3‫[ وا‬/ 5.‫ ت اآ[ ! ه‬J‫ او‬WJY‫ ت ا‬/ ‫ان ه ك‬
517
:‫ اآة‬0‫دا‬
‫ي و‬.‫ وا‬the ending condition of the simulation ‫آ ة‬
‫ ا‬,9 U ‫ن ط‬h‫ ا‬:
Expressions ,9H‫ة ا" رات ا‬.; ‫ ود م‬9:‫ة ا‬.; M`J‫ ا‬، ‫ي ا‬:‫ ا‬9:‫ا‬
T‫ او‬System Numeric Attributes ‫ م‬N ,9‫ " ا ` ت ا"د‬3‫ ا‬N Window
‫ إ ر‬،‫آ ة‬
‫ ا‬,9 U ! ‫آ ! ز‬eI
Window / Simulation Window / Expressions Window
, 3;‫ار و‬2 ‫ 'وق ا‬3; Edit Expressions Window ‫ ا" رات‬9 I ‫ة‬.; a`I
3‫ ا‬N 9 ‫ا‬.‫ ه‬AC1 S‫ اآ‬Expression field , 3;‫ و‬Time S‫ اآ‬Label field
utilization , "; 3‫ إ‬N ‫ن‬h‫ ا‬Memorize 3 ‫ و‬View 3 wYV‫ ا‬،3 ‫ ! ا‬G‫ا‬
, :‫ ل ا‬Label field , 3;‫ار و‬2 ‫ 'وق ا‬3; (_‫اء ! أ‬G-e‫_ )آ‬I U‫ط ا‬27
‫ ـ‬, ‫ ا‬, :‫ال ا‬
Expression field ‫ ا" رات‬, 3;‫ و‬Util ‫ ـ‬, ‫ا‬
‫ي‬.‫ ! ا‬G‫ ا‬w2 _f ‫ واا د‬Memorize 3‫ و‬View 3 wYV‫وا‬SR$Sets
‫ ـ‬, ‫ ا‬, :‫ ال ا‬Label field , 3;‫ار و‬2 ‫ 'وق ا‬3`; ،_I U‫ ا‬w ,; MYO9
‫ ـ‬, ‫ ا‬, :‫ ال ا‬Expression field "‫ ا‬, 3;‫ و‬Avg. Call Time
U "9 ‫ ه‬, "`‫ ا‬OK wYV‫ ا‬%X
Memorize 3‫ و‬View 3 wYV‫وا‬ST$Sets
Y‫ ! ا‬G‫د " ا‬2-‫ ! و‬%^ ‫ا‬./‫ وه‬83% , "; U ‫ط‬27‫ء ! ا_ وي ان ا‬GH‫آ‬
. "‫ة ا‬.; Y .‫ل‬2: ^ "9 ‫ر‬2 7‫ ا‬3; e‫م ;ن ا‬
‫ إ ر‬،‫ ت‬2‫ ا‬.;‫ا‬2 " a`
Window / Simulation Window / Storages Window
‫“ ا ي‬6T Storages Window Detail View !9G‫ة ا‬.; M ` N 37"9 ‫ا‬.‫ه‬
(Min and Max values) "‫ ! ا" ت ا` وا‬. 83% f9‫ط ه ا‬27‫ ا‬, ";
‫ط‬27‫! ا‬
2 ‫ او‬1 ‫ و‬0 U; W ‫ ت آ‬J‫آ ة آ ن ه ك او‬
‫ ا‬3; ‫ن ا م ي ان‬G ‫ول‬H‫ة ا‬.; ; ‫ إذا‬.›J I 3‫ ا‬%:‫ ه ا‬O ‫ة‬.; ‫ ا‬M`‫ ا‬3; G ‫د ا‬2 "‫ إم ا‬،,2YO
‫ إ ر‬،‫ ت‬/ ‫ ا‬, /I , ‫ز‬0 ‫اري‬/‫ ;ى ا رج ا‬Table Window
Window / Simulation Window / Table Window
518
‫ ا وق‬3; Transit , /‫آ ة ; ي ا‬
‫ ا‬5.‫ ه‬3; w:; 6‫ول وا‬- -29 &‫ ا‬P6‫و‬
! ‫ ز‬w2 ،M ‫ آ‬M/O ‫ول‬H‫ي ا‬I 36 ‫ة‬.; ‫ ا‬/I ! ‫آ‬eI OK ‫ إ ر‬، ‫ا‬
Expressions "‫ة ا‬.; 3; ST SNA ‫ ! ـ‬2‫ه‬
‫ة‬.; 3; ‫ ه‬O
‫ آ‬,:J‫ د‬2.99 2‫ ت ه‬/ ‫ا‬
‫ آ‬,:J‫ د‬14.27 2‫ ه‬, / ‫ ! إ دة ا‬G‫ ا‬w2 !/‫و‬Window
‫ إذا‬, / ‫ ا‬SC ‫ا @ دة‬- M92C ! ‫ا ز‬2f:9 ! 7‫ أي ان ا‬Table Window ‫ول‬H‫ا‬
.‫ل‬2: ^ ‫ا‬.‫ وه‬,2YO ‫ط‬27‫ ا‬W ‫'ف وآ‬
‫ إ ر‬، Transactions ! ` ‫ ا‬%‫ن اي ه‬h‫ ا‬N
Window / Simulation Window / Blocks Window
SC ‫وا إ دة‬N9 ‫ن‬2 ‫ ز‬15 -29 &‫“ ا‬6T Blocks Window S‫ا‬2:‫ة ا‬.; 5.‫ه‬
Entry Count ‫ل‬2‫د د ا‬2 3; S :‫ل ا‬2‫ د‬d9‫ ر‬N‫ ا‬،%UI /
Figure 2—1. Blocks Window Detailed View Showing TRANSFER Block.
ADVANCE S J ‫ا‬2‫! د‬9.‫ ا‬Transaction ! " ‫ د ا‬3‫ ا‬N‫ ث ه ؟ ا‬9 ‫ي‬.‫ا‬
“6 ., / 200 w:; W9-‫! ا‬/‫ و‬561! (‫ ت‬/ ‫ ر إ دة ا‬[email protected] ) 3 [‫ ا‬Block
519
‫آة‬
‫ي ا‬H ‫ف‬2 Ctrl+Alt+1 aI ` ‫ و ام‬Blocks Window S‫ا‬2:‫ة ا‬.; ! C ‫ ث؟ ة‬9 ‫ي‬.
‫ هت‬M‫ ه‬،‫ ة‬20 ‫ او‬15 g‫ ذ‬M";‫ إ‬، 9‫و‬9 ‫ة‬27 ‫ة‬27
‫ ة‬S7‫ ر و إ دة ا‬[email protected]‫ ا‬%U‫ و‬,2YO ‫ط‬27‫وا ا‬H9 S7‫"ون ا‬9 !9.‫ ت وا‬/ .;‫ا‬2‫ ا‬R - M`: ‫ أ‬., 2‫ ر‬.;‫ا‬2 ‫ ! ل ة‬UI‫ ه‬O ‫اء و‬-‫م دة إ‬2: ‫ف‬2 .‫ات‬
Model ‫ و‬Journal ‫ و‬Blocks .;‫ا‬2 ‫ى‬
R : ‫ ه‬N`6 3‫ ا‬%: ‫ و‬Expressions Window ,9H‫ة ا" رات ا‬.; a; "
Active
wO‫ ا‬M " ‫ ا‬%J‫ ر‬f9‫ ا‬2‫ي ه‬.‫ وا‬call number
, / ‫ ا‬%J‫ ر‬,; V‫إ‬
‫ إ ر‬، Transaction number
Window / Simulation Window / Expressions Window
, 3;‫ و‬Call no S‫ اآ‬Label field , 3;‫ ا" رات و‬9 I ‫ار‬26 ‫ 'وق‬3;
MJ‫ و‬Memorize 3‫ و‬View 3 wYV‫ ا‬XN1 S‫ اآ‬Expression field "‫ا‬
M/; ‫ا‬.U ‫و‬T‫آ ة ا‬
‫ ا‬3; ‫ ه‬N`6 3‫ وا‬: ,ƒ2` ‫ ا" رات ا‬R- ‫ة‬.; ‫` ل ا‬J‫إ‬
"‫ ا‬M‫ر آ‬2Uƒ " ‫ أا و‬View 3 %X Expression 3 wYV‫ إ‬,ƒ2`
.,?
‫ رة‬
[email protected]‫ و `ا"ادات ا‬Transactions ! " ‫ ا‬M‫ ‹ ! آ‬OK 3 wYV‫ا‬
‫ إ ر‬Main Menu ,?‫ة ا‬.; ‫; ! ا‬
Command / Clear
‫ذج‬2 ‫ ا‬3; 0‫ ا‬S :‫ق ا‬2; ‫ ا` رة‬A ‫ك‬6 Blocks Window S‫ا‬2:‫ة ا‬.; 3;‫و‬
The 3‫ و‬The TRANSFER Block 3 wYV‫ إ‬TRANSFER S J 2‫ي ه‬.‫وا‬
‫ و‬Journal ‫ و‬Blocks ,X[‫ ا‬.;‫ا‬2‫ك ا‬6 %X Place Icon in the Debug Toolbar
‫ إ‬،‫ح‬2V2 UI‫ ه‬O g/ 9 P
Expressions
Command / START
_J2 ‫آ ة‬
‫ ا‬OK wYV‫ وإ‬1000,NP ‫ ـ‬a
Continue ‫آ ة‬
‫ ا‬M ‫ أآ‬.‫ ^ا‬7 H9 % S 7‫! ان ا‬9 ‫ا‬.‫ وه‬S :‫ل ا‬2 ,‫و‬
‫آة‬
‫ ا‬6‫ا‬2‫ار ل ا‬2 ‫ 'وق ا‬3;‫و‬
‫اول‬
‫ ا‬U; _J2I ‫ ة‬M‫ آ‬3; ‫ ة ات‬, "‫ ا‬5.‫ آر ه‬Ctrl+Alt+C 3 wYf g‫وذ‬
S C 3 ‫آ ن‬
M‫_ آ‬J2‫ ا‬3; I ‫ف‬2 ‫آ ة‬
520
‫ ا‬Stop Condition _J2‫ ط ا‬W I
Journal ‫ة‬9H‫ة ا‬.; 3; trace messages R‫ ا‬M? ‫ ه ر‬OI ‫ف‬2‫ و‬N9 ‫ ان‬, / ‫ا‬
Stopped _J2 ‫ ا‬M " Transaction number M " ‫ ا‬%J‫! ر‬I 3‫ وا‬Window
‫ذج‬2 ‫ ا‬3; w:; 6‫ وا‬GENERATE Block 2I S J -29 &‫ ا‬P6 ، Transaction
‫ ه ك‬W ‫_ و; إذا آ‬J2I ‫ ان‬, / ‫ ا‬3 ‫ ة‬%‫ آ‬M " ‫ ا‬%J‫ ر‬,7‫ا‬2 ‫ ان ي‬/ ;
., [‫ ة ا‬,`J2 ‫ ت‬/
The
3 wYV‫ إ‬Blocks Window S‫ا‬2:‫ة ا‬.; 3`; _J2‫ ط ا‬M9G ‫ن‬h‫د ا‬
.;‫ا‬2 M`J‫ ا‬%X The Remove Icon in the Debug Toolbar 3‫ و‬Transfer Block
Expressions ‫و‬Blocks
. Ctrl+Alt+C 3 wYf g‫آ ة وذ‬
‫اء ا‬-‫ إ‬3; ‫ا‬
Storages Window Non- ‫ة‬.; ‫ ! ل‬g‫ي وذ‬HI 3‫آ ة وه‬
‫ ا‬SJ‫ف ا‬2
‫ إ‬Detailed View
Window / Simulation Window / Storages Window
‫ إ‬Main Menu ,?‫ة ا‬.; ‫و ! ا‬
Edit / Entity Details
Non-Detailed View ‫ة‬.; M"`
‫ إ ر‬، 9 2‫ة وه‬e ‫ ت ا‬/ ‫اري‬/‫ن ا رج ا‬h‫ ه ا‬O
Window / Simulation Window / Table Window
3 wYV‫ ا‬g. ‫ ه‬N‫ار ا‬2 ‫ 'وق ا‬3; ‫د‬2-2 & ‫ وإ‬w:; 6‫ول وا‬- -29 &‫ ا‬P6‫و‬
OK
، b WJ‫ ا& اي و‬N‫! ا‬/ 9‫ و‬3/ 9‫اري د‬/I ‫ رج‬T‫ إ‬2‫ه‬
%U S9 ‫ا‬.‫" ه‬C‫ ة و‬, ‫ ا‬3 M
Transit ‫ول ا‬H‫ا‬
9T !? G‫ ! ا‬9 ‫ول ان‬H‫ ! ا‬af9
.‫ ج‬[email protected]‫[ ! ا‬/‫ا‬
521
wYV , "; !9G‫ة ا‬.; M"-‫ إ‬.‫ ن‬X‫ ! إ‬T ‫ط‬27 4 3‫ط اآ[؟ آ‬27 `V‫ ا‬2 ‫ذا‬
‫ ا ر‬%X OK %X Command / Clear ‫ ا ر‬%X The Storages Window 3
S‫ار اآ‬2 ‫ 'وق ا‬3;‫ و‬Command /Custom
OK %X Sets Storage 4
3;‫ و‬Command / START ‫ ا ر‬،‫ ى ذا ث‬._I U‫ط ا‬27 ‫ا "ل د‬.‫ه‬
OK wYV‫ إ‬%X 1000 ‫ ـ‬a
‫ ا‬6‫ا‬2‫ار ال ا‬2 ‫'وق ا‬
&‫ ا‬H , / ‫ل ا‬27 ‫اري‬/‫ ا رج ا‬3‫ ا‬N ، ‫[ ! ا‬/ MJ‫_ ا‬I U‫ط ا‬27 , ";
S J ‫ ه ان‬O M ` ‫ ا‬U/ 3; S‫ا‬2:‫ة ا‬.; 3‫ ا‬N 2 RJ‫ا‬2‫ ا‬3; ،[/ Mf;‫ا‬
‫و ان‬9‫ و‬.S7‫ ج إ دة ا‬9 % ! 7‫ن اي ! ا‬0 g‫ د وذ‬I9 % TRANSFER Block
g‫ وذ‬,?
6‫ إ‬,:97 ‫ا‬.‫ ه‬,‫ ه‬SH9 ,:: ‫ ا‬3; .,: ‫ ا‬M‫ آ‬O ‫ ا‬M‫ آ‬W‫ط ازا‬27 ," ‫ار‬
ANOVA Command 0
.]? ‫ رن ا‬J‫_ و‬I ‫ط ه‬27 ,XX ‫ب‬- :!9 I
522
‫ دور‬.=‫> ا‬$4 ‫آة ;م‬# -3
:/BJ‫ض ا‬2
.‫ة‬6‫ و‬1000 ! ‫ن‬2/9 3?‫ون ا@ ا‬G ‫ ا‬. 2‫ ا‬,9‫ دور‬,"-‫ ا‬,7‫ا‬2 & %/ 9 3? U ] ‫ون‬G
M9"I ‫ اي ان‬،‫ة‬6‫ و‬1000 2‫ف ه‬U ‫ون ا‬G ‫ ا‬.‫ ل وي‬6 ‫ة و‬6‫ و‬63 ‫ و‬40 ! Y9 3 2‫ ا‬S7‫ا‬
‫ة او‬6‫ و‬800 2‫د ه‬2-2 ‫ون ا‬G ‫ ;ذا آ ن ا‬.‫ة‬6‫ و‬1000 ‫د و‬2-2 ‫ون ا‬G ‫ ا`ق ! ا‬S7 %9 ‫ون‬G ‫ا‬
M'2 lead time ‫م‬:‫ ز ! ا‬.‫ع‬2z ‫ م‬9‫ ا‬, ‫ م‬N M "I ,‫آ‬O‫ ا‬.‫ع‬2T‫ ا‬g. ‫ون‬G ‫"ل ا‬9 !; [‫اآ‬
‫ون‬G ‹: ‫ ; إذا آ ن ه ك اي‬I‫م و‬29 200 ‫ون ة‬G ‫ م ا‬N 3‫ آ‬6 .6‫ع وا‬2‫ ا‬2‫ ه‬,7‫ا‬
stockouts
:g#6‫ض ا‬2
; GPSS World Sample File - PERIODIC.GPS, by Gerard F. Cummings
*******************************************************************
*
*
Periodic Review Inventory Model
*
*
Time units are in days
*
*********************************************************************
*
Definitions of non block entities
RMULT
39941
Stock
STORAGE
10000
;Warehouse can hold 10000
Stock
TABLE
S$Stock,100,100,20
;Table for inventory amts
Orderqty VARIABLE
Target-S$Stock
;Order quantity
Demand
VARIABLE
[email protected]+40
;Daily demand
Target
EQU
1000
;Initial stock level
Reorder
EQU
800
;Reorder point
*********************************************************************
*
The reorder process
GENERATE
5,,,,1
TEST L
S$Stock,Reorder,Skip ;Is stock < Reorderpt
ASSIGN
2,V$Orderqty
;Parameter 2=Order quantity
5
;Lead time is 5 days
Stock,P2
;Stock increases by P2
Custwait ADVANCE
ENTER
Skip
;Review xact, Priority=1
TERMINATE
;Ordering xact is finished
*********************************************************************
523
*
The daily demand decrements quantity on hand
GENERATE
1
;Daily demand transaction
ASSIGN
1,V$Demand
;Parameter 1(P1)=daily
TABULATE
Stock
;Record daily stock
TEST GE
S$Stock,P1,Stockout
;Can order be filled
LEAVE
Stock,P1
;Remove demand from stock
TERMINATE
1
;Daily timer
Stockout TERMINATE
1
;Daily timer
demand
*********************************************************************
*
Initialize the inventory
GENERATE
,,,1,10
;Set initial stock
ENTER
Stock,Target
;Set init stock level=target
TERMINATE
;Xact is terminated
*********************************************************************
: ‫ذج‬1‫ ا‬9H‫و‬
RMULT
3?‫ا‬2O"‫ ا‬Y‫ ا‬XeI ‫ س‬J / 9 ‫اة‬2‫ ا‬Y .,?‫ا‬2O"‫اد ا‬T‫ ا‬2 ‫اة‬2 Rf9 0‫ا ا‬.‫ه‬
GPSS 3; ANOVA ‫ إام ا‬3; ‫ س‬0‫ ا‬M/O9 ‫آ ة‬
‫ار ا‬/I ،W ‫ا‬
STORAGE
[/ ‫ ا‬3‫ وه‬10000 ," & W7‫ ا‬Storage Entity Stock ‫ون‬G !9G‫آ ?! ا‬
!/ 9 &‫ ا‬P6 warehouse ‫ن‬G ,/‫ ا‬,"‫ ا‬M[ 9‫! ا" دي و‬9G‫ى ا‬2 !
Storage ‫ن‬G ‫ي ا‬2
.‫ف‬U ‫ون ا‬G ‫ ! ا‬9G9 ‫ون ن‬G ‫ى ا‬2 ‫ا ح‬
3 ‫ون ا‬G ‫ي ا‬2 ‫ا ;ن‬.U .3 ‫ون ا‬G ‫ى ا‬2 M[ & ‫ف‬2 ‫ا م‬
S$Stock 3 I SNA ,9‫ م د‬N ,` ‫آ ة آ‬
‫; ل ا‬2
TABLE
3 2‫ون ا‬G ‫ى ا‬2 d9‫ ر‬I R H RV‫ وو‬Stock 3 9 ‫ول‬ORDERQTY
524
‫دة‬2-2 ‫ون ا‬G ‫ ا‬, ‫‹ آ‬J Target ‫ف‬U ‫ون ا‬G ‫ى ا‬2 3‫ وه‬UC R G ‫ ا‬, /‫ا‬
stock on hand
DEMAND
‫ ا‬G 9 @ M "‫ ا‬.,9‫ت و‬T 6 ‫ة و‬6‫ و‬63 3‫ ا‬40 ! Y9‫ و‬3 2‫ ا‬S7‫ا‬
3‫ إ‬999 ‫ و‬0 ‫ ل‬H ‫ ! ا‬3?‫ا‬2O"‫ ا‬%J‫ل ا‬2 9 2U; modulo arithmetic , :‫ " ا‬3J ‫ا‬
, M
]I ‫ ا‬3?‫ا‬2O"‫ ا‬%J‫ ا‬40 ,; V ,? U‫ ا‬,H‫ ا‬3 M
‫ و‬23 ‫ و‬0 ‫ ل‬H ‫ا‬
V$Demand ‫ ا ة‬SNA ‫ م‬N ,9‫ ا"د‬,` ‫! ل ا‬
TARGET
9‫ و‬RV‫ و‬J‫ و‬Target 3 9‫ و‬target stock level ‫ف‬U ‫ون ا‬G ‫ى ا‬2
S7‫ إ دة ا‬,:9C 3 ‫ رب‬HI ‫اء‬-‫ إ‬MU‫ ا‬0‫ ا‬M"H9 %: ‫ إام ا ء‬1000
reorder scheme
REORDER
‫ آ ذآ‬800 ‫ ـ‬,9‫ و‬W"V‫ وو‬Reorder ‫ و ه‬reorder point S7‫ إ دة ا‬,7:
S7‫ إ دة ا‬,:9C 3 ‫ رب‬HI ‫اء‬-‫ إ‬MU‫ ا‬0‫ ا‬M"H9 %: ‫ إام ا ء‬: reorder scheme
Transactions ! " ‫ ا‬U9 3‫ ا‬S‫ا‬2:‫"ف ا‬I 3‫ ت ا‬J"‫ ا‬3‫ن إ‬h‫ ا‬N
.‫آ ة‬
‫اء ا‬-‫إ‬
GENERATE
! .‫آ ة‬
‫ م‬9‫ أ‬5 M‫ ة آ‬Transaction ! " ‫ ا‬29 GENERATE Block S J
S J ‫ در‬Y9 M "
‫ ه‬.‫آ ة‬
‫ ا‬5.U , ‫ة ز‬62‫م آ‬2‫ إام ا‬SH9 ‫ا‬
S7‫ون وإ دة ا‬G ‫ى ا‬2 ‫ض إ ر‬Y ‫آ ة‬
; ‫ن‬h‫ا‬
‫ م‬9‫ ا‬, M‫ آ‬GENERATE
.w:; ,- ‫ا‬
TEST
525
, J W ‫ ث إذا آ‬9 ‫ا‬.‫ وه‬T ‫وري ام‬V S7‫ د ; إذا آ ن إ دة ا‬9 TEST Block S J
‫ ?& ون‬U‫ إ‬%9 ‫ و‬Skip 3‫ إ‬G`:9 M‫ اا‬M " ‫ ;ن ا‬T‫ وإ‬Reorder ! MJ‫ ا‬S$Stock
.SC ‫آ ة إ دة‬
ASSIGN
‫;ن‬
reorder condition SC ‫ ط إ دة‬3‫ ه‬TEST Block S J ,H W ‫إذا آ‬
parameter 2 %J‫ ر‬%" ‫ ا‬37"9 ‫ا‬.‫ وه‬ASSIGN Block S :‫ ! ل ا‬9 M " ‫ا‬
. UC ‫" د‬9 3‫ ا‬, /‫ ا‬M " ‫ا ا‬.Unumber 2
ADVANCE
S7 ‫م‬:‫ ز ! ا‬M[ I 3‫آ ة وا‬
‫ م‬9‫ ا‬5 N9 S7‫_ ط إ دة ا‬O/9 ‫ي‬.‫ ا‬M " ‫ا‬
.S7‫ا ! ا‬2" 9T !9h‫“ ان ا " ! ا‬6T order lead time
ENTER
3‫_ ا‬f9‫ و‬ENTER Block S J M9 M " ‫ م ;ن ا‬9‫ ا‬, " S7‫ل ا‬2'‫ و‬
parameter number 2 2 %J‫ ر‬%" ‫ ا‬3; ‫دة‬2-2 ‫ ا‬, :‫ ا‬S$Stock , J
TERMINATE
‫ ) اد‬Termination Count ‫ ء‬[email protected]‫ ص اد ا‬:‫ ون إ‬Transactions ‫ن‬2 " ‫ ا‬U9
(‫آ ة‬
‫ ا‬,9 U ‫م "! ط‬9 ‫ ء‬[email protected]‫ا‬
GENERATE
‫آة‬
‫م‬29 M‫ ة آ‬2I ،3 2‫ ا‬S7‫ ا‬M[ 9 M "
ASSIGN
M " 1 %J‫ ر‬%" ‫ ا‬3; RV29 3 2‫ ا‬S7‫ا‬
TABULATE
526
: I MJ ‫ون‬G 3 2‫ى ا‬2 ‫اري‬/‫د ا رج ا‬H9 TABULATE Block S J
‫ ت‬C ‫اي‬
TEST
S7‫ ا‬: 9 ; ‹: -‫ ;ذا و‬stockout ‫ون‬G ‫‹ ا‬: ! : 9 TEST Block S J
Stockout ‫ ـ‬%" ‫ ا‬S :‫ ا‬3‫ إ‬M " ‫ ا‬M9‫و‬
LEAVE
‫م‬2:9‫ و‬3 2‫ ا‬S7‫ار ا‬: S$Stock ! ‹:9 M " ‫ون آ ف ;ن ا‬G ‫ى ا‬2 ‫إذا آ ن‬
( operand B ) B %" ‫ آ‬1 %J‫ ر‬%" ‫"! ا‬I‫ و‬LEAVE Block S J &2 ‫ا‬.U
TERMINATE
‫م‬29 ,9 U ‫ا‬A 1 ‫ار‬:
Termination Count ‫ ء‬[email protected]‫‹ اد ا‬:9‫ و‬M " ‫ ا‬U9
‫آة‬
TERMINATE
3 29 M " " ‫ إذا‬w:; M9 Stockout G %" ‫ ا‬TERMINATE Block S J
&:: I !/ 9T 3 2‫ ا‬,C ‫ان‬
GENERATE
‫ون‬G ‫ى ا‬2 ‫آ ة ء‬
‫ ا‬,9‫ ا‬6‫ وا‬M " 29 GENERATE P [‫ ا‬S :‫ا ا‬.‫ه‬
!9h‫ " ! ا‬M79 T 3/ ,f;‫و& ا ا‬
ENTER
Y ENTER Block S :‫م ا‬9 initializing Transaction 3? ‫ ا‬M " ‫ا‬
‫آة‬
‫ ا‬,9‫ف ا‬U ‫ى ا‬2 S$Stock , J
TERMINATE
527
‫‪ 3U9‬ا " ‪ M‬ا ?‪ 3‬ون إ‪ :‬ص اد ا@‪ U‬ء‪.‬‬
‫‪ N6‬ت‪:‬‬
‫‪ Y ˆ/ 3‬ت ا ‪ ,H‬ذات ا‪ R7‬ا" م ;ن ‪" a 9 GPSS‬ة " ! ‪2‬ا‪ 3; -‬ا آ!‬
‫`‪ 3; ,‬ا‬
‫آ ة اي ‪ ,N‬ز ‪ 3; .,‬ه‪.‬ا ا ‪2‬ذج ‪ 29‬ا " ! آ‪ ! M‬ا[‪,X‬‬
‫‪2J‬ا‪ GENERATE S‬وا‪ ,XX 2I 3‬ا‪2‬اع `‪ ! ,‬ا " !‪ 3`; .‬ا‪GH‬ء ا‪29 0‬‬
‫" ‪ M‬آ‪ , M‬ا‪ 9‬م ‪ M‬ا‪ ,"-‬ا ‪G‬ون وإ دة ا‪ S7‬إذا ا‪ 6‬ج ا‪ . 0‬و " ‪ ,‬ا‪ 9‬م‬
‫‪ M 9‬ا‪ S7‬و‪ R RV29‬ا ‪G‬ون‪ 3; .‬ا‪GH‬ء ا‪0‬و‪ w‬ا " ! ه ‪2[ 9‬ا ا‪ S7‬ا‪ 3 2‬و‬
‫‪29‬ا ;‪ 3‬إزا‪ ,6‬ا‪62‬ات ! ا ‪G‬ون إذا آ ‪ W‬ا‪ , /‬آ ;‪ ،,‬و‪ : I MJ !/‬ا‪H9 ,7‬ول‬
‫‪2‬ى ا ‪G‬ون ;‪ 3‬ا‪H‬ول ‪ . Stock‬ا " ‪ M‬ا‪ 62‬ا ‪ 3; 2‬ا‪GH‬ء ا‪, J Rf9 0‬‬
‫ا ‪G‬ون اا?‪ 3‬ـ ‪ 1000‬و‪6‬ة و‪ & 37"9‬ا‪ 3‬ا;‪e 36 ,f‬آ ا& ‪2/‬ن اول " ‪wO M‬‬
‫‪Active Transaction‬‬
‫و‪6‬ات ا‪ ! G‬ه ه‪ 3‬ا‪2‬م‪ .‬ا ‪2‬ى ا ‪ !? / 3‬ا ‪G‬ن ‪ Storage Entity‬ا ‬
‫‪2 M[ 9 Stock‬ى ا ‪G‬ون ا ‪ 3‬وه‪ 5.‬ا‪9 , :‬‬
‫‪ SNA ! U M‬ا ‪S$Stock‬‬
‫ا‪H‬ول ا ‪ R H9 Stock‬رج ‪/I‬اري ‪2‬ى ا ‪G‬ون ا‪ .3 2‬ا‪ %:‬ا ة‬
‫‪ Target‬و ‪- ! U ! " M[ I Reorder‬ا ‪.U‬ا ا ‪2‬ذج ;ـ ‪2 RfI Target‬ى‬
‫ا ‪G‬ون ا ‪U‬ف و ‪2 RfI Reorder‬ى ا ‪G‬ون ا‪.‬ي ‪ S9‬إ دة ا‪ .S7‬ام‬
‫‪Y‬ات إ ‪ YI ,2U / 9 ,‬ه‪ 5.‬ا " ‪ _O/ 3/ %‬ا?‪ M‬اى‪.‬‬
‫إ=اء اآة‪:‬‬
‫@‪-‬اء ا‬
‫آ ة و‪ 2I‬ا‪ 9:‬ا " ري ا ر ‪ File / Open‬و;‪' 3‬وق ا ‪2‬ار ا ر‬
‫‪ %X PERIODIC‬ا‪.?" Open wYV‬ن ‪ 2‬ا‬
‫آ ة ‪ ،‬ا ر ‪Command / Create‬‬
‫‪ %X Simulation‬ا ر ‪ Command / START‬و;‪' 3‬وق ا ‪2‬ار ل ‪, : 1‬‬
‫‪ %X 200‬ا‪ 3U OK wYV‬ا‬
‫آ ة " ‪ ،3 29 SC 200 : I‬إ‪ U‬ء ا‬
‫ا ] ‪ 3; 9:I‬ا _ ‪ . Periodic.1.1‬و‪"9‬ض ا‪. ? :I 9:‬‬
‫‪ J1#‬ا‪:g1‬‬
‫‪528‬‬
‫آ ة ‪29‬‬
‹: ‫ ! اي‬3 "9 %‫ و‬, 2‫ ت ا‬7‫ ا‬M‫ آ‬: 9 ‫ون‬G ‫ م ا‬N ‫ ان‬aV29 Stock ‫ول‬H‫ا‬
M ‫! ان‬9 ‫ا‬.‫ وه‬300 ! MJ‫ ا‬,‫و‬H 3 29 ‫ى‬2 , J ‫ اي‬-2IT &‫“ ا‬6 ‫ آ‬outage
.V ‫ م‬N‫ا‬
:‫ اآة‬0‫دا‬
‫ هت‬O ‫ة ا" رات‬.; ‫ء‬3U T‫ او‬.‫ ا " ري‬9:‫ي و ا‬.‫آ ة وا‬
‫ ا‬,9 U , 6 _O/
‫ ا ر‬.! J
Window / Simulation Window / Expressions Window
S‫ اآ‬Label G ‫ ا‬, 3;‫ ا" رات و‬9 I ‫ة‬.; 3;
No. Stockouts
wYV‫ ا‬stock outages ‫ ه‬O "H ‫ا‬.‫ ه‬N$Stockout S‫ ا" رات اآ‬, 3;‫و‬
maximum stock level 3 J0‫! ا‬9G‫ي ا‬2 _f Memorize ‫ و‬View
"‫ ا‬, 3;‫ و‬Max Stock ‫ ـ‬, ‫ ا‬, :‫ ال ا‬Label ‫ار‬2 ‫ 'وق ا‬3`;
_f Memorize 3 ‫ و‬View 3 wYV‫ ا‬SM$Stock ‫ ـ‬, ‫ ا‬, :‫ال ا‬
, :‫ ال ا‬Label , 3;
current stock level 3 ‫ون ا‬G ‫ي ا‬2 f9‫ا‬
3‫ و‬View 3 wYV‫ن ا‬h‫ ا‬S$Stock ‫ل ـ‬I "‫ ا‬, ‫ و‬Stock ‫ ـ‬, ‫ا‬
3‫ ا" رات ا‬, ‫ و‬Day 3‫ ا‬G ‫ ا‬, ^ ،‫م‬2‫ ا‬%J‫_ اا ر‬f Memorize
3; a- N OK 3 wYV‫ أا ا‬Memorize 3‫ و‬View 3 wYV‫ ا‬%X AC1
‫ون‬G ‫ ا‬stockouts ‫ون‬G ‫‹ ا‬: ‫ د‬, J ! ‫ ه‬O ‫ آ‬outages ‫ون‬G ‫‹ ا‬: R
‫آ‬
3‫ ا‬2‫آ ة وه‬
‫ون ل ا‬G ‫ي ا‬2 , J 3 J‫! أ‬9 Max Stock 3 J0‫ا‬
.RJ2
‫ & ر‬M
3 2‫ون ا‬G ‫ى ا‬2 ‫اري‬/‫ا رج ا‬
Window / Simulation Window / Table Window
OK wYV‫ إ‬6‫ول وا‬- -29 &‫ا‬
529
‫و‬
,G ‫ ا‬R? f‫ ا‬3; M7" ‫ ا ل ا‬M[ 9 ‫ا‬.‫ وه‬785.45 2‫ون ه‬G ‫ى ا‬2 w2 ‫“ ان‬6T
Stock ‫ول‬- !N6 ‫آ ة‬
‫ي ة‬HI U"H‫آ ة و‬
‫ ا‬R ،‫ م‬N‫ ا‬,`/ ‫ س‬: 2‫وه‬
‫ف أ ا‬2 ،‫ة ا" رات‬.; ‫ ه‬O ! ‫م و‬2‫ ا‬%J‫ ر‬SJ‫ ا‬f9‫ا‬
100,NP ‫ ـ‬1 ‫ار ال‬2 ‫ 'وق ا‬3;‫ و‬Command / START ‫ إ ر‬.‫م‬29 100
‫م‬29 ,b ‫ ل ا‬R HI 3‫ ه ا ت وه‬O ، OK ‫ ا ر‬%X (9:I 2IT 3"I NP)
‫ء‬GH‫ ! ا‬M " ‫ ا‬,9‫ اا‬،,7 ‫ا‬- ‫آ ة‬
,‫ اا‬, "‫ ا‬.MYO‫ ! ا‬,; [email protected]‫ا‬
‫م‬29 M‫ آ‬3; ‫ن‬.?" . Stock 3 ‫ ا‬Storage Entity ‫ن‬G ‫أ آ ?! ا‬9 ‫ذج‬2 ‫ ا‬3; P [‫ا‬
3; 29 SC ‫ إ دة‬M " ‫م‬29 ˆ M‫ذج وآ‬2 ‫ ! ا‬w‫و‬0‫ء ا‬GH‫ ا‬3; 29 SC M "
‫ول‬H‫ ا‬3I.; M`J‫ ا‬.‫ م اى‬9‫ ا‬, " T‫ إ‬: 9T S7‫ إ دة ا‬.‫ذج‬2 ‫ ! ا‬0‫ء ا‬GH‫ا‬
. Expressions ‫ و ا" رات‬Tables
. ‫ ا ر‬،M ` ‫ ا‬UO ‫ ا‬3; S‫ا‬2:‫ة ا‬.; ‫ن‬h‫ ا‬a`
Window / Simulation Window / Blocks Window
! " ‫ل ا‬2 3/‫ا ! ا"د ا‬.‫ه‬
M ` ‫ ا‬UO ‫ ا‬3; S‫ا‬2:‫ة ا‬.; M/
‫ و ا ر‬OK ‫ ا ر‬%X Command / Clear ‫ ا ر‬، ‫آ ة‬
‫ي ا‬- d9‫ ر‬I ‫ ه‬O ‫ف‬2
“6T OK wYV‫ وا‬100,NP ‫ ـ‬1 ‫ار ال‬2 ‫ 'وق ا‬3;‫ و‬Command / START
530
‫_ ا‪ C O‬ت ;‪ 3‬ا‪G-0‬اء ا `‪ 3; ,‬ا‬
‫آ ة ‪ ،‬آ ‪ OI‬ه ‪ ,XX -2I‬ا‪2‬اع `‪! ,‬‬
‫ا " !‬
‫‪- :!9 I‬ب ` ا ‪G‬ون ا ‪U‬ف إ‪ 800 3‬و‪6‬ة و‪ ,7:‬ا‪ S7‬إ‪ 600 3‬و‪6‬ة‪.‬‬
‫‪ J‬رن ا ?]‪.‬‬
‫‪531‬‬
‫>ن‬/4 @ /4 7‫آة ور‬# -4
:/BJ‫ض ا‬2
‫ة‬GU-0 overhaul ,9‫ اور‬, 6‫ إ'ح وا‬M ‫ن‬29G`I ‫ة‬GU-‫ إ'ح ا‬,‫م ور‬I
,9‫ اور‬, ‫ ا‬. U6 3; ,"9 ‫ ت‬6' ‫ م‬:‫ ?! و‬G‫ة ا‬GU-‫ ا‬, ‫ة و‬-A ‫ ا‬,‫ر‬2‫ا‬
,"9‫ ت ا‬6'@‫ ا‬. U ‫ @آ‬, 10±1 ‫ق‬YI‫ و‬, 40±8 M‫أ آ‬I ,‫ر‬2‫ة ا‬GU-0
15±5 ‫ق‬YI‫ و‬,:J‫ د‬90±10 M‫ آ‬M I‫ و‬9‫ر‬2; ‫ي‬HI ‫ات‬2J M9"I ‫ز او‬2; YI M[
‫ق‬YI‫ و‬, 5±1 M‫ آ‬M I ,9‫ د‬, '‫ ج إ'ح و‬I 3‫ ?! ا‬G‫ة ا‬GU-‫ أ‬.,:J‫د‬
‫ة‬GU-0 ,9‫ اور‬, ‫ ! ا‬a ‫ ا‬3; ,f;0‫ ا‬U !? G‫ة ا‬GU-‫ أ‬. U? [email protected] ,:J‫د‬120±30
.,‫ر‬2‫ا‬
.‫م‬29 50 ‫ ة‬,‫ر‬2‫ ا‬M ‫ آ‬6
-3
.!? G‫ ا‬, 3; e‫ وا‬a ‫ ا‬M , "; ‫د‬6
-4
:g#6‫ض ا‬2
; GPSS World Sample File - TVREPAIR.GPS, by Gerard F. Cummings
*****************************************************************
*
Television Maintenance Man Model
*
*****************************************************************
*
Repair of rented sets, one each week
*
*
Time unit is one minute
*
*****************************************************************
GENERATE
2400,480,,,1
;Overhaul of a rented set
QUEUE
Overhaul
;Queue for service
QUEUE
Alljobs
;Collect global statistics
SEIZE
Maintenance
;Obtain TV repairman
DEPART
Overhaul
;Leave queue for man
DEPART
Alljobs
;Collect global statistics
ADVANCE
600,60
;Complete job 10+/-1 hours
RELEASE
Maintenance
;Free repairman
TERMINATE
;Remove one transaction
*****************************************************************
*
On the spot repairs
GENERATE
90,10,,,3
;On-the-spot repairs
532
QUEUE
Spot
;Queue for spot repairs
QUEUE
Alljobs
;Collect global statistics
PREEMPT
Maintenance,PR
;Get the TV repairman
DEPART
Spot
;Depart the 'spot' queue
DEPART
Alljobs
;Collect global statistics
ADVANCE
15,5
;Time for tuning/fuse/fault
RETURN
Maintenance
;Free maintenance man
TERMINATE
****************************************************************
*
Normal repairs on customer owned sets
GENERATE
300,60,,,2
;Normal TV Repairs
QUEUE
Service
;Queue for service
QUEUE
Alljobs
;Collect global statistics
PREEMPT
Maintenance,PR
;Preempt maintenance man
DEPART
Service
;Depart the 'service' queue
DEPART
Alljobs
;Collect global statistics
ADVANCE
120,30
;Normal service time
RETURN
Maintenance
;Release the man
TERMINATE
*****************************************************************
*
GENERATE
480
TERMINATE
1
;One xact each 8 hr. day
Day counter
*****************************************************************
*
Tables of queue statistics
Overhaul QTABLE
Overhaul,10,10,20
Spot
QTABLE
Spot,10,10,20
Service
QTABLE
Service,10,10,20
Alljobs
QTABLE
Alljobs,10,10,20
*****************************************************************
:‫ذج‬1‫ ا‬2 9H‫و‬
GENERATE
3; S :‫ا ا‬.‫ ه‬3; 2I ,9‫ دور‬, ' 3‫ ج ا‬I 3‫ ا‬,‫ر‬2‫ة ا‬GU-‫ا ا‬2[ 9 !9.‫ا " ! وا‬
,I &92‫ او‬MJ‫ ا‬37"I ‫ ت‬6'@‫ ا‬5.‫ ه‬.? J ‫ن‬2/ ! G‫ة ا‬6‫ و‬., 40 M‫ آ‬w2 ‫ا‬
.1
533
QUEUE
‫ر‬2 7‫ ?! ا‬/ QUEUE S J .‫? ت `دة‬
.,9‫ اور‬, ‫ة ا‬GU-0 ‫ اء‬, ‫? ت از‬
6‫ إ‬R H QUEUE ! J ‫م‬I ‫ه‬
6‫ إ‬R H9 Overhaul 3 ‫ا‬Queue Entity
!‫ ا آ‬3; ‫ر‬/9 Alljobs 3 ‫ ا‬Queue Entity ‫ر‬2 7‫ ?! ا‬/ 3 [‫ ا‬QUEUE S J
.‫ة‬.U ‫ى ! ا ت آ‬0‫اع ا‬2q ‫? ت‬
6‫ إ‬R H9 3/ ‫اى‬
SEIZE
,U‫ ?! ا‬/ M[ I a ‫ ا‬M ‫ إه م‬3 M
I‫ و‬NI 3‫ ا‬,9‫ اور‬, ‫ ت ا‬6'‫إ‬
Maintenance ‫ ا ة‬Facility Entity
DEPART
‫ ن‬X‫ إ‬.5‫ ر‬N‫ إ‬WJ‫ و‬3U9 a ‫ ا‬M ,UI 5 ‫ إ‬3 ,9‫ دور‬, ' M " M
9 .,` Queue entities ‫ر‬2 C !? / ‫ ر‬[email protected]‫ ا‬WJ‫ و‬MHI DEPART S‫ا‬2J !
ADVANCE
.,:J‫ د‬600 ±60 ,9‫ اور‬, ‫ ز ! ا‬3‫ آ‬9 S :‫ا ا‬.‫ه‬
RELEASE
M 3; M[ ‫ ا‬,U‫ آ ?! ا‬M 39 U[ 9 ‫ي‬.‫ ا‬M " ‫ ;ن ا‬,9‫ دور‬, ' ‫ إآ ل‬
.‫أ‬I ‫ ان‬3; ‫ اى‬, a 9
a ‫ا‬
TERMINATE
Termination ‫ ء‬[email protected]‫ ص اد ا‬:‫ن إ‬2 ‫آ ة و‬
‫ ! ا‬U9 ,9‫ دور‬, M[ ‫ ا‬M " ‫ا‬
Count
GENERATE
534
M‫ آ‬w2 ‫ ا‬3; S :‫ا ا‬.‫ ه‬3; 2I ,9‫ر‬2`‫ ت ا‬6'z ![ ‫ ا‬Transactions ! " ‫ا‬
.,9‫ اور‬, ‫ أ ! ا‬,f;‫ أ‬%U‫ و‬,:J‫د‬90
QUEUE
‫ر‬2 7‫ ?! ا‬/ QUEUE S J .‫? ت `دة‬
6‫ إ‬R H QUEUE ! J ‫م‬I ‫ه‬
S J .,9‫ر‬2`‫ ا‬, ‫ة ا‬GU-0 ‫ اء‬, ‫? ت از‬
6‫ إ‬R H9 Spot 3 ‫ا‬Queue Entity
‫ ا آ! اى‬3; ‫ر‬/9 Alljobs 3 ‫ ا‬Queue Entity ‫ر‬2 7‫ ?! ا‬/ 3 [‫ ا‬QUEUE
.‫ة‬.U ‫ى ! ا ت آ‬0‫اع ا‬2q ‫? ت‬
6‫ إ‬R H9 3/
PREEMPT
,9‫ر‬2`‫ ا‬, ![ ‫ى ;ن ا " ! ا‬T‫ ا‬, ‫اع ا‬2‫ ا‬M‫ آ‬R7:I ,9‫ر‬2`‫ ا‬, ‫ان ا‬
M 3 M
I 3/ PREEMPT Block ‫ إء‬S : ,92‫ر أو‬2C 3; ‫ل‬2‫ ول ا‬I
.,9‫ او د‬,9‫ دور‬, ' , ‫ اي‬WJA M/O _J2 ‫ا‬.‫ وه‬a ‫ا‬
DEPART
S‫ا‬2J ! ‫ ن‬X‫ إ‬. .5‫ ر‬N‫ إ‬WJ‫ و‬3U9 a ‫ ا‬M ,U ,9‫ر‬2; , ' M " ‫ إ ك‬
.,` Queue entities ‫ر‬2 C !? / ‫ ر‬[email protected]‫ ا‬WJ‫ و‬MHI DEPART
ADVANCE
.,:J‫ د‬15±5 a ‫ ا‬WJ‫ و‬3‫ آ‬9 ADVANCE Block S J
RELEASE
M 3; M[ ‫ ا‬,U‫ آ ?! ا‬M 39 U[ 9 ‫ي‬.‫ ا‬M " ‫ ;ن ا‬,9‫ر‬2; , ' ‫ إآ ل‬
.‫أ‬I ‫ ان‬3; ‫ اى‬, a 9
a ‫ا‬
TERMINATE
Termination ‫ ء‬[email protected]‫ ص اد ا‬:‫ن إ‬2 ‫آ ة و‬
‫ ! ا‬U9 ,9‫ر‬2; , M[ ‫ ا‬M " ‫ا‬
Count
535
GENERATE-TERMINATE
,9‫ر‬2`‫ ا‬, ‫ ان ا‬P6 ،6‫ ; رق وا‬R ‫ء ا‬GH ‫آ‬
I M "9 ‫ذج‬2 ‫ء ! ا‬GH‫ا ا‬.‫ه‬
‫ا‬.U‫ و‬,9‫ اور‬, ‫ ا‬w:; R7:I ,9‫ ا" د‬, ‫ ان ا‬T‫ ا‬،‫ى‬T‫ ا‬, ‫اع ا‬2‫ اي ! ا‬R7:I
!f;0‫ ! ا‬R:I ,f;‫ ) ا‬2 ,9‫ و‬,f;‫ ا‬,9‫ د‬, ' M[ 9 ‫ي‬.‫ ا‬M " ‫ ا‬37" ;
(‫ى‬T‫ا‬
GENERATE
.‫آ ة‬
‫ ت‬8 M‫ آ‬29 6‫م وا‬29 ‫ ء‬f:‫م " إ‬9 M "
TERMINATE
‫ ء‬[email protected]‫ ! اد ا‬1 ‹:9 ‫ا‬.‫ ه‬. 9‫ر‬2; U9 Counting Transaction "‫ ا‬M "
) A M "‫آ ة ام ا‬
‫ل ا‬2C 3 ‫ة‬7
a 9
Termination Count
START Command ‫ ا‬3; (operand A
QTABLE
M‫ر آ‬2 7‫? ت ا‬
[email protected] ,9‫ار‬/I ‫ ت‬-‫"ف ر‬I Overhaul ‫أ ـ‬I 3‫ ا‬QTABLE ‫ رة‬
‫“ ه ا‬6T .‫ ا " ري‬9:‫ ا‬3; ‫"ض‬I 3‫ وا‬Table Window ‫ول‬- ‫ة‬.; 3; U
‫? ت‬
[email protected]‫ن ا‬0 Qtables ‫ر‬2 7‫اول ا‬H TABULATE Blocks S‫ا‬2J RV‫ ج و‬T
.3" ‫ ا‬DEPART Block S J 3‫ل ا‬2‫ ? ا‬:I MHI
‫و‬T‫ ا‬,X[‫اء ا‬G-0‫ ا‬.! " ‫ع _ ! ا‬2 & ‫ء‬G- M‫ آ‬.‫اء‬G-‫ ة أ‬3; %N ‫ذج‬2 ‫ا‬
3 ˆ; I U‫ة آ‬.‫ ه‬.SI‫ ا‬3 ,9‫ ا" د‬, ‫ وا‬,9‫ر‬2`‫ ا‬, ‫ وا‬,9‫ اور‬, ‫ ا‬M[ I
.a ‫ ا‬M M[ I 3‫ وا‬Maintenance ‫ة ا ة‬62‫ ا‬Facility Entity ,U‫ا‬
.,f;‫ ا‬MJ‫ ا‬W7‫ ا‬,9‫ اور‬, ‫وƒ ?_ ا‬
S J .‫آ‬
M ‫م‬29 M‫ آ‬M " ‫ ء‬U‫ وإ‬2 g‫آ ة وذ‬
‫ ا‬WJ29 ‫ذج‬2 ‫ ! ا‬3`‫ء ا‬GH‫ا‬
‫ ! ل‬7"9 ‫ي‬.‫‹ وا‬J ‫ ا‬3; ‫ ء‬[email protected]‫ "اد ا‬S9 ‫ي‬.‫ ا‬62‫ ا‬2‫ ه ه‬TERMINATE
‫ ء‬[email protected]‫ اد ا‬a 9
‫آ ة‬
‫_ ا‬J29 ‫ي‬.‫ وا‬START Command 0‫ا‬
.MJ‫ '`ا أو أ‬Termination Count (TG1)
536
Queue entities ‫ر‬2 7‫ آ ? ت ا‬,7‫ا‬2 R HI , ‫اع ا‬2‫ع ! ا‬2 M/ ‫ ر‬[email protected]‫ ت ا‬J‫أو‬
!? ‫ آ‬,7‫ا‬2 R HI _? ƒ2‫ ا‬R H e‫ ت ا‬J‫ أو‬Service ‫ و‬Spot ‫ و‬Overhaul ‫ا ة‬
.a ‫أ ا‬9 36 e‫ ا‬w:; a ‫ ت ا‬J‫ أو‬M OIT ‫ ت‬J‫و‬0‫ ا‬5.‫ ه‬Alljobs ‫ر‬2 7‫ا‬
,U ,:9C ‫ة‬.‫ وه‬Queue Entity ‫ر‬2 C !? ‫ آ‬M/ ‫ ; ه‬Qtable entities ‫آ ? ت‬
.‫ع‬2 M/ ‫ ر‬[email protected]‫ ت ا‬J‫و‬0 3? :I ‫اري‬/I ‫ رج‬3 ‫ل‬2
:‫إ=اء اآة‬
‫ار ر‬2 ‫ 'وق ا‬3;‫ و‬File / Open ‫ " ري ر‬9:I 2I‫آ ة و‬
Command /
‫آ ة ر‬
‫اء ا‬[email protected]
‫ ! ا‬h . Open ‫ ر‬%X TVREPAIR
‫ار ل‬2 ‫ 'وق ا‬3;‫ و‬Command / START ‫ ر‬%X Create Simulation
OK wYV‫ وإ‬50 ‫ ـ‬a
‫ ا‬6‫ا‬2‫ا‬
‫ا‬.‫ وه‬TERMINATE Block S : Transactions M " 50 ‫آ ة " ور‬
‫ ا‬3UI
.M ‫م‬29 50 M[ 9
‫ا‬.‫"ض ه‬9 . TVRepair.1.1 _ ‫ ا‬3; ‫ " ري‬9:I GPSS S/9 ‫آ ة‬
‫ ا‬,9 U .9‫ ر‬:‫ة ا‬.; 3; ? :I 9:‫ا‬
:g1‫ ا‬J1#
‫ ر‬[email protected]‫ ت ا‬J‫ او‬w2 . 78% & "; W ‫ إذ آ‬- M/O T2YO ‫ آ ن‬a ‫ ا‬M ‫“ ان‬69
‫ ه ك اي‬-29 % .,9‫ة ا" د‬GU-0‫ ا‬, ,:J‫ د‬51 ‫ و‬,9‫ة اور‬GU-0‫ ا‬, ,:J‫ د‬25 W ‫آ‬
M O9T ‫ا‬.‫ وه‬,:J‫ د‬12 3‫ا‬26 3/‫ ر ا‬[email protected]‫ ز ! ا‬w2 .,9‫ر‬2`‫ ا‬, ‫ƒ ?_ ا‬2 eI
DEPART Blocks S‫ا‬2J RV2 ‫ا‬N "C , ‫ ت ا‬J‫او‬
:‫ اآة‬0‫دا‬
.‫ ا " ري‬9:‫ ا‬2I ‫آ ة‬
537
‫ ا‬,9 U , 6 3‫ إ‬N
‫ ر‬Model Window ‫ذج‬2 ‫ة ا‬.; 3; , ? :‫ ! ا‬،a ‫ ا‬M , "; ! ‫آ‬e T‫او‬
wYV‫ ا‬%X FR$Maintenance S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / SHOW
. OK
‫ م‬N ,9‫ ا"د‬,` ‫ ا‬5.U ‫ذج‬2 ‫ة ا‬.; 3; Status line 7 3; ‫ هه‬O 3‫ ا‬, "`‫ا‬
78% W ‫ آ‬3‫اء ! ا_ وا‬G-e‫ آ‬U " SNA
‫ت‬U‫ة ا‬.; a` a ‫ ا‬M M[ I 3‫ ا‬Facility ,U‫ ا‬, 6 3‫ إ‬N 3/
Facilities Window
N ‫ن‬h‫ ! ا‬Window / Simulation Window / Facilities Window ‫ ر‬
.,:J‫ د‬52 3‫ا‬26 a ‫ ز ! ا‬w2 ،‫ة‬.; ‫ ا‬5.U M ` ‫ ا‬N ‫ ا‬3‫ا‬
‫اري‬/‫ ى ا رج ا‬Overhaul Table ‫ ـ‬Table Window ‫ول‬H‫ة ا‬.; ; ‫إذا‬
Window / Simulation Window / Table
‫و ا ر‬
The Down Arrow
‫ ر‬._? ƒ2‫ ر ا‬N‫ إ‬, ‫ز‬0
3 wYV‫ار إ‬2 ‫ 'وق ا‬3;‫ و‬Window
OK %X OVERHAUL
,9‫ول ا ت اور‬-.
538
‫ ه‬O 3/ .‫ ا" ري‬9:‫ ا‬3; Overhaul Table ‫ول‬- 3; ‫ ت آ‬2" ‫ `ˆ ا‬37"9 ‫ا‬.‫ه‬
‫ أو‬Spot ‫ او‬Service ‫ ء‬0‫! ر ا‬/‫ و‬: ‫;" ة‬
‫ر‬/ ،‫ى‬T‫ ا‬Qtable entities
.!9 ‫ا آ‬.‫ك ه‬9‫ و‬.‫ار‬2 ‫ 'وق ا‬3; Alljobs
., ‫ ا‬.;‫ا‬2‫ ا‬R - M`J‫أ‬
Model
‫ذج‬2 ‫ة ا‬.; 3; .,:J‫ د‬30 M‫ƒ ?_ آ‬2‫ ا‬M I
‫ ث‬9
‫ن‬h‫ ا‬N
! ,9‫ ا" د‬, ‫ء ا ص‬GH‫ ا‬3;) P [‫ ا‬GENERATE S J ! P Window
5 ‫ وي‬9 B ‫ و‬30 ‫ وي‬9 A S :‫ا ا‬.‫ ه‬operands ‫ ل‬a I P
‫ا‬.‫ ^ ه‬.(‫ذج‬2 ‫ا‬
GUH . Command / Retranslate ‫ذج ر‬2 ‫ ا‬, -I ‫ أ‬. 60 ‫ و‬300 ! T
Window / Simulation Window / Plot ‫ ر‬،‫آ ة‬
3;
‫اء ا‬-‫ إ دة إ‬MJ 3 %
‫ ا ت آ‬M‫ أد‬Edit Plot Window ‫ ت‬2‫ ا‬9 I ‫ة‬.; 3; %X Window
،3 ‫ ا‬%‫ا‬
‫ ت‬2‫ ا‬9 I ‫ة‬.; 539
3 ‫ و‬Plot 3 wYV‫ إ‬،%‫ `ˆ ا‬3 a ‫ ا‬M , ";‫ و‬, ‫ر ا‬2 C % ‫ف‬2.
, 3; Maintenance Util S‫ اآ‬، U ‫اد ر‬9 3‫ ا‬, ‫ ا‬%:‫ ا‬M‫ أد‬%X Memorize
%X Memorize ‫ و‬Plot 3 wYV‫ ا‬%X ‫ ا" رة‬, 3; FR$Maintenance ‫ و‬G ‫ا‬
Command / START ‫ ا ر‬%X ‫ح‬2V2 UI‫ ه‬O !/ 9 P
‫ة‬.; ‫ ا‬J ‫ آ‬.OK
OK %X 5 , : 1 ‫ار ل‬2 ‫ 'وق ا‬3;‫و‬
, "`‫ر ا‬2 7 %‫ر‬
،‫ة اى‬.; ‫ ا‬3‫ ا‬N ._J2I ‫ ون‬M "9 M "‫ة وا‬GU-0 ,b W '‫ ا‬,‫ر‬2‫ ان ا‬aV‫وا‬
Window / Simulation Window ‫ ا ر‬،‫ت‬U‫ة ا‬.; a;‫ ت و ا‬2‫ة ا‬.; M`J‫أ‬
,2:90‫ا و ا‬2I ‫ ه‬9‫ رأ‬3‫ وا‬, "`‫آ ا‬AI ‫ة‬.; ‫ ا‬5.‫“ ان ه‬6T / Facilities Window
Window / ‫ ا ر‬،,`ƒ‫ و‬62 3‫ا‬26 ،‫ة‬N ‫ƒ ?_ ا‬2 M92C ‫ر‬2 C !I (icon)
‫ول‬H‫ ا‬%‫ وأ ر إ‬5‫ا‬I ‫ ان‬9I ‫ول‬- M/ Simulation Window / Table Window
.UN9 ‫ي‬.‫ار ا‬2 ‫ ! 'وق ا‬Service ‫ أو‬Spot ‫ أو‬Alljobs ‫ أو‬Overhaul ،S ‫ا‬
T‫ا ا "ل وإ‬.U M I _? ƒ2‫ ة إذا ا ت ا‬3‫ ا‬,- 6 3; a ‫ ا‬M ‫ ه ان‬N‫! ا‬
.!? G‫[ ! ا‬/‫ ا‬:` ,‫ر‬2‫;ن ا‬
540
‫ =دة‬A B‫آة ;م ا‬# -5
:/BJ‫ض ا‬2
‫و‬0‫ ا‬, "‫ ا‬.‹ ` !:J RI U M‫ آ‬،‫ ! ا" ت‬," 9C ! ,"7J R I
‫ و‬15% ‫ إ‬U M‫ ج آ‬I ,[ [‫ وا‬, [‫ ا" ! ا‬. U" I ‫ " د‬R7:‫ ! ا‬20% ‫ ج إ‬I
.I ‫ `& و‬I ‫ن‬2/I U" I ‫ ا " د‬R7:‫ ! ا‬60% .3‫ا‬2‫ ا‬U" I ‫ " د‬R7:‫ ! ا‬5%
.;‫ ا‬U %I 3‫ ا‬, "‫ ! ا‬,H " ‫ إ دة‬3‫ ج ا‬I ,J ‫ ا‬40% ‫ واـ‬، scrapped
7"9 ‫و‬T‫ ا‬, " ! G‫ ا‬.3‫ ا‬R9‫ز‬2 ,:J‫ د‬30 M‫ آ‬w2 ‫ ا‬3; %9 ‫ة‬9- ,"7J , '
:3 ‫ول ا‬H
Time For First Process
Frequency
.05 .13 .16 .22 .29 .15
Process time (mins) 10 14 21 32 38 45
‫ و‬,:J‫ د‬24 w2 3"C R9‫ز‬2I & ‫ة‬0‫ ا‬, "‫ ? وز ! ا‬J‫ د‬15±6 ‫ق‬YI , [‫ ا‬, "‫ا‬
.? J‫ د‬4 ‫إ اف " ري‬
., / ,"7J 100 ‫ ـ‬R ‫ ت ا‬3‫ آ‬6 -1
.,V2; ‫ ا‬R7:‫ ود ا‬g. ‫زم‬h‫ ! ا‬G‫ ! ا‬-2
:g#6‫ض ا‬2
; GPSS World Sample File - QCONTROL.GPS, by Gerard F. Cummings
*****************************************************************
*
*
*
Quality Control Program
*
*
Time units are in minutes
*
*****************************************************************
RMULT
*
93211
Definitions
Transit
TABLE
M1,100,100,20
541
;Transit Time
Process
FUNCTION
RN1,D7
0,0/.05,10/.18,14/.34,21/.56,32/.85,38/1.0,45
*****************************************************************
Stage1
GENERATE
(Exponential(1,0,30))
ASSIGN
1,FN$Process
SEIZE
Machine1
ADVANCE
P1
RELEASE
Machine1
ADVANCE
2
;Inspection
TRANSFER
.200,,Rework1
;20% Need rework
;Process time in P1
;Process 1
*****************************************************************
Stage2
SEIZE
Machine2
ADVANCE
15,6
RELEASE
Machine2
ADVANCE
2
;Inspection
TRANSFER
.150,,Rework2
;15% Need rework
;Process 2
*****************************************************************
Stage3
SEIZE
Machine3
ADVANCE
(Normal(1,24,4))
RELEASE
Machine3
ADVANCE
2
;Inspection 3
TRANSFER
.050,,Rework3
;5% need rework
TABULATE
Transit
;Record transit time
TERMINATE
1
;Process 3
*****************************************************************
Rework1
TRANSFER
.400,,Stage1
TERMINATE
Rework2
TRANSFER
.400,,Stage2
TERMINATE
Rework3
TRANSFER
.400,,Stage3
TERMINATE
: ‫ذج‬1‫ ا‬9H‫و‬
RMULT
‫اة‬2 Y ; ‫آ ة‬
‫ارات‬/I ‫اء‬[email protected] ,- ‫ ا‬. 1 %J‫ ر‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬2 ‫اة‬2 ‫ء‬
.w:; ,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬2
542
TABLE
‫ ه‬O ‫ي‬.‫اري وا‬/‫ ا ت رج ا‬R H9 ‫ف‬2 Table Transit 3 :@‫ول ا‬H‫ا‬
. `I
FUNCTION
10, 14, 21, (! ‫أ ! ا ر‬J‫ )إ‬, :‫ ا‬37"I PROCESS 5 ‫ ا‬GPSS ,Y ,‫دا‬
SH9 GPSS Functions ‫ دوال‬3; &‫“ ا‬6T .‫ ة‬7" ‫ت ا‬T [email protected]‫ ا‬S 32, 38, 45
!" Cumulative Distribution Functions
3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫إام دا‬
.‫ت‬T [email protected]‫ا‬
GENERATE
,Y 3‫ اا‬30‫ ا‬R9‫ز‬2‫ أ ا‬.3‫ ا‬R9‫ز‬2 w2 ‫ ا‬3; ,:J‫ د‬30 M‫ة آ‬9- R7J R I
.GPSS
ASSIGN
M " parameter number 1 ‫ول‬0‫ ا‬M "‫ ا‬3; RV‫ و‬M " ‫و‬T‫ ا‬,6 R ‫ز ! ا‬
Transaction
SEIZE
Machine1 3 ‫ ا‬Facility Entity ,U‫ آ ?! ا‬NI ‫ أو‬g I ,`ƒ2‫ او ا‬M "‫ا‬
ADVANCE
parameter 1 ‫ول‬0‫ ا‬M "‫ ا‬3; ‫ن‬G ‫ ! ا‬G‫ار ا‬:
,2YO Machine1 ,`ƒ2‫ ا‬3:I
.,`ƒ2 M[ ‫ ا‬M " RELEASE
543
‫ إذا‬N ‫ ا‬M " U Y‫ إ‬.? !/ 9 3‫ وا‬Machine1 ‫ك‬9 ,`ƒ2 M[ ‫ ا‬M " ‫ا‬
.-‫و‬
ADVANCE
.‹ `‫ ز ! ا‬3‫ آ‬9 ADVANCE Block S :‫ا‬
TRANSFER
‫ إ‬S‫ه‬. ! " ‫ ! ا‬20% 3?‫ا‬2O M/O ‫ ر‬9 ‫ف‬2 TRANSFER Block S J
! 80% ‫ اـ‬. Stage1 ! ,HI ‫ ا‬,"7:‫ ا‬MO; M[ 9 ‫ا‬.‫ ه‬. Rework1 G ‫ ا‬S :‫ا‬
., ‫ ا‬,6 ‫ وا‬9 T‫ا " ! ا‬
SEIZE
.Machine2 ‫ ا ة‬Facility Entity ,U‫ ا‬N9 ‫ او‬g 9 ‹ `‫ي ! ا‬.‫ ا‬M " ‫ا‬
ADVANCE
.stage 2 , [‫ ا‬,6 ‫ ز ! ا‬3‫ آ‬9 ADVANCE Block S :‫ا‬
RELEASE
‫ إذا‬N ‫ ا‬M " U Y‫ إ‬.? !/ 9 3‫ وا‬Machine2 ‫ك‬9 ,`ƒ2 M[ ‫ ا‬M " ‫ا‬
.-‫و‬
ADVANCE
.‹ `‫ ز ! ا‬3‫ آ‬9 ADVANCE Block S :‫ا‬
TRANSFER
544
‫ إ‬S‫ه‬. ! " ‫ ! ا‬15% 3?‫ا‬2O M/O ‫ ر‬9 ‫ف‬2 TRANSFER Block S J
! 85% ‫ اـ‬. Stage2 ! ,HI ‫ ا‬,"7:‫ ا‬MO; M[ 9 ‫ا‬.‫ ه‬. Rework2 G ‫ ا‬S :‫ا‬
., ‫ ا‬,6 ‫ وا‬9 T‫ا " ! ا‬
SEIZE
.Machine3 ‫ ا ة‬Facility Entity ,U‫ ا‬N9 ‫ او‬g 9 ‹ `‫ي ! ا‬.‫ ا‬M " ‫ا‬
ADVANCE
‫زع‬2 ‫ق‬Y ‫ ! ا‬G‫ ا‬.stage 3 , [‫ ا‬,6 ‫ ز ! ا‬3‫ آ‬9 ADVANCE Block S :‫ا‬
. "C
RELEASE
‫ إذا‬N ‫ ا‬M " U Y‫ إ‬.? !/ 9 3‫ وا‬Machine3 ‫ك‬9 ,`ƒ2 M[ ‫ ا‬M " ‫ا‬
.-‫و‬
ADVANCE
.‹ `‫ ز ! ا‬3‫ آ‬9 ADVANCE Block S :‫ا‬
TRANSFER
‫ إ‬S‫ه‬. ! " ‫ ! ا‬5%
! 95%
3?‫ا‬2O M/O ‫ ر‬9 ‫ف‬2 TRANSFER Block S J
‫ اـ‬. stage 3 ! ,HI ‫ ا‬,"7:‫ ا‬MO; M[ 9 ‫ا‬.‫ ه‬. Rework3 G ‫ ا‬S :‫ا‬
., / ‫ ا‬R7:‫ا ا‬2[ 9 T‫ا " ! ا‬
TABULATE
545
‫ول‬H ‫اري ا ص‬/‫_ ز ! ا@آ ل ا ا رج ا‬f9 TABULATE Block S J
3; ,9‫ار‬/I ‫ ت‬-‫ ه آ ر‬OI‫ ا " ري و‬9:‫ ا‬3; ? :I ‫اول‬H‫ ا‬S/I ، Transit ‫ا‬
.‫ة‬6 3 M‫اول آ‬H‫ ا‬.;‫ا‬2
TERMINATE
!" ‫آ ة د‬
/ 9 .‫ ء‬[email protected]‫‹ اد ا‬:9‫ و‬M " ‫ ا‬3U9 TERMINATE Block S J
START ‫ ( ! رة‬operand A) A M "‫ ا‬3; R7J ‫ ام اد‬, / ‫ ا‬R7:‫! ا‬
.statement
TRANSFER
‫" د‬9 ‫ ان‬3; 40% ‫ ل‬6‫و ;ن & إ‬T‫ ا‬,6 ‫ ا‬3; R7:‫( ; ‹ ا‬,"7J) M " MO`9 . U" I ‫" د‬9 ,"7J M[ 9 ‫ا‬.‫ وه‬.‫و‬T‫ ا‬,6 ‫إ ا‬
TERMINATE
. M[ 9 ‫ا‬.‫ وه‬., / ‫ ا‬R7:‫ ص اد ا‬:‫آ ة ون إ‬
‫ ! ا‬%U? U‫ إ‬%9 !9h‫ا " ! ا‬
.R7:‫ ا‬scrapping
TRANSFER
S :‫ا ا‬.‫ ا ه‬M9‫ و‬, [‫ ا‬,6 ‫ ا‬3; R7:‫( ; ‹ ا‬,"7J) M "
MO`9
M[ 9 ‫ا‬.‫ وه‬. ., [‫ ا‬,6 ‫" د ا ا‬9 ‫ ان‬3; 40% ‫ ل‬6‫ن & إ‬2/9 TRANSFER Block
. U" I ‫" د‬9 ,"7J
TERMINATE
. M[ 9 ‫ا‬.‫ وه‬., / ‫ ا‬R7:‫ ص اد ا‬:‫آ ة ون إ‬
‫ ! ا‬%U? U‫ إ‬%9 !9h‫ا " ! ا‬
.R7:‫ ا‬scrapping
TRANSFER
546
‫" د إ‬9 ‫ ان‬3; 40% ‫ ل‬6‫ ;ن & إ‬,[ [‫ ا‬,6 ‫ ا‬3; R7:‫( ; ‹ ا‬,"7J) M " MO`9 . U" I ‫" د‬9 ,"7J M[ 9 ‫ا‬.‫ وه‬.,[ [‫ ا‬,6 ‫ا‬
TERMINATE
. M[ 9 ‫ا‬.‫ وه‬., / ‫ ا‬R7:‫ ص اد ا‬:‫آ ة ون إ‬
‫ ! ا‬%U? U‫ إ‬%9 !9h‫ا " ! ا‬
.R7:‫ ا‬scrapping
, ,‫ ودا‬Transit Table 3 :‫ول إ‬- _9"I " .‫اء‬G-‫ ة أ‬3; %N ‫ذج‬2 ‫ا‬
M‫ آ‬.R I , M[ 9 U M‫ذج آ‬2 ‫اء‬G-‫ أ‬,XX -29 &‫ ا‬H Process Function
‫ت‬T 6‫ إ‬U ‫ة‬27 M‫ آ‬.? J‫ ا‬3‫ ! ه‬G‫ات ا‬6‫ و‬.R ‫ ا‬M6‫ ا‬6‫ ا‬3; ,"7J M[ 9 M "
Rework2 ‫ أو‬Rework1 ‫ة‬G ‫ ا‬S‫ا‬2:‫ ا‬6‫ إ أ‬M " ‫ ا‬M9 , ‫ ا‬5.‫ ه‬3; 3‫ وا‬،MO;
"I T‫ وإ‬.I ‫ ان‬3; 60% ‫ ل‬6‫ إ‬U U" I ‫ ا " د‬R7:‫ ا‬.3‫ا‬2‫ ا‬Rework3 ‫أو‬
.‫ة‬0‫ ا‬UI27
:‫إ=اء اآة‬
‫ار ر‬2 ‫ و ! 'وق ا‬File / Open
Command / ‫آ ة ر‬
‫ ر‬,?‫ة ا‬.; ‫ ا‬3;
‫ ا‬SH9 %X ! ‫ و‬Open wYf‫و‬QCONTROL
‫ ـ‬1 ‫ار ل‬2 ‫ 'وق ا‬3; Command / START ‫ ر‬%X Create Simulation
OK wYV‫ إ‬%X 100
TERMINATE Block S J Transactions M " 100 M9
QControl.1.1 _ ‫ " ري ا ا‬9:I S/9 ‫ آ " د‬., ‫ آ‬,"
‫آ ة‬
‫ ا‬3UI
,"7J 100 M[ 9 ‫ا‬.‫وه‬
.9‫ ر‬:‫ة ا‬.; 3; 3? :I M/O f9‫ ا‬UN9 9:‫ا ا‬.‫ ه‬.
:g1‫ ا‬J1#
3‫ا‬26 ‫ ? أو‬J‫ د‬4153.8 ‫ق‬Y‫ ا " ري ى ا& ا‬9:‫ ا‬3; End Time ‫ ء‬[email protected]‫! ز ! ا‬
‫ د‬H9‫ إ‬R7 Block entry counts S‫ا‬2:‫ل ا‬2‫"اد د‬I ! .,"7J 100 ‫ @آ ل‬, 69
547
Rework3 ‫ و‬Rework2 ‫ و‬Rework1 S‫ا‬2:‫ل ا‬2 3/‫ ا"د ا‬.,V2; ‫ ا‬R7:‫د ا‬
R7J 4 ‫ و‬, [‫ ا‬,6 ‫ ا‬3; WO; ,"7J 14 ‫و و‬T‫ ا‬,6 ‫ ا‬3; WO; ,"7J 22 ‫! ان ه ك‬9
.‫ت‬. ,"7J (11+7+3) 21 U , ; ,"7J 40 M/O9 ‫ا‬.‫ ه‬.,[ [‫ ا‬,6 ‫ ا‬3; WO;
:‫ اآة‬0‫دا‬
0‫ م ا‬. ‫ ا " ري ا‬9:‫ ه ا‬2I 3‫آ ة ا‬
System Numeric
‫ ا‬,9 U , 6 _O/
‫ م‬N ,9‫ إ " ا ` ت ا"د‬N SHOW Command
3;‫ و‬Command / SHOW ‫آ ة ر‬
‫ ا‬,9 U ! ‫آ ! ز‬e T‫ او‬.Attributes
! G‫ ه ان ا‬O Status Line , ‫ ا‬7 3; OK wYV‫ ا‬%X AC1 S‫ار أآ‬2 ‫'وق ا‬
3;‫ و‬Command / SHOW ‫ ر‬. ‫ ا‬9:‫ ا‬3; ‫آ ة‬
‫ ا‬,9 U ! ‫ ز‬9‫ و‬3 ‫ا‬
3‫ ا‬R7:‫ د ا‬2‫( ه‬22) , :‫ ا‬5.‫ ه‬، OK wYV‫ ا‬%X N$Rework1 S‫ار أآ‬2 ‫'وق ا‬
.‫و‬T‫ ا‬,6 ‫ ا‬3; WO;
‫ ر‬،‫ ت‬2‫ ا‬.;‫ا‬2 " ‫ ه‬O
Window / Simulation Window / Facilities Window
R7:‫ د آ ! ا‬-29 &‫ا وا‬- , Machine1 , "; ‫“ ان‬6T .‫ت‬U‫ة ا‬.; 5.‫ه‬
‫ل‬2YO ‫ر ا‬
‫ا ا‬.‫ ه‬M 9 &0 : [ Machine1 MO`‫وا أن "ل ا‬9 ،‫ة‬N ‫ا‬
.&:79
[‫ا اآ‬-
‫ إ& ر‬N ،‫ ا@آ ل‬, ‫ز‬0 ‫اري‬/I ‫ رج‬2‫ ه‬Table Transit ‫ول‬H‫ا‬
Window / Simulation Window / Table Window
wYf ‫آ ة‬
‫ ا‬3; 6‫ول وا‬- -29 &‫ ا‬P6 w:; Transit , ‫ار ى آ‬2 ‫ 'وق ا‬3;‫و‬
OK ‫ن‬h‫ ا‬.,:J‫ د‬800 ! [‫ اآ‬.‫ ا‬R7:‫ ان " ا‬T‫ ا‬,:J‫ د‬321 ‫ ء آ ن‬[email protected]‫ ز ! ا‬w2 ‫ ان‬%^
.‫اول‬H‫ت وا‬U‫ ا‬.;‫ا‬2 M`J‫أ‬
‫ ر‬.‫ ت‬2" ‫ ا‬5.‫ ه‬7"I ‫ف‬2 S‫ا‬2:‫ة ا‬.; ‫؟‬R7:‫! ا‬9‫ن أ‬h‫ ا‬N‫ا‬
548
Window / Simulation Window / Blocks Window
! ‫آة‬
‫ي ا‬H ‫ف‬2 . ASSIGN S J 3; Machine1 NI ,"7J 30 -2I &‫“ ا‬6T
%:‫ " ا‬Ub"‫ة ا" رات و‬.; a` ‫ أ‬.‫ ت‬2‫ ا‬.;‫ا‬2 " ‫ هه ! ل‬O‫ و‬9‫ة‬.; a`‫آ ة و‬
‫ ه إ ب ا‬O 3/ &62` S‫ا‬2:‫ة ا‬.; 3: . UN6 3; S^ 3‫ا‬
‫ ر‬.‫آ ة‬
‫ى ا‬HI ‫ ا رة‬%:‫ هت " ا‬O "‫ا‬
Window / Simulation Window / Expressions Window
S‫ ا" أآ‬, 3;‫ و‬Rework1 S‫ أآ‬G ‫ ا‬, 3;‫ ا" رات و‬9 I ‫ 'وق‬3;
‫ء‬G- ‫“ ان‬6T U" I ‫ @ دة‬W‫ ار‬,"7J %‫ف ى آ‬2 ‫ة‬.; ‫ ه ا‬O N$Rework1
" R ‫ ا إ دة ا‬N‫ ا‬%X Memorize ‫ و‬View wYV‫ ا‬..9 ‫ف‬2 U
3; , ‫ ا‬, :‫ار ال ا‬2 ‫ 'وق ا‬3;‫ ا" رات و‬9 I ‫ة‬.; 3; ., [‫ ا‬,h ,H " ‫ا‬
N$Rework2 ‫ ـ‬, ‫ ا‬, :‫ ا" ال ا‬, 3;‫ و‬Rework2 , : G ‫ ا‬, ‫ ـ‬G ‫ة ا" رات آ ل ا‬.; 3; ,[ [‫ ا‬,h ,H " ‫ " ا‬R ‫ ا إ دة ا‬N‫أا أ‬
‫ا‬.‫ ه‬. Memorize ‫ و‬View wYV‫ ا‬%X N$Rework3 ‫ وا" ـ‬Rework3
! `‫ ه ا " ! ا‬O ‫ف‬2 S‫ا‬2:‫ة ا‬.; 3; f9‫ ا‬،, `‫ ا‬R7:‫ هت ا‬O !
/ Rework3 ‫ و‬Rework2 ‫ و‬Rework1 S‫ا‬2: !‫اا‬
Part S‫ أآ‬G ‫ ا‬, 3;‫ار و‬2 ‫ 'وق ا‬3; ،wO‫ ا‬M " ,"7:‫ ا‬%J‫ ا ر‬N
OK %X Memorize ‫ و‬View wYV‫ ا‬XN1 S‫ ا" رات أآ‬, 3;‫ و‬number
‫ ر‬,?‫ ا‬, ? :‫ ! ا‬.,?
[email protected]‫ ا " ! و ` ا"ادات ا‬M‫‹ ! آ‬
‫ف‬2 Clear q XeI T U0 ` I % Part no. , :‫ ا‬. OK ‫ و‬Command / Clear
Command ‫ ر‬. " UNI P
"‫ وا‬S‫ا‬2:‫ ا‬3I.;‫ك ا‬6 .‫آ ة‬
‫د ء ا‬H YI
OK %X 50 ‫ ـ‬1 ‫ و ل‬/ START
‫؟‬gI N6 S‫ أآ‬."‫ وا‬S‫ا‬2:‫ ا‬3I.; “6T
‫وث‬6 ‫آ ة‬
‫_ ا‬J2 ‫ د‬.MO`I % R7:‫ ا‬%N" ‫ ;ن‬WN6T ‫ آ‬. "‫ة ا‬.; M`J‫ن ا‬h‫ا‬
‫ ر‬S‫ا‬2:‫ة ا‬.; 3;‫( و‬Ctrl+Alt+H) Halt ‫آ ة‬
‫_ ا‬J‫ أو‬.‫و‬0‫ ا‬,6 ‫ ا‬3; ,"7: MO;
S :‫ ا‬3 ‫ ا` رة‬A RV ،‫ هة ا ة‬O ‫ ا‬3‫ل ا‬2 3/ View / Entity Details
549
7 3; Place wYV‫ ا‬%X (&2 Y9) ‫ را‬a ; & wYV‫ وأ‬Rework1 G ‫ا‬
M " MO; ‫آ ة‬
‫_ ا‬J2 . (Ctrl+Alt+C) 3 wYf ‫آ ة‬
‫ن‬h‫ ا‬.!I (Ctrl+Alt+1) wYf ‫ة‬27 ‫ة‬27 ‫آ ة‬
‫ إ ا‬.‫دوات‬0‫ا‬
‫ى ا‬-‫ن ا‬h‫ ا‬Rework1 ‫؟‬gI N6 ‫ اى ودون‬M?‫ب ا‬- .g` ‫ذج‬2 ‫ ا‬, H %J
550
:-/C D*1 >$4 ‫آة ;م‬# -6
:/BJ‫ض ا‬2
SC , ‫ وآ‬،‫ة‬6‫ و‬600 W"V‫ و‬، order point SC ,7: & %/ I !9GI ‫ م‬N
.‫ة‬6‫ و‬700 ,‫و‬0‫ون ا‬G ‫ ا‬, ‫ آ‬.‫ة‬6‫ و‬500 ! economic order quantity ,9‫د‬
J‫إ‬
lead time ‫م‬:‫ ز ! ا‬.‫ وي‬,‫ز‬2 ‫ة‬6‫ و‬63 ‫ إ‬40 ‫ ل‬H ‫ ا‬3; 3 2‫ ا‬S7‫ا‬
!
.‫ م‬9‫ أ‬5 R? f‫ ا‬M'2I 36 S7‫ا‬
‫م‬29 100 ‫! ة‬9G‫ م ا‬N 3‫ آ‬6
,"`‫ ا‬, 2‫ون وا " ت ا‬G ‫ ا‬R9‫ز‬2I !
:g#6‫ض ا‬2
; GPSS World Sample File - ORDERPNT.GPS, by Gerard F. Cummings
*********************************************************************
*
*
Order Point Inventory System
*
*
*
*
*********************************************************************
*
Initialize and define
INITIAL
X$EOQ,500
INITIAL
INITIAL
Inventory TABLE
Sales
TABLE
;Economic order qty.
X$Point,600
X$Stock,700
;Order point
;Set initial stock=700
X$Stock,0,50,20
P$Demand,38,2,20
;Table of stock levels
;Table of sales levels
Var2
VARIABLE
[email protected]+40
*********************************************************************
Again
GENERATE
TEST L
,,,1
X$Stock,X$Point
;Order placed on successful
ADVANCE
5
;Lead time = 1 week
SAVEVALUE
TRANSFER
Stock+,X$EOQ
,Again
;Economic order
;Cycle transaction again
test
*********************************************************************
GENERATE
1
;Daily demand xact
ASSIGN
TABULATE
Demand,V$Var2
Inventory
;Assign daily demand
;Record inventory
TEST GE
X$Stock,P$Demand
;Make sure order can be filled
551
SAVEVALUE
Stock-,P$Demand
;Remove demand from stock
SAVEVALUE
TABULATE
Sold,P$Demand
Sales
;X$Sold=Daily demand
;Record daily sales
TERMINATE 1
;Daily timer
*********************************************************************
‫م‬2:9 ‫ي‬.‫ `د وا‬M " 29 ‫ول‬0‫ ا‬GENERATE S J .‫اء‬G-‫ ة أ‬3; SI ‫ذج‬2 ‫ا‬
;‫ إ ر ر‬S J , 6 3; ‫ل‬2‫ ر ا‬N &J‫ و‬%N" 3f 9 M " ‫ا ا‬.‫ ه‬.S7‫ دة ا‬
‫ون‬G ‫ى ا‬2 ,
"O9 ‫ا‬.‫ ا@ ر ه‬S J . Again G refuse mode TEST
N ‫ ا‬M " ‫ ;ن ا‬S7‫ ا‬,7: W I ‫ون‬G ‫ى ا‬2 ‫ن‬2/9 .S7‫ ا‬,7: W I ‫ن‬2/I
WJ2 N9 %X ‫ون‬G ‫ إ ا‬S7‫_ ا‬f9‫ م و‬9‫ أ‬5 N9‫ و‬ADVANCE S J ‫ إ‬9
.S7‫ ا‬,7: ! MJ‫ون أ‬G ‫ى ا‬2 ‫ن‬2/9 3 ‫ا‬
!/9 % ‫ إذا‬.!? G‫ ت ا‬C M[ I 3‫ وا‬, 2‫ ا " ! ا‬29 3 [‫ ا‬GENERATE S J
S‫ا‬2: ;‫ إ ر ر‬S J M‫ آ‬,C 6‫ إ‬g/ 9 . TEST S J ‫& إ‬2‫ د‬R 9 SC : I /
.‫ ه ك‬e‫ا ! ا‬9:I ‫ إذا اردت‬DEPART ‫ و‬QUEUE
:‫إ=اء اآة‬
‫ار ر‬2 ‫ 'وق ا‬3;‫ و‬File / Open ‫ا " ري ر‬9:I 2‫آ ة و‬
3; !9Y & ! ‫ ه‬O %‫ ر‬GUH ‫آ ة‬
‫ي ا‬H 3/
‫ ان أ ا‬MJ Open %XORDERPNT
‫ ر‬،%‫ة ا‬.; ‫ل إ‬2'2‫ ا‬R7 36 ‫آ ة‬
‫ ا‬SH9 ‫ا‬.‫ ه‬MJ !/ .‫ذج‬2 ‫ا‬
‫ ر‬%X Command / Create Simulation
Window / Simulation Window / Plot Window
:3 ‫ ا‬M/O‫ ا‬3; ! 2‫ ت آ ه‬2" ‫ ا‬M‫ ت أد‬2‫ ا‬9 I ‫ة‬.; 3;‫و‬
552
‫ ت‬2" ‫ ا‬M‫ أد‬:,N6 ) .%‫ `ˆ ا‬3 ‫ون‬G ‫ي ا‬2 ‫ و‬3 2‫ ا‬S7‫ ا‬% ‫ف‬2
,2 H M‫ أد‬%X Memorize %X Plot wYV‫ ( إ‬Enter ‫ ` ح‬3 wYfI ‫ون أن‬
Inventory Level ‫دة ـ‬2-2 ‫ ا‬, :‫ ل ا‬G ‫ ا‬, 3; ، U ‫ ر‬9 3‫ ا‬, [‫ ا‬%:‫ا‬
‫ و‬Plot wYV‫ إ‬%X X$Stock ‫دة ـ‬2-2 ‫ ا‬, :‫ ا" ل ا‬, 3;‫و‬
‫ إ ر‬%X ‫آ ة‬
‫ ء ا‬X‫ هة ا‬O ‫ ا‬,U U"H9 M/O %‫ة ا‬.; ‫ك‬6 OK %X Memorize
OK %X 100 ‫ ـ‬1 ‫ار إل‬2 ‫ 'وق ا‬3;‫ و‬Command / START
‫ آ‬Orderpnt.1.1 _ ‫ ا " ري إ ا‬9:‫ ا‬S/9‫م و‬29 100 ‫آ ة " ور‬
:3 ‫آ ة آ‬
‫ ا‬3UI
‫ ء ا‬X‫ وا أ‬%‫ة ا‬.; .9‫ ر‬:‫ة ا‬.; 3; ‫"ض‬9
553
‫ ت‬2‫ة ا‬.; :g1‫ ا‬J1#
.Y9 ‫ون‬G ‫ى ا‬2 ‫ ه أن‬O P6 aV‫ون وا‬G ‫ م ا‬N ‫ ف‬I ‫ أن‬%‫وا ! ا‬9
.‫ة‬6‫ و‬300 ! ‹:9 % !9G‫ى ا‬2 ‫! ان‬I 9:‫ ا‬3; ‫ون‬G ‫ول ا‬-
:‫ اآة‬0‫دا‬
SHOW 0‫ م ا‬. ‫ ا‬9:‫ ه ا‬2I 3‫آ ة وا‬
‫ ا‬,9 U , 6 ‫ن‬h‫_ ا‬O/
S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / SHOW ‫ون‬G ‫ى ا‬2 w2 N
OK %X TB$Inventory
612 .‫ون‬G ‫ ا‬3; ,C2 ‫ ا ل ا‬, / ‫ س‬: 2‫ وه‬.‫ون‬G ‫ى ا‬2 w2 ! ‫ا‬.‫ه‬
!9G‫ م ا‬N 3; ‫ " ا ت‬Y ‫; " ا ل‬2I R7
‫ ر‬.R`I ‫وا‬9
.‫آ‬
‫ا‬
‫ول‬- ‫ة‬.; a;‫ أ‬. :6T U- 0 ‫م‬2‫ة ا‬.; Y' T‫ أو‬.‫ ت‬2‫ إ " ا‬N
Window / Simulation Window / Table ‫ إ ر‬Inventory Table ‫ون‬G ‫ا‬
5.‫ ه‬. OK wYV‫ار إ‬2 ‫ 'وق ا‬3; ‫دة‬2-2 Inventory Table ‫ان‬
554
‫ و‬Window
SJ‫ ا‬.3 2‫ون ا‬G ‫ى ا‬2 R9‫ز‬2I !9 ‫ول‬H‫ا ا‬.‫ ه‬Inventory Table ‫ول‬- ‫ة‬.; ‫ ر‬،‫ م اى‬9‫ ا‬,"f ‫ ط‬O
‫ول‬H‫ة ا‬.; M`J‫ ا‬OK %X 100,NP S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / START
‫“ ان‬6 Window / Simulation Window / Blocks Window S‫ا‬2:‫ة ا‬.; a`‫و‬
3`‫ء ا‬GH‫ وا‬،SC ‫ ط إ دة‬N9 0‫ء ا‬GH‫ ا‬3; M " ‫ ا‬.‫ا‬- w ‫ذج‬2 ‫ا ا‬.‫ه‬
‫ة‬.; 3; ‫“ ا@ ب‬6T‫آ ة ة اى و‬
‫ ا‬-‫ إ‬., 2‫ا ا " ت ا‬2[ 9 ! " 9
. OK %X 50,NP S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / START ‫ إ ر‬.S‫ا‬2:‫ا‬
T 400 ‫ إ‬3‫و‬0‫ون ا‬G ‫ وا‬600 ! T 300 ‫ إ‬S7‫ ا‬,7: ‫ م ل‬N‫ ا‬3; b Y
%X
Clear Off S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / Custom ‫ ر‬، 700 !
Savevalue ,ƒ2` ‫ ا‬%:‫ ا‬M‫ ` آ‬9 ,‫ا‬
‫ ا " ! آ‬M‫ آ‬M9G9 CLEAR 0‫ ا‬.OK
" w:; Y ‫ف‬2‫ و‬,ƒ2` ‫ ا‬%: , ‫ ا‬%:‫ ا‬3 3:9 ‫" ة‬- Off M "‫! ام ا‬/‫و‬
S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / Custom ‫ ر‬,ƒ2` ‫ ا‬%: ‫ ا رة‬%:‫ا‬
INITIAL S‫ `ˆ ا وق أآ‬3; %X Enter wYV‫ إ‬%X INITIAL X$Point,300
! ‫ و‬%‫ ا ا‬N . 500 MN ‫ إذ‬, 27 ‫ ا‬, /‫ ا‬Y % . OK %X X$Stock,400
‫م‬2‫ة ا‬.; ‫ آ‬، ‫ ا‬%‫ '` ا‬CLEAR 0‫ ا‬.S‫ا‬2:‫ة ا‬.; M`J‫ ا‬T‫ أو‬،‫آ ة‬
‫ي ا‬H
‫ث‬6 ‫ إذا‬,;" ‫ ج‬.OK %X 100,NP S‫ اآ‬%X Command / START ‫آ ة‬
‫وأ أ ا‬
Window / ‫ إ ر‬Inventory ‫ول‬H‫ & ! آ ?! ا‬M
‫ا‬.‫ وه‬stockout ‫ون‬G ‫` ذ‬
OK %X Simulation Window / Table Window
0 U J 3‫ار ا" ا‬/‫ ا‬,b; ‫ن‬0 aV‫ا وا‬.‫ ه‬.‫ ع‬V ‫ او‬:; ‫ اي‬3 "9 % ‫ون‬G ‫“ ان ا‬6T
f9‫ ا‬., :‫ ر ا‬9 ‫ي إ‬.‫د ا‬2 "‫ ا‬3; ?‫ دا‬,2 O ‫ن‬2/I ,9‫ار‬/‫ ت ا‬b` ,9 ‫ ا‬%:‫ ا‬.,^‫; ر‬
MJ . ‫ذج ا‬2 ‫ ! ا‬- ! I ‫ا‬.‫ وه‬. 329.1 w:; 2‫ون ه‬G ‫ى ا‬2 w2 ‫ ه ان‬O
,‫ أي ا‬,; Ie9 % !-‫ذ‬2 ‫ ان ه! ان ا`ق ! ا‬SH9 ]? ‫ ا‬5.‫ ! ه‬9:I %9:I
‫?ت‬
[email protected]‫ ! ا‬starting conditions ‫ اء‬, 6 ! ‹‫ ا‬SH9
‫ آ‬.W
3?‫ا‬2O
. ANOVA 0‫ ا‬R :6T ,OJ ‫ي‬.‫ وا‬RESET 0‫ ام ا‬g‫ وذ‬,? U‫ا‬
555
‫و‬B‫! إ‬D ! 14 ‫آة ;م‬# -7
:/BJ‫ض ا‬2
‫ ا ت‬e"I R9‫ز‬2‫ ا‬%J 3; ., J‫ ت ر‬, ‫م‬2:9 ‫و ت‬/‫ إ‬,‫ آ‬3; R ‫ ا‬%J
%H6 .‫ن‬2‫ز‬2 ‫ ا‬U79 3‫ ت ا‬/ ‫ة "ض‬G‫ ه‬- S 3; ,b"I ,( ,7‫ا‬2 3? :I M/O
:, ‫ ا‬,‫ ا‬7"9 S7‫ا‬
Order Size
6
12
18
24 30
36
48
Frequency .10 .25 .30 .15 .12 .05 .03
, X 120 SC M/ ,b"‫ ز ! ا‬. ‫زع أ‬2 ,:J‫ د‬15 ‫ ت‬7‫ل ا‬2'‫ ! ! و‬G‫ ا‬w2
3; , J‫] ا ت ا‬9 R ‫ ا‬%J .S7‫ ا‬3; e"I , J‫ ر‬, M/ ‫ان‬2X 10 ‫ إ‬,; [email protected]
.,:J‫ د‬455 3; ‫ة‬6‫ و‬60 %H
‫ ت‬2 H
:, ‫ ت ا‬2" ‫ ا‬37"I 3/ ,‫آ‬O‫ ط ا‬O ! ‫ م‬9‫ أ‬5 3‫ آ‬6
,b"‫ ا‬%J 3; ‫ة‬N ‫ ت ا‬7‫ د ا‬w2 -1
‫م‬29 M‫ آ‬,‫ز‬2 ‫ ا‬, J‫ ا ت ا‬, ‫ آ‬-2
‫ ت‬7 transit times , :@‫ ت ا‬J‫و‬0‫ ا‬R9‫ز‬2I -3
:g#6‫ض ا‬2
; GPSS World Sample File - MANUFACT.GPS, by Gerard F. Cummings
*********************************************************************
*
Manufacturing Company
*
*********************************************************************
*
*
Time Unit is one hour
*
Sizeorder FUNCTION
RN1,D7
;Order size
.10,6/.35,12/.65,18/.80,24/.92,30/.97,36/1.0,48
Transit
TABLE
M1,.015,.015,20
556
;Transit time
Number
TABLE
X1,100,100,20
;No. packed each day
Ptime
VARIABLE
.0028#P1+0.0334
;Packing time
Amount
EQU
1000
;Initial stock amount
Stock
STORAGE
4000
;Warehouse holds
;
4000 units
*********************************************************************
GENERATE
(Exponential(1,0,0.25)) ;Order arrives
ASSIGN
1,1,Sizeorder
;P1=order size
TEST GE
S$Stock,P1,Stockout
;Is stock sufficient?
LEAVE
Stock,P1
;Remove P1 from stock
QUEUE
Packing
SEIZE
Machine
DEPART
Packing
ADVANCE
V$Ptime
;Packing time
RELEASE
Machine
;Free the machine
SAVEVALUE
1+,P1
;Accumulate no. packed
TABULATE
Transit
;Record transit time
;Get a machine
TERMINATE
Stockout
TERMINATE
*********************************************************************
GENERATE
0.75,0.08334,1
;Xact every 40+/-5 mins
ENTER
Stock,60
;Make 60, Stock
*
Stockad
increased by 60
TERMINATE
*********************************************************************
GENERATE
8
TABULATE
Number
SAVEVALUE
1,0
TERMINATE
1
;Xact every day
*********************************************************************
GENERATE
,,,1,10
;Initial stock xact
ENTER
Stock,Amount
;Set initial stock
TERMINATE
*********************************************************************
-2I Storage ‫ و‬variable ‫ و‬function ‫ ? ت‬/‫_ ا‬9"I " .‫اء‬G-‫ ة أ‬3; %N ‫ذج‬2 ‫ا‬
! " ‫ وا‬،‫ ت‬7‫ا ا‬2[ 9 ‫ذج‬2 ‫ ! ا‬0‫ء ا‬GH‫ ا‬3J ! " ‫ ا‬.‫ذج‬2 ‫اء ! ا‬G-‫ أ‬R ‫أر‬
‫ء‬GH‫ ا‬3; ! " ‫ ا‬،‫ون‬G ‫ إ ا‬, J‫ ر‬, 60 ! ‫ ت‬2 H ‫ا‬2`f9 3 ‫ء ا‬GH‫ ا‬3;
557
0‫ء ا‬GH‫ ا‬3; M " ‫ وا‬،‫ م‬90 3/‫ ة ا‬/ ‫ا ز ! ا‬2J29‫ و‬, 2‫ا ا " ت ا‬2‫و‬H9 3 ‫ا‬
.‫ة‬6‫ و‬1000 ‫ون إ‬G ‫ى ا‬2 MU9 ‫ذج‬2 ‫! ا‬
‫ى‬2 ‫ ا‬2‫ وه‬، S$Stock Y M[ ‫ون‬G ‫ى ا‬2 .‫ ! ت‬G‫ات ا‬6‫ س و‬:I
‫ون و‬G ‫ ! ا‬.e 3/ LEAVE ‫ا م‬.U ‫ و‬Stock ‫ون‬G ‫ آ ?! ا‬3; 3 ‫ا‬
,6 . stockouts 3U ‫ون‬G 3‫ ت ^ ا ة ه‬7‫ ا‬.&‫_ إ‬f / ENTER
‫ ـ‬MU9 S$Stock ‫ ـ‬M[ ‫ون ا‬G ‫ى ا‬2 .‫ة‬6‫ و‬4000 ‫ ـ‬3`/I ,6 ‫ ا‬R? f‫! ا‬9GI
.‫ذج‬2 ‫ ! ا‬0‫ء ا‬GH‫ ا‬3; ,f;‫ ذا ا‬M " ,7‫ا‬2 ‫آ ة‬
.‫آ ة‬
‫ ا‬,9‫ة ا‬6‫ و‬1000
‫ ا‬3; ‫ ك‬9 ! ‫ن أول‬2/ M " ‫ا ا‬.‫ه‬
:‫إ=اء اآة‬
MANUFACT ‫ار ر‬2 ‫ 'وق ا‬3;‫ و‬File / Open ‫ " ري ر‬9:I 2‫آ ة و‬
Command ‫ ر‬%X Command / Create Simulation 0 ‫آ ة‬
S J ! " 5 ‫ل‬2‫آ ة د‬
‫ي ا‬H 3/
‫ ا‬%X Open wYf %X
‫ ا‬3U OK %X ‫دة‬2-2 ‫ ا‬1 , J ! T 5 S/‫و‬/ START
_ ‫ " ري إ ا‬9:I S/ ‫ آ " د‬.R
‫ ا‬M ! ‫ م‬9‫ أ‬5 M[ 9 ‫ا‬.‫وه‬TERMINATE 1
.9‫ ر‬:‫ة ا‬.; 3; I‫"ض ذا‬9 9:‫ا ا‬.‫ آ ان ه‬Manufact.1.1
:g1‫ ا‬J1#
:9:‫ ا‬3; ,HI ‫ ت ا‬2" ‫ ! ا‬,/O ‫ ض ا‬3; ,6‫و‬7 ‫ ا‬,b0‫ ا‬, [email protected]‫ ا‬R7
3; Ave. Cont. , J ! 2‫ وه‬. 0.12 w:; 2‫ ه‬,b"‫ ا‬%J 3; ‫ة‬N ‫ ت ا‬7‫ د ا‬w2
.Queue Entity Packing W I 9:‫ا‬
. Table Number 3; 7" 29 ,‫ز‬2 ‫ ا‬, J‫ ا ت ا‬R9‫ز‬2I
:‫ اآة‬0‫دا‬
‫ إ‬N SHOW 0‫ م ا‬.9:‫ ا‬U9 2I 3‫آ ة وا‬
‫ ا‬,9 U , 6 ‫ن‬h‫"ض ا‬
، 5 : ‫ ت ا‬7‫ د ا‬T‫ أو‬. System Numeric Attributes ‫ م‬N ,9‫" ا ` ت ا"د‬
‫ ه‬OI ‫ف‬2 . OK %X N1 S/ ‫ار‬2 ‫ 'وق ا‬3;‫ و‬Command / SHOW ‫ ر‬
Journal ‫ة‬9H‫ة ا‬.; 3;‫ و‬,?‫ة ا‬.; ‫ ا‬3; Status Line , ‫ ا‬7 3; 169 ,H‫ا‬
558
، stockout ‫ون‬G ‫ ` ذ ا‬U; ‫ث‬6 3‫ن د ا ات ا‬0‫ف ` ‹ ا‬2 .g.‫ آ‬Window
. OK %X N$Stockout ‫ار‬2 ‫ 'وق ا‬3; S/ %X Command / SHOW ‫ ر‬
‫ ر‬،, 2‫ ا‬.;‫ا‬2‫ ه " ا‬O
Window / Simulation Window / Storages Window
‫ ت‬92 M[ 9 stock level ‫ون‬G ‫ى ا‬2 Storages Window ‫ة ا زن‬.; 3‫وه‬
‫ن‬G ‫ ا‬W I , :‫ ا‬5.‫ ه‬H 898 ‫ ه‬U J 3‫ وا‬Storage Entity ‫ون‬G ‫ ?! ا‬/ , ‫ا‬
‫ون‬G ‫ى ا‬2 . Storages Window ‫ة ا زن‬.; 3; Storage In Use ‫ا م‬
_O/O .‫ى ا@ ج‬2 ‫ ص‬:‫ إ‬SH; ‫ دة ا " ت‬9‫! ! ز‬/ % ‫ إذا‬،‫ا‬- R`I 3 ‫ا‬
Window / Simulation
‫ ر‬.‫ة ا زن‬.; ‫ أى " إ^ق‬, 2‫ ر‬.;‫ا‬2
‫ن‬2 .‫ا‬- ,f` ,b"‫ت ا‬T( , "; ‫ ه أن‬O . Window / Facilities Window
‫ء‬GH‫ ا‬3; g ,6 ‫ى ا‬0‫ ا‬%:‫ة ا‬N 3:‫ ا‬. 6 ,2YO ,h‫! أن ا‬9 ,2:9h‫ا‬
‫ ر‬Transit Table 3 :@‫ول ا‬H‫ ا‬3‫ن إ‬h‫ ا‬N .‫ة‬.; ‫ ! ا‬M ` ‫ا‬
Window / Simulation Window / Table Window
R9‫ز‬2I !9 ‫ا‬.‫ ه‬OK ‫ إ ر‬%X Transit wYV‫ إ‬Transit -‫ار او‬2 ‫ 'وق ا‬3;‫و‬
Number Table ‫اد‬0‫ول ا‬- ‫ إ‬N . order transit times ‫ ت‬7 , :@‫ز ن ا‬0‫ا‬
‫إ ر‬
Window / Simulation Window / Table Window
‫ول‬- ، OK wYVe; ‫ إ‬J Number 3 ‫ول ا‬H‫ ان ا‬H ‫ار‬2 ‫ 'وق ا‬3;
.‫م‬29 M‫ آ‬,b" ‫ ا‬, J‫اري ت ا‬/‫! ا رج ا‬9 ‫اد‬0‫ا‬
‫ا‬2 ‫ون أ‬G ‫ن ا‬2/9 SC :, ‫ ا‬, H %: .‫ ت‬2‫ة ا‬.; M`J‫إ‬
Window / Simulation Window / Blocks
‫ ر‬S‫ا‬2:‫ة ا‬.; a` .&
R9 ‫ي‬.‫ذج ) ا‬2 ‫ ا‬3; TERMINATE S J ‫ ا` رة إ ر اول‬A , "@ Window
_J2I ‫ ط‬Rf ‫ن‬h‫ ا‬.‫ء‬3f9 S :‫ن ا‬2 ‫ ه ان‬O .& wYV‫ ( وأ‬TABULATE S J
The Place Icon in the Debugging wYV‫ إ‬،S :‫ا ا‬.‫ ه‬Stop Condition
559
OK %X 5,NP S‫ار أآ‬2 ‫ق ا‬2' 3;‫ و‬Command / START ‫ ا ر‬%X Toolbar
،S7 ‫ذج ا ص‬2 ‫ء ا‬G- ‫ إ‬0‫ إ ا‬wO‫ ا‬M " ‫ك ا‬6 ‫آ ة‬
‫_ ا‬J2I
، OK %X TRANSFER ,2 S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / Custom ‫إ ر‬
“6T .‫ "ة ات‬Ctrl+Alt+1 ‫ة ام‬27 ‫ة‬27 ‫آ ة‬
‫اء ا‬- S7‫“ ا‬6T ‫ن‬h‫ا‬
.gI N6 ‫ا ?] ودون‬
.gI N6 ‫ دون‬%X ‫ ث‬9 “6T‫ م و‬N‫ ا‬% " ‫ رب‬H‫ " ا‬%J
560
‫‪# -8‬آة 'ق ‪#‬آ>ي‬
‫‪2‬ض ا‪:/BJ‬‬
‫‪ M 9‬ا‪ !? G‬را‪2 %UI‬ق ;‪2 3‬ق آ‪G‬ي‪ _J2 .‬ا‪2‬ق ‪ R9‬ـ ‪ 650‬رة‪ .‬إذا ‪%‬‬
‫‪ !/ 9‬ا‪2 G‬ن ! إ‪ H9‬د ‪ _J2‬ر‪ Y9 ,I‬در ون أن ‪29‬ق‪ .‬ا ;‪ ,‬ا‪9 3‬ه ا‪2 G‬ن !‬
‫ا ‪ _J2‬ا دا‪ M‬ا‪2‬ق ‪YI‬ق ;‪ 3‬ا ‪ ., X 60 w2‬ا‪2 2:9 !? G‬ا ‪O‬اء‬
‫! ‪ 5‬إ‬
‫‪2 R7J 100‬ز‪2I ,‬ز‪ "9‬و‪ . 9‬ا‪ !? G‬ا‪O9 !9.‬وا ‪ R7J 10‬أو أ‪2 9 MJ‬ا ‪ g.‬ل‬
‫وا‪2 , 70 U -29 3‬ق‪ .‬ا‪ !? G‬ا‪O9 !9.‬وا أآ[ ! ‪2 9 R7J 10‬ا ‪ g.‬ت‬
‫وا‪2 , 650 U -29 3‬ق‪ .‬ز ! ا‪2‬ق ‪ M/‬ز ‪2‬ن ‪ "9‬د ا‪ R7:‬ا ‪O‬ا‪5‬‬
‫وه‪2X 10 2‬ان ‪ " .,"7J M/‬إ ره‪ 9O %‬ت ‪ 9‬ا ‪2J2‬ن ‪2 C Je‬ر‬
‫‪,‬‬
‫وا‪ ”9 3‬ده ‪17‬‬
‫‪ .S‬ا‪ !? G‬ا‪ !9.‬أوا أ‪ %U 7 R7J 10 ! MJ‬ا‪2J2‬ف‬
‫‪2 7‬ر ص ‪ R9‬‬
‫‪Y9 ,‬ق ‪O ,"7J M/ , X 2‬ا‪ ,; [email protected] ،5‬إ‬
‫‪ .,‬ز ! ا‬
‫ز ! ا;‪ R‬ا‪.‬ي ‪Y9‬ق إ ‪ 25‬أو ‪ 30‬أو ‪ ., X 35‬ه‪.‬ا ا‪ ! G‬ا@‪ ,:9C "9 3; V‬ا;‪R‬‬
‫إ ‪:‬ا أو ‪ ) gO‬‬
‫;‪ (3‬او ‪ ,J 7‬إ د وا‪ ˆ` " - U 3‬ا@‪ 6‬ل ;‪ 3‬ا@ام‪.‬‬
‫" ‪ ,9 U‬ا ب ‪ &H9‬ا‪2 G‬ن إ ر‪26 3; &I‬ا‪ , X 60 3‬و‪ &I 9O M 9‬و‪ Y9‬در‬
‫ا ‪" ._J2‬ل و'‪2‬ل ا‪ !? G‬إ ا‪2‬ق ا آ‪G‬ي ‪2‬زع أ ا ـ ‪ 600‬ز ‪2‬ن ;‪ 3‬ا ‪,‬‬
‫ ة _ ‪ ,‬و ‪ 900‬ز ‪2‬ن ;‪ 3‬ا ‪ ,‬ة ‪ ,‬و ‪ 450‬ز ‪2‬ن ;‪ 3‬ا ‪ ,‬ة ‪ ,‬و‬
‫‪ 300‬ز ‪2‬ن ;‪ 3‬ا ‪29 ,: ,‬م ا‪2‬ق‪.‬‬
‫‪ -1‬أ‪-‬‬
‫آ ة ة ‪ 3‬ت‪.‬‬
‫‪ ! -2‬ا‪ transit time ! G‬ا@‪.!? G 3 :‬‬
‫‪ _J2 , "; ! -3‬ا رات و ت ا‪2‬ق ول وا‬
‫!‪.‬‬
‫‪- -4‬ول د ا‪ 3; !? G‬ا‪2‬ق ا آ‪G‬ي ‪.,:J‬‬
‫‪2‬ض ا‪:g#6‬‬
‫‪; GPSS World Sample File - SUPERMRK.GPS, by Gerard F. Cummings‬‬
‫*********************************************************************‬
‫*‬
‫*‬
‫*‬
‫‪561‬‬
*
Supermarket Simulation Model
*
*
Time Unit = 1/10 Of a Second
*
*********************************************************************
*
RMULT
1187
First
EQU
2
Last
EQU
18
Qty
VARIABLE
([email protected]+5)
Finance
VARIABLE
([email protected]+1)#50+200
Transit
TABLE
M1,10000,10000,7
;Time in system
Items
TABLE
P$Quantity,10,10,10
;No. of items bought
Shoppers TABLE
X$Customers,100,50,12 ;No. of shoppers
Baskt
STORAGE
70
Cart
STORAGE
650
Park
STORAGE
650
Checkout VARIABLE
(P$Quantity)#20+P$Payment
Tshop
VARIABLE
P$Quantity#100
INITIAL
X$Customers,0
*********************************************************************
*
Beg
TRANSFER
Both,,Lost
;Tries to park or leaves
ENTER
Park
;Park in parking lot
ADVANCE
600
;Time to walk from car
SAVEVALUE
Customers+,1
;One more customer
ASSIGN
Quantity,V$Qty
;Param quantity = No.
; items bought
ASSIGN
Payment,V$Finance
;Param payment = Method
;
payment
TEST LE
P$Quantity,10,Qcart
;Items >10 Get cart
GATE SNF
Baskt,Qcart
;Check basket available
QUEUE
Basket
;Queue for a basket
ENTER
Baskt
;Get a basket
DEPART
Basket
;Leave queue
ASSIGN
Carrier,Baskt
;Param carrier
; assigned baskt
TRANSFER
,Shop
;Proceed to shop
*********************************************************************
*
Qcart
QUEUE
Carts
;Queue for a cart
562
ENTER
Cart
;Get a cart
DEPART
Carts
;Depart carts queue
ASSIGN
Carrier,Cart
;Param carrier assigned
ADVANCE
V$Tshop
;Shopping time elapses
TEST LE
P$Quantity,10,Norm
;Items < 10 go to express
COUNT L
Where,First,Last,1,Q ;Any empty checkouts?
TEST E
P$Where,0,Norm
;Some empty checkouts?
QUEUE
Xpress
;Queue at express
SEIZE
Xpres
;Get express checkout
DEPART
Xpress
;Depart express queue
ADVANCE
V$Checkout
;Checkout time
RELEASE
Xpres
;Free express checkout
LEAVE
P$Carrier
;Leave the basket
TRANSFER
,Fin
cart
Shop
*********************************************************************
*
Norm
Fin
SELECT MIN
Minque,First,Last,,Q ;Find minimum queue
QUEUE
P$Minque
;Join the min queue
SEIZE
P$Minque
;Get the checkout
DEPART
P$Minque
;Depart the queue
ADVANCE
V$Checkout
;Checkout time
RELEASE
P$Minque
;Free the checkout
LEAVE
P$Carrier
;Leave the cart
TABULATE
Transit
;Record transit time
TABULATE
Items
;Record items bought
SAVEVALUE
Customers-,1
;One customer leaves
ADVANCE
600
;Walk to the car
LEAVE
Park
;Leave the car park
TERMINATE
Lost
TERMINATE
;One customer lost
*********************************************************************
*
*
Arrivals for 0 - 30 min.
GENERATE
(Exponential(1,0,60)),,,300
;A Customer
; arrives
TRANSFER
*
,Beg
Arrivals for 30 - 90 min.
GENERATE
(Exponential(1,0,40)),,18000,900 ;Arrival rate
; after .5
hours
563
TRANSFER
*
,Beg
Arrivals for 90 - 150 min.
GENERATE
(Exponential(1,0,80)),,54000,450 ;Arrival rate
; after 1.5
hrs
TRANSFER
*
,Beg
Arrivals for 150 min +
GENERATE
(Exponential(1,0,120)),,90000
;Arrival after
; 2.5 hours
TRANSFER
,Beg
*********************************************************************
*
GENERATE
600
;Xact each minute
TABULATE
Shoppers
;Record number of
TERMINATE
1
customers
*********************************************************************
Storage ‫ و‬Variable Entities Y ‫_ آ ? ت ا‬9"I " .‫اء‬G-‫ ة أ‬3; %N ‫ذج‬2 ‫ا‬
.‫ذج‬2 ‫اء‬G-‫ أ‬,XX -2I Savevalues “` ‫ ا‬%J ‫ل‬U‫ و إ‬Entities
-‫ إذا و‬،‫_ ا رات‬J2 ! ‫ د‬:‫ ?! ا‬G‫ا ا‬2[ 9 ‫ذج‬2 ‫ ا‬3; 0‫ء ا‬GH‫ ا‬3; ! " ‫ا‬
‫ن ^ در ون‬2 ‫ ز‬M[ 9 ‫ا‬.‫ وه‬،‫آ ة‬
‫ در ا‬Y9 &; †
3; ‫ وا‬9‫ و‬, ‫ أو‬, 3 ‫ا‬2
3; TEST S J .,
Park ‫ن ا‬G ‫ آ ?! ا‬M "
9 ‫ل‬2‫ا ! ا‬2/ 9 !9.‫ ?! ا‬G‫ ا‬.‫ق‬2‫ل ا‬2‫د‬
‫ر‬2 C Je 9 R7J 10 ! [‫ن أآ‬2 G‫ ا‬R ‫ إذا آ ن‬،‫ق‬2‫ا‬
G ‫ ا‬S :‫ إ ا‬M " ‫ا ا‬.‫ ه‬M[ M9‫ا ا@ ر و‬.U ‫م‬2:9 ‫ذج‬2 ‫ ! ا‬P [‫ء ا‬GH‫ا‬
Rf9 ‫ي‬.‫ذج وا‬2 ‫ ! ا‬R ‫ء اا‬GH‫ ا‬3; SELECT S : ‫ د‬9 J0‫ر ا‬2 7‫ ا‬، Normal
10 %U9 !9.‫ " ! ا‬. Minque ‫ ا‬M " ‫ ا‬%" 3; S ‫ر ا‬2 7‫ آ ?! ا‬%J‫ر‬
& J ‫ر ا‬2 7‫` ‹ آ ? ت ا‬9 ‫ذج‬2 ‫ ! ا‬P [‫ء ا‬GH‫ ا‬3; COUNT S J ‫ ;ن‬MJ‫ أو أ‬R7J
,
‫ر ا‬2 7 M " ‫ ا‬9 ‫ة‬6‫ وا‬-2I % ‫ ;ذا‬،, ,
,7: 20 6‫ و‬4 !
a`I 3‫ وا‬GENERATE S‫ا‬2J ‫ى ة‬2 9 ‫ذج‬2 ‫ ! ا‬0‫ ا‬MJ
‫ء‬GH‫ ا‬.R9‫ا‬
!/ ‫ آ ن ! ا‬،‫ل‬2'2‫ ! "ل ا‬Y S ‫ ا‬WJ2‫ ا‬turn on and off M`:I‫و‬
3; ! " ‫ ا‬.‫آ ة‬
‫ ا‬, 3 "9 3‫ دا‬Y
6‫ وا‬GENERATE S J ‫إام‬
.‫ ء‬[email protected]‫‹ اد ا‬:I ‫ و‬,:J‫ د‬M‫ آ‬,9 U !? G‫ول أاد ا‬HI‫آ ة و‬
564
‫ ا‬WJ2I 0‫ء ا‬GH‫ا‬
:‫إ=اء اآة‬
‫آ ة ر‬
‫ ا‬، Open %X SUPERMRK %X
File / Open
‫ ر‬
180 S‫ وأآ‬Command / START ‫ ر‬%X Command / Create Simulation
OK %X
‫ ت‬3 ‫ ور‬M[ 9 ‫ا‬.‫ وه‬TERMINATE 1 S J M " 180 ‫ل‬2‫آ ة " د‬
‫ ا‬3UI
‫"ض‬9 g.‫ وآ‬Supermrk.1.1 _ ‫ ا" ري إ ا‬9:‫ ا‬S/9 ‫ آ " دة‬.‫ق‬2‫ ا‬M 3
.9‫ ر‬:‫ة ا‬.; 3; I‫ذا‬
:g1‫ ا‬J1#
394 ‫ أو‬, X 23640 ‫ق آ ن‬2‫ ز ! ا‬w2 ‫ أن‬Table Transit 3 :@‫ول ا‬H‫! ا‬
‫ا‬.U .‫;ة‬2 ‫ ا‬,"‫ ا‬wJ M 9 % ‫"اد‬I J‫ن ى أن أ‬G ‫ ?! ا‬/ 3?GH‫ ا‬9:‫ ! ا‬.,:J‫د‬
!/‫ و‬،‫ ! ال وا" ت‬,; ‫_ ا رات و أاد آ‬J2 3; ‫;ة‬2 !‫ دا? ا آ‬-29 &;
3; ‫ا‬2f 9 ‫ا‬.U %U; ،,
‫ا ا‬2C 3; !9N !? G‫ ! ا‬397 ‫د د آ‬2-‫“ و‬6
‫ رج‬37"9 Table Shoppers ‫ول‬H‫ ا‬.‫ق‬2‫ ا‬3; & ‫ ر‬[email protected]‫ ا‬3; ‫ل‬2C‫ ا‬WJ‫ و‬w2 ‫ا‬
398.7 w2 ‫ ا‬3; -29 ،,:J‫ د‬M‫ آ‬,9 U sampled !9 " ‫ق‬2‫ ا‬3; !? G ‫اري‬/I
.,
‫ا ا‬2C 3; ‫وا‬N9 %‫ أآ[ه‬9:I ،‫ق‬2
:‫ اآة‬0‫دا‬
" ‫ إ‬N SHOW 0‫ م ا‬.9:‫ ا‬2I ‫آ ة‬
‫ ا‬,9 U , 6 ‫ن‬h‫"ض ا‬
‫ إ ر‬،‫ ل‬, "`‫ ا‬w2 ‫ ه‬O T‫ أو‬._0‫اء ! ا‬G-e M[ I 3‫ م وا‬N ,9‫ا ` ت ا"د‬
،‫ ا" ت‬, "; g‫ " ذ‬SR$Baskt ‫ار‬2 ‫ 'وق ا‬3; S‫ أآ‬%X Command / SHOW
_J‫ا‬2 , "; %X SR$Cart S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / SHOW ‫إ ر‬
MU‫ أ‬، SR$Park S‫ار أآ‬2 ‫ 'وق ا‬3;‫ و‬Command / SHOW ‫ إ ر‬،‫ا رات‬
، Storages Window ‫ة ا زن‬.; a; 9C ! ‫ن‬2/9 ‫ ا`" ت‬5.‫ هت ه‬O ,:9C
‫! آ ? ت ا زن‬9 ‫ا‬.‫ ه‬. Window / Simulation Window / Storages ‫ ر‬
‫ ى أن ˆ ه ك اي‬J0‫ ا@ام ا‬%J ! ،‫_ ا رات‬J‫ا‬2 ‫ " ت وال و‬,[ ‫ا‬
565
‫ ت‬J‫و‬0 ‫اري‬/‫ن ا رج ا‬h‫ ه ا‬O ‫ أن‬/ 9 .‫آ ة‬
‫ ت ام آ ل ا‬/ @‫ ا‬5.‫! ه‬
Window / Simulation Window / Table Window ‫ ر‬،‫ق‬2‫ا‬
5‫ا‬O ‫ ا‬R7: ,9‫ار‬/‫ ت ا‬-‫ ه ا ر‬OI ‫ أن‬g/ 9 ، OK ‫ إ ر‬%X Transit wYV‫إ‬
-‫ا‬2I !‫ة أ آ‬N 3: . Shoppers ‫ و‬Items 5 ‫اول‬H‫ ا‬5.‫ ه‬،‫ق‬2‫ ا‬3; !? G‫و‬
‫ ر‬،! " ‫ا‬
Window / Simulation Window / Blocks Window
SELECT S : 3 ‫( ا‬30 %J‫ ر‬S J) QUEUE S J 3; ! " ‫ ! ا‬9"‫د ا‬2-‫“ و‬6T
.‫ ا ب‬R;‫ا د‬2‫ و‬9 !9.‫ ?! ا‬G‫ا ا‬2[ 9 ‫ن‬2 " ‫ء ا‬TA‫ ه‬SEIZE S J ‫ل‬2‫وا د‬N9
Window / Simulation Window / ‫ ر‬،!
‫ا ا‬2C ‫ن إ‬h‫ ا‬N
Facilities Window
) R9‫ ا‬,
‫ر ا‬2 7 ,[ ‫ ا‬,U‫ة ك إ ا‬.; ‫ ا‬S - 3; ‫ق‬[email protected]‫د ا‬2 ‫إم‬
R9‫ ا‬,
(‫ه‬
J0 ‫ة‬.; ‫أو آ ا‬
‫ ت ا‬7
R - ‫“ ان‬6T
‫ر ا‬2 7 ,[ ‫ت ا‬U‫ة ا‬.; , ‫ر ا‬2 C ‫ ى‬,92C ‫ا‬2C U‫ه و‬
J0 ,
,
M`J‫ أ‬.!? G‫[ ! ا‬/‫وا ا‬:` T‫ م وإ‬6G‫ا ا‬.‫ ه‬SHI ‫ق‬2‫ ان إدارة ا‬aV‫ وا‬،R9‫ا‬
566
‫‪2‬ا;‪ .‬ا‪ 2‬ت ا `‪ &62‬ود ‪H‬ب إ‪10 ,; V‬‬
‫‪7‬ت‬
‫‪ ,‬و‪ N‬إذا آ ن ه‪.‬ا ‪M‬‬
‫" ه‪ 5.‬ا ‪ O‬آ‪ , J ^ ،M‬ا‪ 7‬ا ‪ G‬ـ ‪ Last‬إ‪ 28‬ه‪.‬ا ‪ 9G‬د‬
‫‪ 7‬ت ا‬
‫‪,‬‬
‫! ‪ 17‬إ ‪ 27‬ر ‪Command / Custom‬‬
‫و;‪' 3‬وق ا ‪2‬ار أآ‪ %X Last EQU 28 S‬إ‪ OK wYV‬إ ر ‪Command / Clear‬‬
‫‪ OK %X‬إ أ ا‬
‫ا‬
‫آ ة ر ‪ Command / START‬وأآ‪,9 U " . OK %X 180 S‬‬
‫آ ة أ‪ N‬إ أ@‪6‬‬
‫ ‪ 7‬ت ا‬
‫? ت ا ‪ , U‬ا‪ OJ 3‬ه ‪ :‬ودون ‪ .gI N6‬أو‪ -‬ا"د ا‪M[ 0‬‬
‫‪ ,‬ا‪ , 3`I 3‬ا‪ !? G‬و‪I T‬ه إدارة ا‪2‬ق ام د‬
‫! أآ[‬
‫! ا‪f‬وري )ز‪ 9‬دة روا‪ .(SI‬ه‪.‬ا ‪"9‬ض ‪ ,/O‬إدارة ا‪2‬ق ;‪ wV 3‬ا‪2‬ازن ! ا‪,`/‬‬
‫وا‪ M‬وإر‪ V‬ء ا‪.!? G‬‬
‫‪567‬‬
GPSS -‫( ا‬1) [/#
ADOPT Blocks are used to change the Assembly Set of the
Active Transaction.
ADOPT A
A - Assembly Set. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
ADOPT 2000
ADVANCE Block delays the progress of a Transaction for a
specified amount of simulated time.
ADVANCE A,B
A - The mean time increment. Required. The operand must be Name, Number, String,
ParenthesizedExpression, SNA or SNA*Parameter.
B - The time half-range or, if a function, the function modifier. Optional. The operand must be
Null, Name, Number, String, ParenthesizedExpression, SNA, or SNA*Parameter.
ADVANCE 101.6,50.3
ALTER Block changes the priority or a Parameter of selected
members of a Transaction Group.
ALTER O A,B,C,D,E,F,G
O - Conditional operator. Relationship of E to F for the alteration to occur. These choices are
explained below. Optional. The operator must be Null, E, G, GE, L, LE, MAX, MIN, or NE.
A - Transaction Group. Group whose members will be tested for alteration. Required. The
operand must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Limit. The maximum number of Transactions to be altered. The default is ALL. Optional.
The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
C - Altered attribute. The member Transaction Parameter to be altered, or PR to alter the
member Transaction priority. The operand must be PR, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
D - Replacement value. The value which will replace attribute C. Required. The operand must
be Name, Number, String, ParenthesizedExpression, SNA, or SNA*Parameter.
E - Test value. PR or Parameter number. The member Transaction Parameter which
determines whether each Group member Transaction should be altered, or PR to use the
Transaction priority for the determination. It is evaluated with respect to the Transaction
568
Group member. Optional. The operand must be PR, Null, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
F - Reference value. The value against which the E Operand is compared. It is evaluated with
respect to the Active Transaction. Optional. The operand must be Null, Name, Number,
String, ParenthesizedExpression, SNA, or SNA*Parameter.
G - Alternate Block number. The alternate destination for the Active Transaction. Optional.
The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
ALTER Inventory,ALL,Price,49.95
ALTER NE Bin7,10,Price,49.95,PartNum,99.95,Out
The conditional operator may be E, G, GE, L, LE, MAX, MIN, or NE. If no conditional operator
is used, E (equality) is assumed. When the condition is true, the Transaction being tested is
altered.
ASSEMBLE Wait for and destroy related Transactions.
ASSEMBLE A
A - Transaction count. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
ASSEMBLE 2
ASSIGN Blocks are used to place or modify a value in a
Transaction Parameter.
ASSIGN A,B,C
A - Parameter number of the Active Transaction. Required. The operand must be Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter, followed by +, -, or Null.
B - Value. Required. the operand must be Name, Number, String, ParenthesizedExpression,
SNA, or SNA*Parameter.
C - Function number. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
ASSIGN 2000,150.6
ASSIGN TEXT,"Look on my works, ye Mighty, and despair."
ASSIGN 2000+,-3
ASSIGN 2000-,-3
BUFFER Block places the Active Transaction on the Current
Events Chain behind its priority peers.
569
BUFFER
CLOSE Block terminates a Data Stream and retrieves its error
code.
CLOSE A,B,C
A - Transaction Parameter. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Data Stream. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter. The default is 1.
C - Alternate Destination. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
CLOSE Error_Parm,2
COUNT Block places an entity count into a Parameter of the
Active Transaction.
COUNT O A,B,C,D,E
O - Conditional operator or logical operator. These choices are explained below. Required.
The operator must be FNV, FV, I, LS, LR, NI, NU, SE, SF, SNE, SNF, SNV, SV, U, E, G, GE,
L, LE, MIN, MAX, or NE.
A - Parameter number to receive count. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Number or name of entity at lower end of range. The entity number of the first entity to be
tested. The entity type is implicitly specified by the logical operator or by Operand E.
Required. The operand must be Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
C - Number or name of entity at upper end of range. The entity number of the last entity to be
tested. Required. The operand must be Name, PosInteger, ParenthesizedExpression, SNA,
or SNA*Parameter.
D - Reference value for E Operand. Required only when in Conditional Mode. Optional. The
operand must be Null, Name, Number, String, ParenthesizedExpression, SNA, or
SNA*Parameter.
E - SNA class name. Entity attribute specifier for Conditional Mode tests. Required only for
Conditional Mode. The type of SNA implies the entity type. You do not specify the entity
number in Operand E. This is done automatically as the entity number range is searched. You
may use any entity SNA class. The operand must be Null or entitySNAclass.
COUNT SF FullCount,Warehouse1,Warehouse13
COUNT E EmptyCount,FirstQueue,LastQueue,0,Q
570
Either a conditional operator or a logical operator is required. The logical operator may be
FNV, FV, I, LS, LR, NI, NU, SE, SF, SNE, SNF, SNV, SV, or U. When the logical operator is
true, the entity being tested is counted.
The conditional operator may be E, G, GE, L, LE, MAX, MIN, or NE.
DEPART Block registers statistics which indicate a reduction in
the content of a Queue Entity.
DEPART A,B
A - Queue Entity name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Number of units by which to decrease content of the Queue Entity. Default value is 1.
Optional. The operand must be Null, Name, PosInteger, String, ParenthesizedExpression,
SNA, or SNA*Parameter.
DEPART WaitingLine
DISPLACE Block moves any Transaction.
DISPLACE A,B,C,D
A - Transaction number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Displaced Transaction destination. Block name or number. Required. The operand must
be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
C - Parameter number. Parameter of displaced Transaction to receive residual time if
preempted Transaction is removed from FEC. Optional. The operand must be Null, Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
D - Alternate destination for the Active Transaction. Block name or number. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
DISPLACE X$Culprit,Compensate,Residual,NotCaught
ENTER Block When a Transaction attempts to enter an ENTER
Block, it either takes or waits for a specified number of storage
units.
ENTER A,B
A - Storage Entity name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Number of units by which to decrease the available storage capacity. Default value is 1.
Optional. The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
571
ENTER Toolkit,2
EXAMINE Block may be used to test for membership in a
Numeric Group or a Transaction Group.
EXAMINE A,B,C
A - Group number. Group whose members will be examined. Required. The operand must be
Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Numeric Mode only. The value to be tested for membership in the Numeric Group.
Optional. The operand must be Null, Name, Number, String, ParenthesizedExpression, SNA,
or SNA*Parameter.
C - Block number. Alternate destination for Active Transaction if no membership is found.
Required. The operand must be Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
EXAMINE ValidColors,P$Color,NotCorrectColor
EXAMINE ValidXNs,,NotValidXN
EXECUTE Block can cause any Block routine in the simulation
to be done on behalf of the Active Transaction.
EXECUTE A
A - Block number. The name or number of the Block to be "performed". required. The
operand must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
EXECUTE P$ActiveBlock
FAVAIL Block ensures that a Facility Entity is in the available
state.
FAVAIL A
A - Facility number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
FAVAIL Teller1
FUNAVAIL Blocks are used to make a Facility Entity unavailable
for ownership by Transactions.
FUNAVAIL A,B,C,D,E,F,G,H
A - Facility name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - REmove or COntinue Mode for owning Transaction. Optional. The operand must be RE,
CO, or Null.
572
C - Block number. New Block for Transaction owning the Facility Entity. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
D - Parameter number. Parameter to receive residual time if owning Transaction is removed
from FEC. Optional. The operand must be Null, Name, PosInteger, ParenthesizedExpression,
SNA or SNA*Parameter.
E - REmove or COntinue Mode for preempted Transactions. Optional. The operand must be
RE, CO or Null.
F - Block number. New Block for Transactions preempted at the Facility Entity. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA or SNA*Parameter.
G - REmove or COntinue Mode for Transactions pending or delayed at the Facility Entity.
Optional. The operand must be RE, CO or Null.
H - Block number. New Block for Transactions pending or delayed at the Facility Entity.
Optional. The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA or
SNA*Parameter.
FUNAVAIL Teller1
FUNAVAIL TELLER,RE,TLR2,300,RE,MGR,CO
GATE Block alters Transaction flow based on the state of an
entity.
GATE O A,B
O - Conditional operator. Condition required of entity to be tested for successful test.
Required. The operator must be FNV, FV, I, LS, LR, M, NI, NM, NU, SE, SF, SNE, SNF,
SNV, SV, or U.
A - Entity name or number to be tested. The entity type is implied by the conditional operator.
Required. The operand must be Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
B - Destination Block number when test is unsuccessful. Optional. The operand must be Null,
Name, PosInteger, ParenthesizedExpression, SNA, SNA*Parameter.
GATE SNF MotorPool
GATE SNE MotorPool,CupboardIsBare
The conditional operator is required. It may be FNV, FV, I, LS, LR, M, NI, NM, NU, SE , SF,
SNE, SNF, SNV, SV, or U. When the condition is true, the Transaction enters the GATE
Block and proceeds to the Next Sequential Block.
GATHER Wait for related Transactions.
GATHER A
573
A - Transaction count. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
GATHER 2
GENERATE Block creates Transactions for future entry into the
simulation.
GENERATE A,B,C,D,E
A - Mean inter generation time. Optional. The operand must be Null, Name, Number, String,
ParenthesizedExpression, or DirectSNA. You may not use Transaction Parameters.
B - Inter generation time half-range or Function Modifier. Optional. The operand must be Null,
Name, Number, String, ParenthesizedExpression, or DirectSNA. You may not use
Transaction Parameters.
C - Start delay time. Time increment for the first Transaction. Optional. The operand must be
Null, Name, Number, String, ParenthesizedExpression, or DirectSNA. You may not use
Transaction Parameters.
D - Creation limit. The default is no limit. Optional. The operand must be Null, Name,
PosInteger, String, ParenthesizedExpression, or DirectSNA. You may not use Transaction
Parameters.
E - Priority level. Optional. Zero is the default. The operand must be Null, Name, integer,
String, ParenthesizedExpression, or DirectSNA. You may not use Transaction Parameters.
GENERATE 0.1
INDEX Block updates a Parameter of the Active Transaction.
INDEX A,B
A - Parameter number. Parameter with source value. Required. The operand must be Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Numeric value. Number to be added to contents of Parameter. The result goes into
Parameter 1. Required. The operand must be Name, Number, ParenthesizedExpression,
SNA, or SNA*Parameter.
INDEX 2,11.7
JOIN Block adds the Active Transaction to a Transaction Group,
or adds a number to a Numeric Group.
JOIN A,B
A - Group entity number. Group to which a member will be added. Required. The operand
must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Numeric value. Number to be added to numeric Group. Optional. The operand must be
Null, Name, Number, String, ParenthesizedExpression, SNA, or SNA*Parameter.
574
JOIN Solditems
LEAVE Block increases the accessible storage units at a
Storage Entity.
LEAVE A,B
A - Storage Entity name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Number of storage units. The default is 1. Optional. The operand must be Null, Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
LEAVE RepairMen,10
LINK Block controls the placement of the Active Transaction on
the User Chain of a Userchain Entity.
LINK A,B,C
A - Userchain number. The Userchain Entity which may receive the entering Transaction.
Required. The operand must be Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
B - Chain ordering. The placement of new Transactions on the Userchain. Required. The
operand must be LIFO, FIFO, ParenthesizedExpression, SNA, or SNA*Parameter.
C - Next Block location. The destination Block for Transactions which find the Link Indicator of
the Userchain in the off state (reset). Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
LINK OnHold,FIFO
LOGIC Block changes the state of a Logicswitch entity.
LOGIC O A
O - Logic operator. Required. The operator must be S, R, or I.
A - Logicswitch Entity number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
LOGIC S PowerSwitch
A logical operator is required. It may be S, R, or I with the following effect:
• S - The logic switch is left in the "set" or on state.
• R - The logic switch is left in the "reset" or off state.
• I - The logic switch is inverted.
575
LOOP Block modifies a Parameter and controls the destination
of the Active Transaction based on the result.
LOOP A,B
A - Parameter containing count. required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Block number. Next Block if count nonzero after decrement. Optional. The operand must
be Null, Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
LOOP Customer_Count,Start_Over
MARK Block places an absolute clock time stamp into the
Active Transaction or into its Parameter.
MARK A
A - Parameter number. Parameter to receive value of system clock. Optional. The operand
must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
MARK Beginning
MATCH A pair of MATCH Blocks cause Transactions to wait for
each other.
MATCH A
A - Block name or number. Conjugate MATCH Block to be tested for a matching (same
Assembly Set) Transaction. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
A_Is_Done MATCH B_Is_Done
B_Is_Done MATCH A_Is_Done
MSAVEVALUE Block updates an element of a Matrix Entity.
MSAVEVALUE A,B,C,D
A - Matrix Entity name or number, with optional + or -. Required. the operand must be Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter, followed by +, -, or Null.
B - Row number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
C - Column number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
D - Value to be stored, added, or subtracted. Required. The operand must be Name, Number,
String, ParenthesizedExpression, SNA, or SNA*Parameter.
576
MSAVEVALUE Sales+,Part23,Cust77,6.234
MSAVEVALUE Parts,Part23,Description,"Zippo lighter"
OPEN Block initializes a Data Stream.
OPEN A,B,C
A - Data Stream descriptor. Required. The operand must be Name, PosInteger, String,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Data Stream number. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter. Default is 1.
C - Alternate Destination Block name or number. Optional. The operand must be Null, Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
OPEN ("MYFILE.TXT"),2,Error_Block
PREEMPT Block displaces a Transaction from ownership of a
Facility Entity.
PREEMPT A,B,C,D,E
A - Facility name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Priority Mode. PR, for Priority Mode, or Interrupt Mode, if omitted. Optional. The operand
must be PR or Null.
C - Block name or number. New destination for Transaction presently owning the Facility.
Optional. The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
D - Parameter number. Parameter of preempted Transaction to receive residual time if
preempted Transaction is removed from FEC. Optional. The operand must be Null, Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
E - REmove Mode. Removes preempted Transaction from contention for the Facility.
Optional. The operand must be RE, or Null. If RE, you must specify a destination in Operand
C.
PREEMPT Teller1
PREEMPT Teller1,,Teller2,101,RE
PREEMPT Teller1,PR,Teller2
PRIORITY Block sets the priority of the Active Transaction.
PRIORITY A,B
577
A - New priority value. Required. The operand must be Name, integer, String,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Buffer option. Places Active Transaction behind priority peers on CEC. Optional. The
operand must be BU or Null.
PRIORITY 10
QUEUE Block updates Queue Entity statistics to reflect an
increase in content.
QUEUE A,B
A - Queue Entity name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Number of units by which to increase the content of the Queue Entity. Default value is 1.
Optional. The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
QUEUE WaitingLine
RELEASE Block releases ownership of a Facility, or removes a
preempted Transaction from contention for a Facility.
RELEASE A
A - Facility number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
RELEASE Teller1
REMOVE Block removes members from a Numeric Group or a
Transaction Group.
REMOVE O A,B,C,D,E,F
O - Conditional operator. Relationship of D to E for removal to occur. These choices are
explained below. Optional. The operator must be Null, E, G, GE, L, LE, MAX, MIN, or NE.
A - Group number. Group from which a member or members will be removed. Required. The
operand must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Removal limit. The maximum number of Transactions to be removed. Optional. The
operand must be ALL, Null, Name, PosInteger, ParenthesizedExpression, SNA or
SNA*Parameter.
C - Numeric value. Numeric value to be removed from a Numeric Group. Optional. The
operand must be Null, Name, Number, String, ParenthesizedExpression, SNA or
SNA*Parameter.
D - Test value. PR or Parameter number. The member attribute which determines whether
each Group member Transaction should be removed, or PR to use the Transaction priority for
578
the determination. It is evaluated with respect to the Transaction Group member. Optional.
The operand must be PR or Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
E - Reference value. The value against which the D Operand is compared. The reference
value is evaluated with respect to the Active Transaction. Optional. The operand must be Null,
Name, Number, String, ParenthesizedExpression, SNA or SNA*Parameter.
F - Block number. The alternate destination for the entering Transaction. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA or SNA*Parameter.
REMOVE Inventory
REMOVE G 3,10,,300,11.6,Jump_Block
The conditional operator may be E, G, GE, L, LE, MAX, MIN, or NE. If no conditional operator
is used, E (equality) is assumed. When the condition is true, the Transaction being tested is
removed from the Group
RETURN Block releases ownership of a Facility, or removes a
preempted Transaction from contention for a Facility.
RETURN A
A - Facility number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
RETURN Teller1
SAVAIL Block ensures that a Storage Entity is in the available
state.
SAVAIL A
A - Storage name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
SAVAIL MotorPool
SAVEVALUE Block changes the value of a Savevalue Entity.
SAVEVALUE A,B
A - Savevalue Entity number. Required. May be followed by + or - to indicate addition or
subtraction to existing value. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter, followed by +, -, or Null.
B - The value to be stored, added, or subtracted. Required. The operand must be Name,
Number, String, ParenthesizedExpression, SNA, or SNA*Parameter.
SAVEVALUE Account,99.95
SAVEVALUE The_Bard,"A rose by any other name ..."
579
SCAN Block passes information from a Transaction Group
member to the Active Transaction.
SCAN O A,B,C,D,E,F
O - Conditional operator. Relationship of B to C for the Transaction Group member to be
chosen. These choices are explained below. Optional. The operator must be Null, E, G, GE,
L, LE, MAX, MIN, or NE.
A - Transaction Group number. Group whose members will be scanned. Required. The
operand must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Test value. PR or Parameter number. The member attribute which determines whether
the Group member Transaction should be selected. It is evaluated with respect to the
Transaction Group member. Optional. The operand must be PR or Null, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
C - Reference value. The value against which the B Operand is compared. The default is 0.
Optional. The operand must be Null, Name, Number, String, ParenthesizedExpression, SNA,
or SNA*Parameter.
D - Retrieved value. PR or Parameter number. The member attribute which is to be assigned
to a Parameter of the Active Transaction. It is evaluated with respect to the Transaction
Group member. Required. The operand must be PR, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
E - Receiving Parameter number. The Parameter number of the entering Transaction which
will receive the value retrieved from Operand D. Required. The operand must be Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
F - Alternate Block number. The alternate destination for the entering Transaction. Optional.
The operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
SCAN MAX Inventory,P$Price,,P$PartNumber,100
SCAN E Lot11,PartNum,127,Price,Price,Phone
The conditional operator may be E, G, GE, L, LE, MAX, MIN, or NE. If no conditional operator
is used, E (equality) is assumed. When the condition is true, the Transaction being tested is
selected
SEEK Block sets the Current Line Position of a Data Stream.
SEEK A,B
A - New Current Line Position. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
B - Data Stream Entity. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA or SNA*Parameter.
SEEK 20,Data_Base
580
SEIZE Block When the Active Transaction attempts to enter a
SEIZE Block, it waits for or acquires ownership of a Facility
Entity.
SEIZE A
A - Facility name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
SEIZE Teller1
SELECT Block chooses an entity and places its entity number in
a Parameter of the Active Transaction.
SELECT O A,B,C,D,E,F
O - Conditional operator or logical operator. These choices are explained below. Required.
The operator must be FNV, FV, I, LS, LR, NI, NU, SE, SF, SNE, SNF, SNV, SV, U, E, G, GE,
L, LE, MIN, MAX, or NE.
A - Parameter name or number to receive the number of the selected entity. Required. The
operand must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Lower entity number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
C - Upper entity number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
D - Reference value for E Operand when in Conditional Mode. Optional. The operand must
be Name, Number, String, ParenthesizedExpression, SNA, or SNA*Parameter. Not used with
MAX or MIN.
E - SNA class name. Entity attribute specifier for Conditional Mode tests. Required only for
Conditional Mode. The type of SNA implies the entity type. You do not specify the entity
number in Operand E. This is done automatically as the entity number range is searched. You
may use any entity SNA class. Optional. The operand must be Null or entitySNAclass.
F - Alternate Block number. The destination Block if no entity is selected. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
SELECT SNF Not_Full,Bin1,Bin3
10 Bin1 EQU 1
20 Bin2 EQU 2
30 Bin3 EQU 3
40 Bin1 STORAGE 11
50 Bin2 STORAGE 1000
581
60 Bin3 STORAGE 150
.
.
100 SELECT SNF,3,Bin1,Bin3,,,No_Room
Either a conditional operator or a logical operator is required. The logical operator may be
FNV, FV, I, LS, LR, NI, NU, SE, SF, SNE, SNF, SNV, SV, or U. When the logical operator is
true, the entity being tested is selected.
Either a conditional operator or a logical operator is required. The conditional operator may be
E, G, GE, L, LE, MAX, MIN, or NE. The conditions are defined as follows:
SPLIT Block creates Transactions in the same Assembly Set as
the Active Transaction.
SPLIT A,B,C
A - Count. Number of related Transactions to be created. Required. The operand must be
Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
B - Block number. Destination for new Transactions. Optional. The operand must be Null,
Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
C - Parameter number. Parameter to receive serial number. Optional. The operand must be
Null, Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
SPLIT 1
SPLIT 3,P20,20
SPLIT 3,Pro,17
SUNAVAIL Block ensures that a Storage Entity is in the
unavailable state.
SUNAVAIL A
A - Storage name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, SNA*Parameter.
SUNAVAIL MotorPool
TABULATE Block triggers the collection of a data item in a Table
Entity.
TABULATE A,B
A - Table Entity name or number. Required. The operand must be Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
582
B - Weighting factor. Optional. The operand must be Null, Name, Number,
ParenthesizedExpression, SNA, or SNA*Parameter.
TABULATE Sales
TERMINATE Block removes the Active Transaction from the
simulation and optionally reduces the Termination Count.
TERMINATE A
A - Termination Count decrement. Default is 0. Optional. The operand must be Null, Name,
PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
TERMINATE 1
TEST Block compares values, normally SNAs, and controls the
destination of the Active Transaction based on the result of the
comparison.
TEST O A,B,C
O - Relational operator. Relationship of Operand A to Operand B for a successful test.
Required. The operator must be E, G, GE, L, LE, or NE.
A - Test value. Required. The operand must be Name, Number, String,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Reference value. Required. The operand must be Name, Number, String,
ParenthesizedExpression, SNA, or SNA*Parameter.
C - Destination Block number. Optional. The operand must be Null, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
TEST G C1,70000
TEST G Q$Teller1_Line,Q$Teller2_Line,Teller1
TRACE Block turns on the Trace Indicator of the Active
Transaction.
TRACE
TRANSFER Block causes the Active Transaction to jump to a
new Block location.
TRANSFER A,B,C,D
A - Transfer Block mode. Described below. Optional. The operand must be BOTH, ALL,
PICK, FN, P, SBR, SIM, fraction, Name, PosInteger, ParenthesizedExpression, SNA,
SNA*Parameter, or Null.
583
B - Block number or location. Parameter name or number when in P Mode. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
C - Block number or location. Increment value in FN or P Mode. Optional. The operand must
be Null, Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
D - Block number increment for ALL Mode. Default is 1. Optional. The operand must be Null,
Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
Unconditional Mode
TRANSFER ,New_Place
Fractional Mode
TRANSFER .75,,New_Place
Both Mode
TRANSFER BOTH,First_Place,Second_Place
All Mode
TRANSFER ALL,First_Place,Last_Place,2
Pick Mode
TRANSFER PICK,First_Place,Last_Place
Function Mode
TRANSFER FN,Func1,5
Parameter Mode
TRANSFER P,Placemarker,1
Subroutine Mode
TRANSFER SBR,New_Place,Placemarker
Simultaneous Mode
TRANSFER SIM,Nodelay_Place,Delay_Place
UNLINK Block removes Transactions from the User Chain of a
Userchain Entity.
584
UNLINK O A,B,C,D,E,F
O - Relational operator. Relationship of D to E for removal to occur. These choices are
explained below. Optional. The operator must be Null, E, G, GE, L, LE or NE.
A - User Chain number. User Chain from which one or more Transactions will be removed.
Required. The operand must be Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
B - Block number. The destination Block for removed Transactions. Required. The operand
must be Name, PosInteger, ParenthesizedExpression, SNA, or SNA*Parameter.
C - Removal limit. The maximum number of Transactions to be removed. If not specified, ALL
is used. Optional. The operand must be ALL, Null, Name, PosInteger,
ParenthesizedExpression, SNA, or SNA*Parameter.
D - Test value. The member Transaction Parameter name or number to be tested, a Boolean
variable to be tested, or BACK to remove from the tail of the chain. Optional. The operand
must be Null, Name, PosInteger, ParenthesizedExpression, SNA, SNA*Parameter or BACK.
E - Reference value. The value against which the D Operand is compared. Optional. The
operand must be Null, Name, Number, String, ParenthesizedExpression, SNA, or
SNA*Parameter. Operand E is not used if Operand D is a Boolean Variable.
F - Block number. The alternate destination for the entering Transaction. Optional. The
operand must be Null, Name, PosInteger, ParenthesizedExpression, SNA, or
SNA*Parameter.
UNLINK OnHold,Reentry,1
The relational operator may be E, G, GE, L, LE, or NE. If no relational operator is used, E
(equality) is assumed. When the relationship is true and the limit condition has not been
reached, the Transaction being tested is removed from the User Chain
UNTRACE Block turns off the Trace Indicator of the Active
Transaction.
UNTRACE
585
GPSS #‫( أوا‬2) [/#
BVARIABLE Command defines a Bvariable Entity.
NAME BVARIABLE X
NAME - Entity Label for this entity. Required. The field must be Name.
X - Expression. Required. Must be Expression. Expressions are discussed in Section 3.4.
LINE11 BVARIABLE (BV$CLK’AND’BV$PHASE2)
CLEAR Command returns the simulation to the unused state.
CLEAR A
A - ON or OFF. If the A Operand is omitted, ON is assumed. Optional. The operand must be
ON, OFF or Null.
CONDUCT Command begins an experiment.
CONDUCT A
A - PLUS Experiment Procedure Call. Optional. The operand must be ProcedureCall.
CONDUCT MyExperiment( NumberOfTellers, StartingReplicateNumber )
CONTINUE Command causes a halted simulation to resume.
CONTINUE
EQU Command evaluates an Expression and assigns the result
to a Named Value.
NAME EQU X
NAME - Named Value to receive a value. Required. The field must be Name.
X - Expression. Required. Must be Expression. Expressions are discussed in Section 3.4.
Price EQU 19.95
EXIT Command concludes the GPSS World Session.
EXIT
FUNCTION Command defines the rules for a table lookup.
NAME FUNCTION A,B
586
NAME - Entity Label this entity. Required. The field must be Name.
A - Function argument. Required. The operand must be Name, PosInteger, String,
ParenthesizedExpression, SNA, or SNA*Parameter.
B - Function type (one letter) followed immediately by the number of data pairs in the
Function Follower Statements. Required.
Type C Functions
Output FUNCTION V$Input,C3
1.1,10.1/20.5,98.7/33.3,889.2
Xpdis FUNCTION RN200,C24
0,0/.1,.104/.2,.222/.3,.355/.4,.509/.5,.69/.6,.915/.7,1.2/.75,1.38
.8,1.6/.84,1.83/.88,2.12/.9,2.3/.92,2.52/.94,2.81/.95,2.99/.96,3.2
.97,3.5/.98,3.9/.99,4.6/.995,5.3/.998,6.2/.999,7/.9998,8
Type D Functions
DIis1 FUNCTION X$A2,D5
1.1,6.9/2.1,7/6.33,9.4/7,10/9.9,12.01
Ran1 FUNCTION RN1,D5
0,0/.2,7.2/.4,6.667/.8,9.92/1.0,10
Type E Functions
Edisc FUNCTION X$QRA,E5
1,S$Stor1/3,S$Stor2/5,S$Stor3/9,S$Stor5/10,S$Stor6
Type L Functions
Listtype FUNCTION Q$Barber,L5
1,PAR1/2,PAR2/3,PAR3/4,PAR4/5,PAR5
Type M Functions
Mlist FUNCTION X$Name1,M5
1,Q$Nnam1/2,Q$NamX/3,Q$Nam4/4,Q$Nam6/5,F$Tan1
FVARIABLE Command defines a "floating point arithmetic"
Variable Entity.
587
NAME FVARIABLE X
NAME - Entity Label for this entity. Required. The field must be Name.
X - Expression. Required. Expressions are discussed in Section 3.4.
VAR1 FVARIABLE 5#LOG(Q$WAITINGLINE)
HALT Command interrupts the simulation and purges the
Command Queue.
HALT
INCLUDE Command Translates a file of Model Statements.
INCLUDE A
A - Filespec. A string representing the file specification of the Secondary Model File or
Command List to be Translated. Required. Operand must be String.
INCLUDE "SAMPLE1.GPS"
INITIAL Command initializes a Logicswitch Entity, Savevalue
Entity, or an element of a Matrix Entity.
INITIAL A,B
A - Logicswitch, Savevalue, or Matrix element specified as SNA. Operand A must have the
form of an LS, X, or MX class SNA. Required. The operand must be LSPosInteger,
LS$Name, XPosInteger, X$Name, MXPosInteger(m,n) or MX$Name(m,n). Coordinates (m,n)
must be Name or PosInteger.
B - Value to be assigned. The default is 1. Optional. The operand must be Null, Number,
String or Name.
INITIAL X$Quote,"Now is the time ... "
INITIAL MX$Inventory(Part_39,Stocklevel),200
MATRIX Command defines a GPSS Matrix Entity.
NAME MATRIX A,B,C
NAME - Entity Label for this entity. Required. The field must be Name.
A - Unused field (for compatibility with older GPSS implementations).
B - Number of matrix rows. Required. The operand must be PosInteger.
C - Number of matrix columns. Required. The operand must be PosInteger.
588
Inventory MATRIX ,1000,5
QTABLE Command initializes a queue time frequency
distribution table.
NAME QTABLE A,B,C,D
NAME - Entity Label for this entity. Required. The field must be Name.
A - Name of Queue Entity. Required. The operand must be PosInteger or Name.
B - Upper limit of first frequency class. The maximum argument which causes the first
frequency class to be updated. Required. The operand must be Number or String.
C - Size of frequency classes. The difference between the upper limit and lower limit of each
frequency class. Required. The operand must be Number or String.
D - Number of frequency classes. The operand must be PosInteger.
WaitTimes QTABLE WaitingLine,100,100,10
REPORT Command causes a report to be created immediately.
REPORT A,B
A - Must be Null.
B - NOW, to write a Standard Report, immediately. Optional. the operand must be NOW or
Null.
RESET Command marks the beginning of a measurement
period.
RESET
RMULT Command sets the seeds for random number
generators.
RMULT A,B,C,D,E,F,G
A - Seed for random number generator number 1. Optional. The operand must be Null, or
PosInteger.
B - Seed for random number generator number 2. Optional. The operand must be Null, or
PosInteger.
C - Seed for random number generator number 3. Optional. The operand must be Null, or
PosInteger.
D - Seed for random number generator number 4. Optional. The operand must be Null, or
PosInteger.
589
E - Seed for random number generator number 5. Optional. The operand must be Null, or
PosInteger.
F - Seed for random number generator number 6. Optional. The operand must be Null, or
PosInteger.
G - Seed for random number generator number 7. Optional. The operand must be Null, or
PosInteger.
RMULT ,,111
SHOW Command sends an Expression for evaluation by the
Simulation Object, and writes the result in the Status Line.
SHOW X
X - Expression.
SHOW 2#LOG(Q$Barber)
SHOW C1
SHOW 4#(SQR(2)+SIN(C1))
SHOW N1^W$Chair
START Command begins a simulation.
START A,B,C,D
A - Termination count. Required. The operand must be PosInteger.
B - Printout operand. NP for "no printout". Default is to print a standard report. Optional. The
operand must be NP or Null.
C - Not used. Kept for compatibility with older dialects of GPSS.
D - Chain printout. 1 to include the CEC and FEC in the standard report. Optional. The
operand must be Null, or PosInteger.
START 1000,,,1
STEP Command causes the simulation to proceed a specified
number of Block entries.
STEP A
A - Block entry count. Required. A must be a positive integer, more formally, PosInteger.
STEP 1
STOP Command sets or removes a Stop Condition.
590
STOP A,B,C
A - Transaction number. A must be a positive integer. If the A Operand is omitted, any
Transaction number will satisfy the condition. Optional. The operand must be Null, or
PosInteger.
B - Block number. If the B Operand is omitted, any Block will satisfy the condition. Optional.
The operand must be Null, Name, or PosInteger.
C - ON or OFF. If the C Operand is omitted, ON is assumed. Optional. The operand must be
ON, OFF or Null.
STOP 100,52
STOP
STOP ,,OFF
STOP 2
STOP ,Chair
STOP ,Chair,OFF
STORAGE Command defines a Storage Entity.
NAME STORAGE A
NAME - Entity Label for this entity. Required. The field must be Name.
A - Total storage capacity. Required. The operand must be PosInteger.
MotorPool STORAGE 20
TABLE Command initializes a frequency distribution table.
NAME TABLE A,B,C,D
NAME - Entity Label for this entity. Required. The field must be Name. The length of a Table
name is limited to 32 characters.
A - Table argument. The data item whose frequency distribution is to be tabulated. Required.
The operand must be ParenthesizedExpression, SNA or SNA*Parameter.
B - Upper limit of first frequency class. The maximum argument which causes the first
frequency class to be updated. Required. The operand must be Number or String.
C - Size of frequency classes. The difference between the upper limit and lower limit of each
frequency class. Required. The operand must be Number or String.
D - Number of frequency classes. Required. The operand must be PosInteger.
SalesTable TABLE P$Price,9.95,10,10
591
VARIABLE Command defines an arithmetic Variable Entity.
NAME VARIABLE X
NAME - Entity Label for this entity. Required. The field must be Name.
X - Expression. Required. Expressions are discussed in Section 3.4.
Var1 VARIABLE 5#LOG(Q$WaitingLine)
592
‫;م‬1/ ‫)د‬.‫( ات ا‬3) [/#
SNAs available in GPSS World:
• A1 - Assembly Set of the Active Transaction. Integer value.
• AC1 - Value of absolute system clock. Simulated time since last CLEAR. Real value.
• BVEntnum - Result of evaluating Boolean Variable Entity Entnum. Real value.
• C1 - Value of relative system clock. Simulated time since last RESET. Real value.
• CAEntnum - Average Userchain content. The time weighted average number of chained
Transactions for Userchain Entnum. Real value.
• CCEntnum - Total Userchain entries. The count of all Transactions chained to Userchain
Entnum. Integer value.
• CHEntnum - Current Userchain content. The current number of Transactions chained to
Userchain Entnum. Integer value.
• CMEntnum - Maximum Userchain content. The maximum number of Transactions chained
to Userchain Entnum. The "high water mark". Integer value.
• CTEntnum - Average Userchain residence time. The average duration of Transactions at
Userchain Entnum. Real value.
• FEntnum - Facility busy. If Facility Entity Entnum is currently busy, FEntnum returns 1.
Otherwise FEntnum returns 0. Integer value.
• FCEntnum - Facility capture count. The number of times Facility Entity Entnum has been
SEIZEd or PREEMPTed by a Transaction. Integer value.
• FIEntnum - Facility Entnum interrupted. If Facility Entity Entnum is currently preempted,
FIEntnum returns 1. Otherwise FIEntnum returns 0. Integer value.
• FNEntnum - Function. Result of evaluating Function Entity Entnum . Real value.
• FREntnum - Facility utilization. The fraction of time Facility Entity Entnum has been busy.
FREntnum is expressed in parts-per-thousand and therefore returns a value 0-1000,
inclusive. May be nonintegral. Real value.
• FTEntnum - Average Facility holding time. The average time Facility Entity Entnum is
owned by a capturing Transaction. Real value.
• FVEntnum - Facility in available state. FVEntnum returns 1 if Facility Entity Entnum is in the
available state, 0 otherwise. Integer value.
• GNEntum - Numeric Group count. GNEntnum returns the membership count of Numeric
Group Entnum. Integer value.
• GTEntnum - Transaction Group count. GTEntnum returns the membership count of
Transaction Group Entnum. Integer value.
593
• LSEntnum - Logicswitch set. LSEntnum returns 1 if Logicswitch Entity is in the "set" state, 0
otherwise. Integer value.
• MBEntnum - Match at Block. MBEntnum returns a 1 if there is a Transaction at Block
Entnum which is in the same Assembly Set as the Active Transaction. MBEntnum returns a 0
otherwise. Integer value.
• MPParameter - Transit Time, Parameter. Current absolute system clock value minus value
in Parameter Parameter. Real value.
• MXEntnum(m,n) - Matrix Savevalue. The value in row m, column n of Matrix Entity Entnum
is returned. In Matrices of more than 2 dimensions, all other indices are assumed to be 1.
Unlike MX class SNAs, PLUS Expressions can refer to any element of a higher dimension
matrix.
• M1 - Transit time. M1 returns the absolute system clock minus the "Mark Time" of the
Transaction. Real value.
• NEntnum - Block entry count. The total number of Transactions which have entered Block
Entnum is returned. Integer value.
• PParameter or *Parameter - Parameter value. PParameter or *Parameter returns the value
of Parameter Parameter of the Active Transaction. Integer, real, or string value.
Indirect addressing uses the notation SNA*Parameter.
• PR - Transaction priority. The value of the priority of the Active Transaction. Integer value.
• QEntnum - Current Queue content. The current count value of Queue Entity Entnum.
Integer value.
• QAEntnum - Average Queue content. The time weighted average count for Queue Entity
Entnum. Real value.
• QCEntnum - Total Queue entries. The sum of all entry counts for Queue Entity Entnum.
Integer value.
• QMEntnum - Maximum Queue content. The maximum count of Queue Entity Entnum. The
"high water mark". Integer value.
• QTEntnum - Average Queue residence time. The time weighted average of the count for
Queue Entity Entnum. Real value.
• QXEntnum - Average Queue residence time excluding zero entries. The time weighted
average of the count for Queue Entity Entnum not counting entries with a zero residence
time. Real value.
• QZEntnum - Queue zero entry count. The number of entries of Queue Entity Entnum with a
zero residence time. Integer value.
• REntnum - Available storage capacity. The storage content (or "tokens") available for use
by entering Transactions at Storage Entity Entnum. Integer value.
• RNEntnum - Random number. RNEntnum returns a random integer 0-999 from Random
Number Generator Entnum. Integer value.
594
• SEntnum - Storage in use. SEntnum returns the amount of storage content (or "tokens")
currently in use by entering Transactions at Storage Entity Entnum. Integer value.
• SAEntnum - Average storage in use. SAEntnum returns the time weighted average of
storage capacity (or "tokens") in use at Storage Entity Entnum. Real value.
• SCEntnum - Storage use count. Total number of storage units that have been acquired
from Storage Entity Entnum. Integer value.
• SEEntnum - Storage empty. SEEntnum returns 1 if Storage Entity Entnum is completely
available, 0 otherwise. Integer value.
• SFEntnum - Storage full. SFEntnum returns 1 if Storage Entity Entnum is completely used,
0 otherwise. Integer value.
• SREntnum - Storage utilization. The fraction of total usage represented by the average
storage in use at Storage Entity Entnum. SREntnum is expressed in parts-per-thousand and
therefore returns a value 0-1000, inclusive. May be nonintegral. Real value.
• SMEntnum - Maximum storage in use at Storage Entity Entnum. The "high water mark".
Integer value.
• STEntnum - Average holding time per unit at Storage Entity Entnum. Real value.
• SVEntnum - Storage in available state. SVEntnum returns 1 if Storage Entity Entnum is in
the available state, 0 otherwise. Integer value.
• TBEntnum - Nonweighted average of entries in Table Entity Entnum. Real value.
• TCEntnum - Count of nonweighted table entries in Table Entity Entnum. Integer value.
• TDEntnum - Standard deviation of nonweighted table entries in Table Entity Entnum. Real
value.
• TG1 - Remaining Termination Count. TG1 returns the count that is decremented by
TERMINATE Blocks with a positive A operand. This value is initialized by START Statements
and indicates completion of the simulation when it is 0. Integer value.
• VEntnum - Result of evaluating arithmetic or floating point Variable Entity Entnum. Real
value.
• WEntnum - Current Block count. The current number of Transactions in Block Entity
Entnum. Integer value.
• XEntnum - Savevalue. The value of Savevalue Entity Entnum is returned. Integer, real, or
string value.
• XN1 - Active Transaction number. The Transaction number of the Active Transaction is
returned. Integer value.
• Z1 - Free memory. Value returned by the Operating System. Integer value.
Special rules apply when a simulation is run in GPSS/PC Compatibility Mode. This
are discussed more fully below.
595
GPSS ‫ل‬2 (4) [/#
Operators
Operators are used to combine data elements in Expressions. Data are coerced if a specific
type is required by the operator. For example, if a numeric operation is to be performed on a
variable with a string value, the numeric equivalent derived from the characters in the string is
used.
A Setting is available in the Simulation Page of the Settings Notebook which switches the
roles of the [*] operator and the [#] operator.
The operators used in GPSS World are:
^
Exponentiation. A^B returns A raised to the power of B.
# (or *)
Multiplication. A # B returns the numeric product of A and B.
/
Division. A / B returns the quotient of A divided by B.
\
Integer Division. A \ B returns the result of integer division of A by B.
@ Integer Remainder. A @ B returns the modulo division of A by B.
-
Subtraction. A - B returns the difference of A and B.
+ Addition. A + B return the sum of A and B.
>= ‘GE’
Greater Than or Equal To. A >= B returns 1 if A is numerically greater than or equal
to B, 0 otherwise.
<= ‘LE’
Less Than or Equal To. A <= B returns 1 if A is numerically less than or equal to B,
0 otherwise.
> ‘G’
Greater Than. A > B returns 1 if A is numerically greater than B, 0 otherwise.
< ‘L’
Less Than. A < B returns 1 if A is numerically less than B, 0 otherwise.
= ‘E’
Equal A = B returns 1 if A is numerically equal to B, 0 otherwise.
!= ‘NE’ Not Equal. A != B returns 1 if A is numerically different from B, 0 otherwise.
& ‘AND’
| ‘OR’
Logical And. A & B returns 1 if and only if both A and B are non zero, 0 otherwise.
Logical Or. A ‘OR’ B returns 1 if A or B or both are non zero, 0 otherwise.
596
Precedence
When Expressions are evaluated, the precedence of operators determines the order of
operations. An operator with a higher precedence is evaluated before an operator with a
lower precedence. The precedence of operators is as follows, from highest to lowest:
^ Exponentiation
# (or *) / \ Multiplication, Division, Integer Division
@ Integer Remainder
-+
Addition, Subtraction
>= <= > < Comparison Operators
= != Equal, Not Equal
& Logical And
| Logical Or
597
GPSS -‫ ا‬4 ‫ل‬B7‫( أ‬5) [/#
598
‫ )‪(6‬‬
‫" أ‪ ,b‬ا@ رات‬
‫ا ‪ ,:‬وإ‪ -‬ت ‪U ,‬‬
‫‪599‬‬
‫ا ا ا‬
‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
‫هـ‬1422/‫هـ‬1421 ‫ول‬0‫ ا‬M `‫إ ر ا‬
( 1 ‫ق ا آ ة‬C ) P 241 ‫ دة‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
& , ‫ ا‬Linear Congruential Method ,7‫ ا‬7‫ق ا‬C ! ‫ إذا آ ن أي‬%; ! (‫أ‬
:, ‫دورة آ‬
a ) X i = (13 X i −1 + 13) ( mod 16 )
b) X i = (12 X i −1 + 13) ( mod 16 )
c) X i = (13 X i −1 + 12 ) ( mod 16 )
:, ‫ ا‬,?‫ا‬2O"‫اد ا‬q (‫ب‬
0.488 0.226 0.221 0.043 0.055 0.743 0.081 0.685 0.364 0.012
0.372 0.543 0.483 0.050 0.628 0.966 0.750 0.697 0.764 0.040
0.404 0.549 0.203 0.990 0.155 0.079 0.789 0.462 0.795 0.190
:, ‫ ا‬,V`‫ آ ي أ ا‬R ‫ إ ر‬
H 0 : Ri ∼ U 0,1
H1 : Ri ≁ U 0,1
:‫ا ‚ال ا‬
‫ة‬:; 3; ,?‫ا‬2O"‫اد ا‬0‫ و ا‬Inverse Transform Method 3/"‫ ا‬M92 ‫ ا‬,:9C (‫ا‬
Exponential Distribution 3‫ ا‬R9‫ز‬2I & 3?‫ا‬2O Y %J , ‫ول و‬0‫ال ا‬A‫)ب( ! ا‬
:, ‫اآ‬I R9‫ز‬2I ,‫ا‬
−
λ
x
1 − e , x ≥ 0
F ( x ) = 
x<0
 0,
‫ ة‬RJ‫ا‬2 ‫ ا‬6e 6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ "د ات إ‬, ‫ب( ا ت ا‬
29 50
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
3
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
39H‫ ا‬R9‫ز‬2‫ ا‬-‫ أو‬،‫ح‬: ‫ ا‬R9‫ز‬2‫ ا‬% " ‫ر‬J‫ ا ت و‬5.U 3 " 3? 6‫ إ‬R9‫ز‬2I -‫أو‬
. f9‫ ت أ‬Empirical Distribution
.‫ م‬9‫ة أ‬O ‫ ا ` ة‬,( 9‫و‬9 ‫ آ‬6 ,: ‫ة )ب( ا‬:`‫ج( ?] ا‬
600
:,-‫ذ‬2 ‫ ت ا‬[email protected]‫ا‬
:3 ‫ آ‬Minitab ] 3; Worksheet M , `' 3; ‫ ا ت‬M T‫أو‬
MTB >
DATA>
DATA>
DATA>
DATA>
DATA>
DATA>
set
0
0
2
0
0
end
c1
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
3
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
. ' R H 3 ‫ار‬/I‫ و‬3 ‫ار‬/I ‫ول‬- ‫ن‬2/9 3 ‫ ا‬0‫ا‬
MTB > tally c1;
SUBC> perc;
SUBC> cump.
‫م‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ د ات إ‬3?‫ا‬2O"‫ ا‬Y ,/ ‫ ا‬%:‫ي ا‬2 9 (C1) ‫ول‬0‫د ا‬2 "‫ا‬
. ‫ ا‬R H ‫ ا‬3‫ار ا‬/‫ ا‬P [‫د ا‬2 "‫ و ا‬3‫ار ا‬/‫ي ا‬2 9 3 [‫د ا‬2 "‫ ا‬،6‫ا‬2‫ا‬
Summary Statistics for Discrete Variables
C1
0
1
2
3
Percent CumPct
62.00 62.00
30.00 92.00
6.00 98.00
2.00 100.00
(C2) ‫د‬2 "‫ ا‬3; 6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ د ات إ‬3?‫ا‬2O"‫ ا‬Y ,/ ‫ ا‬%:‫ ا‬Rf
,‫ دا‬3‫ ه‬5.‫( وه‬C3) ‫د‬2 "‫ ا‬3; (100 ,‫ارات ا‬/‫ ا‬, : U M ) ,92b ‫ ا‬,‫ارات ا‬/‫وا‬
6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ د ات إ‬3?‫ا‬2O"‫ ا‬Y , [email protected]‫ ا‬,/‫ا‬
MTB >
DATA>
DATA>
MTB >
DATA>
DATA>
DATA>
DATA>
DATA>
set c2
0 1 2 3
end
set c3
.62
.3
.06
.02
end
(C1) 6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ د ات إ‬3?‫ا‬2O"‫ ا‬Y ,/ ‫ ا‬%:‫ ! ا‬, J 50 !9 "
29 50 ‫ ا ` ة‬,( ‫ آ ة‬M[ I 5.‫( وه‬C4) 3; U"f‫( و‬C3) ‫ت‬T [email protected]‫ام ا‬
MTB > rand 50 c4;
SUBC> disc c2 c3.
3 ‫آ ة آ‬
‫ ا‬%: ,‫ارات ا‬/‫ ا‬-2
MTB > tally c4;
SUBC> perc.
Summary Statistics for Discrete Variables
C4
0
1
2
3
Percent
68.00
28.00
2.00
2.00
‫ د‬3?‫ا‬2O"‫ ا‬Y , [email protected]‫ ا‬,/‫ ا‬,‫ دا‬3‫ ه‬5.‫( وه‬C5) 3; ‫ ا آ ة‬%: ,92b ‫ ا‬,‫ارات ا‬/‫ ا‬M
(‫ هة‬O ‫ ا آ ة )ا‬6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ات إ‬
MTB > set c5
DATA> .68 .28 .02 .02
DATA> end
‫ د ات‬3?‫ا‬2O"‫ ا‬Y , [email protected]‫ ا‬,/‫ ا‬,‫ أن دا‬,9` ‫ ا‬,V`‫ آ ي @ ر ا‬R ‫ن ر‬h‫م ا‬2:
Y , [email protected]‫ ا‬,/‫ ا‬,‫_ ! دا‬IT (‫ هة‬O ‫ ا آ ة )ا‬6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫إ‬
,Y (‫ول‬0‫ال ا‬A‫ ا‬3; , 2 ‫ )ا‬,"J2 ‫ ا‬6‫ا‬2‫م ا‬2‫ ا‬3; ‫ ول‬b `6 ,( ‫ ل‬7‫ د ات إ‬3?‫ا‬2O"‫ا‬
601
n
χ n2−1 = ∑
(Oi − Ei )
2
Ei
i =1
k1 3; &"f9‫ آ ي و‬R S 9 3 ‫ ا‬0‫ ا‬،,"J2 ‫ ا‬%:‫ي ا‬2 I C3 ‫ هة و‬O ‫ ا‬%:‫ي ا‬2 I C5 P6
MTB > let k1=sum((c5-c3)**2/c3)
K1
0.0338065
&96 ‫ ت‬-‫ در‬3 ‫ ـ‬, 2 ‫ آ ي ا‬R , J 3‫ ه‬5.‫ه‬
MTB >
SUBC>
MTB >
MTB >
cdf k1 k2;
chis 3.
let k3=1-k2
print k3
Data Display
K3
0.998363
MJ‫ أ‬3‫( وه‬k2) 0.00163651 2‫ ه‬0.0338065 , :‫ ل ا‬6‫ ره ) إ‬9 ‫ إ‬0.998363 ,6 I 3‫وه‬
,9` ‫ ا‬,V`‫; ا‬T ‫ ( أي‬0.025 !
,Y ‫ ا‬S I , ‫وا ا‬0‫ا‬
4
E ( X ) = ∑ xi p ( xi )
i =1
MTB > let k4=sum(c2*c3)
MTB > let k5=sum(c2*c5)
MTB > print k4 k5
(k5 , J) 0.38 3‫آ ة ه‬
Data Display
K4
K5
‫ ت ا‬,"J2 ‫ ا‬, :‫( وا‬k4 , J) 0.48 3‫ ه‬5‫ ه‬O ‫ ت ا‬,"J2 ‫ ا‬, :‫ا‬
0.480000
0.380000
V (X ) = E(X
2
,Y ‫ ا‬S I , ‫وا ا‬0‫ا‬
)− E (X )
2
MTB > let k6=sum((c2**2)*c3)-k4**2
MTB > let k7=sum((c2**2)*c5)-k5**2
MTB > print k6 k7
k7 ‫ و‬k6 3; ‫ ت‬9 ‫ا‬
Data Display
K6
K7
0.489600
0.395600
k9 ‫ و‬k8 3; ,9‫ ا@ ا; ت ا " ر‬37"I ,: ‫ ا‬%: 3" ‫ر ا‬GH‫ا‬
MTB > let k8=sqrt(k6)
MTB > let k9=sqrt(k7)
MTB > print k8 k9
Data Display
K8
0.699714
K9
0.628967
MTB >
‫ا ا ا‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﻫـ‬1422/‫ﻫـ‬1421 ‫ﺇﺧﺘﺒﺎﺭ ﺃﻋﻤﺎﻝ ﻓﺼﻠﻲ ﺃﻭﻝ ﻟﻠﻔﺼﻞ ﺍﻟﺜﺎﻧﻲ‬
602
‫ﻟﻤﺎﺩﺓ ‪ 241‬ﺑﺤﺚ ) ﻃﺮﻕ ﺍﻟﻤﺤﺎﻛﺎﺓ ‪( 1‬‬
‫ا‪, 2 ! G‬‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫ا ت ا ‪" ,‬د ات إ‪ 7‬ل (‪ b `6 ,‬ول ;‪ 3‬ا‪2‬م ا‪2‬ا‪ 6e 6‬ا ‪2‬ا‪ RJ‬ة ‪50‬‬
‫‪29‬‬
‫‪1‬‬
‫‪0‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪3‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪2‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪2‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫)أ( أو‪ -‬دا‪ ,‬ا‪ ,/‬ا@‪" , 6‬د ات ا@‪ 7‬ل ا‪ ،3 2‬و ‪ U‬او‪ -‬د ات ا@‪T 7‬ت‬
‫ا ‪ 29 ,"J2‬و ا@ اف ا " ري "د ات ا@‪ 7‬ل ا‪3 2‬‬
‫)ب( أو‪ -‬دا‪ ,‬ا‪2‬ز‪ R9‬ا‪" Empirical Distribution 39H‬د ات ا@‪ 7‬ل ا‪.3 2‬‬
‫ا ‚ال ا‪:‬‬
‫)أ( ‪ 6‬آ ‪9‬و‪ ,( 9‬ا ` ة ‪ . 29 50‬و ! ?] ا آ ة أو‪ -‬ا ‪ 7‬ت ;‪ 3‬ا`‪:‬ة )أ( !‬
‫ا‪A‬ال ا‪0‬ول‪.‬‬
‫)ب( ام إ ر ‪ R‬آ ي‪ ،‬ه‪ -29 M‬إف ! دا‪ ,‬ا‪ ,/‬ا@‪ , 6‬ا ‪ O‬هة ) !‬
‫ا ‪ /‬ة( وا ‪) ,"J2‬ا ‪ 3; , 2‬ا‪A‬ال ا‪0‬ول(‪ ،‬أ در‪95% ,:X ,-‬‬
‫‪603‬‬
‫‪0‬‬
‫‪0‬‬
‫‪2‬‬
‫‪0‬‬
‫‪0‬‬
‫ا ا ا‬
‫د‬2" g ‫ ا‬," ‫م‬2"‫ ا‬,‫آ‬
‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
‫ هـ‬1422/1421 3 [‫ ا‬M `‫ ل ا‬0 3 [‫ا@ ر ا‬
(1 ‫ ) ا آ ة‬P 241 ‫ دة‬
, 2 :! G‫ا‬
:, ‫ ا‬,b0‫ ا‬R - S-‫أ‬
:‫ول‬0‫ال ا‬A‫ا‬
,XX ! ," 2 Linear Congruential Method ,7‫ ا‬,: 7‫ ا‬,:97‫)أ( إم ا‬
X 0 = 27, a = 8, c = 47, m = 100 %:‫ ! ا‬J‫ ذات ر‬,?‫ا‬2O ‫ م‬J‫أر‬
," 2 Multiplicative Congruential Method ,` f‫ ا‬,: 7‫ ا‬,:97‫)ب( إم ا‬
X 0 = 117, a = 43, m = 1000 %:‫ م ا‬J‫ ار‬,XX ‫ ذات‬,?‫ا‬2O ‫ م‬J‫ أر‬," ‫! ار‬
:3 [‫ال ا‬A‫ا‬
‫ ; إذا‬,V`‫ @ ر ا‬Kolmogorov-Smirnov ‫ف‬2 – ‫روف‬2-2 2‫إم إ ر آ‬
,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬W ‫آ‬
0.136
0.394
0.513
0.531
0.844
0.715
0.681
0.276
0.154
0.880
0.239
0.888
0.090
0.631
0.245
. α = 0.05 . ‫؟‬T ‫[ ام‬0,1] ‫ ا`ة‬%N R9‫ز‬2I U
:P [‫ال ا‬A‫ا‬
, 6‫ إ‬R9‫ز‬2I ,‫ & دا‬X 3?‫ا‬2O Y
x≤2
0,

2
  x − 1 ,
2< x≤3
 2 
F (x) = 
2
x
 1
1 − 3  3 − 2  , 3 < x ≤ 6

x>6
1,
.3?‫ا‬2O"‫ ا‬Y , J 15 ! , ‫)أ( و‬
.,9N‫ ا‬, : U‫ ر‬J‫ و‬,"‫ ا‬w2 S6‫)ب( أ‬
604
‫ا ا ا‬
‫ هـ‬1422/1421 3 [‫ ا‬M `‫ ل ا‬0 3 [‫ ر ا‬z , ‫ ت‬-‫إ‬
(1 ‫ ) آ ة‬P 241 ‫ا ة‬
:‫ول‬0‫ال ا‬A , -‫إ‬
( ‫)أ‬
Linear Congruential Method
X i +1 = ( aX i + c ) mod m, i = 0,1, 2,...
Xi
, i = 1, 2,...
m
X 0 = 27, a = 8, c = 47, m = 100
Ri =
X 1 = ( 8 × 27 + 47 ) = 263 = 63 mod100
X 1 63
=
= 0.63
m 100
X 2 = ( 8 × 63 + 47 ) = 551 = 51 mod100
R1 =
X 2 51
=
= 0.51
m 100
X 3 = ( 8 × 51 + 47 ) = 455 = 55 mod100
R2 =
R3 =
X 3 55
=
= 0.55
m 100
0.63, 0.51, 0.55 :3‫ ه‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫إذا ا‬
(‫)ب‬
Multiplicative Congruential Method
X i +1 = aX i , mod m, i = 0,1, 2,...
Xi
, i = 1, 2,...
m
X 0 = 117, a = 43, m = 1000
Ri =
X 1 = 43 × 117 = 5031 = 031 mod1000
031
= 0.031
1000
X 2 = 43 × 031 = 1333 = 333 mod1000
R1 =
333
= 0.333
1000
X 3 = 43 × 333 = 14319 = 319 mod1000
R2 =
319
= 0.319
1000
X 4 = 43 × 319 = 13717 = 717 mod1000
R3 =
R4 =
717
= 0.717
1000
605
0.031,0.333, 0.319, 0.717 :3‫ ه‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫إذا ا‬
:3 [‫ال ا‬A , -‫إ‬
‫ف‬2 -‫روف‬2-2 2‫ارزم إ ر آ‬2
,V`‫@ ر ا‬
H 0 : {R1 , R2 ,..., RN } ~ U [0,1]
H1 : {R1 , R2 ,..., RN } L U [0,1]
P
:, ‫ات ا‬27‫ ا‬R
i ,I‫ هة ذات ا‬O ‫ ا‬3‫ إ‬G I R(i ) ‫ دع‬.‫آ‬q Y'0‫ ا ت ! ا‬SI‫ ر‬: 1 ‫ة‬27‫ا‬
R(1) ≤ R( 2 ) ≤ ... ≤ R( N ) ‫ن‬2/9
‫ ت‬/‫ ا‬S6‫ أ‬: 2 ‫ة‬27‫ا‬
i

D + = max  − R(i ) 
1≤i ≤ N  N

i −1

D − = max  R(i ) −

1≤i ≤ N 
N 
D = max ( D + , D − ) S6‫ أ‬: 3 ‫ة‬27‫ا‬
‫ف‬2 -‫روف‬2-2 2/ ,- ‫ ا‬%:‫ول ا‬- ! Dα ,- ‫ ا‬, :‫ ! ا‬: 4 ‫ة‬27‫ا‬
7" ‫ ا‬N ,"‫ ا‬%H ‫ ا د و‬α ,92" ‫ى ا‬2 ,V`‫ ; ; ا‬Dα ,- ‫ ا‬, :‫ أآ ! ا‬D ,"‫ ا‬,? 6‫ إ‬W ‫ إذا آ‬: 5 ‫ة‬27‫ا‬
‫ي‬2" ‫ ;ق‬-29T &‫ر ا‬: ; D ≤ Dα W ‫ إذا آ‬.%N R9‫ز‬2I ! 3IeI ,"‫ أن ا‬,9` ‫ا‬
.%N ‫ ا‬R9‫ز‬2‫{ وا‬R1 , R2 ,..., RN } ‫ م‬J‫ر‬q 3:: ‫ ا‬R9‫ز‬2‫! ا‬
:3 ‫ول آ‬- 3; , [email protected]‫ ا‬SI
R(I)
0.09
0.136
0.154
0.239
0.245
0.276
0.394
0.513
0.531
0.631
0.681
0.715
0.844
0.88
0.888
I
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
I/N
(I-1)/N R(I)-(I/N) ((I-1)/N)-R(I) |R(I)-(I/N)| |((I-1)/N)-R(I)| max|(R(I)-(I/N)| max|((I-1)/N)-R(I)| D
0.0667
0 0.02333
-0.09 0.023333
0.09
0.124
0.09 0.124
0.1333 0.0667 0.00267 -0.0693333 0.002667 0.069333333
0.2 0.1333
-0.046 -0.0206667
0.046 0.020666667
0.2667
0.2 -0.0277
-0.039 0.027667
0.039
0.3333 0.2667 -0.0883 0.02166667 0.088333 0.021666667
0.4 0.3333
-0.124 0.05733333
0.124 0.057333333
0.4667
0.4 -0.0727
0.006 0.072667
0.006
0.5333 0.4667 -0.0203 -0.0463333 0.020333 0.046333333
0.6 0.5333
-0.069 0.00233333
0.069 0.002333333
0.6667
0.6 -0.0357
-0.031 0.035667
0.031
0.7333 0.6667 -0.0523 -0.0143333 0.052333 0.014333333
0.8 0.7333
-0.085 0.01833333
0.085 0.018333333
0.8667
0.8 -0.0227
-0.044 0.022667
0.044
0.9333 0.8667 -0.0533 -0.0133333 0.053333 0.013333333
1 0.9333
-0.112 0.04533333
0.112 0.045333333
D = 0.124 0‫د ا‬2 "‫ و ! ا‬D − = 0.09 ‫ و‬D + = 0.124 H 0‫ ا‬MJ !9‫د‬2 "‫! ا‬
H N = 15 7‫ وا‬D0.05 ‫د‬2 "‫ ا‬W I‫ف و‬2 -‫روف‬2-2 2/ ,- ‫ ا‬%:‫ول ا‬- !
D0.05,15 = 0.338 3‫ ه‬,- ‫ ا‬, :‫ان ا‬
606
‫ هات‬O ‫ أن ا‬,9` ‫ ا‬,V`‫ ; ا‬T ; D = 0.124 < D0.05,15 = 0.338 ‫ أن‬:‫ار‬:‫ا‬
.%N R9‫ز‬2I ! 3IeI
:P [‫ال ا‬A , -‫إ‬
( ‫)أ‬
For 2 < X ≤ 3
2
1
X

R =  − 1 , 0 < R ≤
4
2

∴X = 2
(
)
R + 1 , when 0 < R ≤ 0.25
For 3 < X ≤ 6
2
1
X 1
R = 1− 3−  , < R ≤ 1
3
2 4
∴ X = 6 − 2 3R , when 0.25 < R ≤ 1
:3 ‫ آ‬3?‫ا‬2O"‫ ا‬Y , J 15 ! , 2 Microsoft Excel ‫ف م‬2
Random Numbers ‫ و ! 'وق ا@ رات ر‬Data Analysis ‫ ر‬Tools ! -1
Number of Random Numbers ‫ و‬Number of Variables (=1) ‫ † ا ت‬%X Generation
and ‫ و‬Between (=0) .e Parameters , 3;‫ و‬Uniform ‫ ر‬Distributions ! ‫=( و‬15)
Output ‫ ر‬Output options 3;‫ و‬31 !/‫ و‬3‫ أو‬%J‫ ر ر‬Random Seed 3;‫=( و‬1)
. OK %X A1:A15 UI.; 3; S/‫ و‬Range
S/ ‫ة ا@د ل‬.; 3; %X B1 ,‫ د ا‬-2
=IF(0<=A1<=0.25,B1=2+SQRT(A1)+1,6-2*SQRT(3*A1))
B15 6‫ و‬B2 9‫ ا‬3; U: ‫ و‬U %X ‫ ة اى‬B1 ,‫ د ا‬-3
];
:3 ‫ا‬
0.004242073
0.404065065
0.548448134
0.839350566
0.028290658
0.074861904
0.199804682
0.215948973
0.939634388
0.117862484
0.03869747
0.8992584
0.979247414
0.6621601
0.621539964
5.774378915
3.798005271
3.434580423
2.826325979
5.417344099
5.052190502
4.451563311
4.390221234
2.642082095
4.810735604
5.318553274
2.715018904
2.572031365
3.181148957
3.268978292
3.976877 ,"‫ ا‬w2 ‫ ان‬H Excel ‫)ب( ام‬
E(X ) =
a + b + c 2 + 3 + 6 11
=
= = 3.66667
3
3
3
607
2‫ ه‬3[[ ‫ ا‬R9‫ز‬2 ‫ي‬N‫ ا‬w2 ‫ا‬
‫‪ %‬ا ا‪ ! 6‬ا‪%6‬‬
‫ء و ‪2‬ث ا" ت‬
‫‪ %J‬ا@‪6‬‬
‫آ‪ ,‬ا"‪2‬م‬
‫‪ ," -‬ا ‪2" g‬د‬
‫ا@ ر ا‪ M ` 3? U‬ا[ ‪ 1422/1421 3‬هـ‬
‫ دة ‪C ) P 241‬ق ا آ ة ‪( 1‬‬
‫ا>‪2' 3 #‬ت‬
‫أ‪ R - S-‬ا‪ ,b0‬ا ‪:,‬‬
‫ا‪A‬ال ا‪0‬ول‪:‬‬
‫‪2I‬ز‪ R9‬ز ! ! ا‪2'2‬ل ‪ ,:J !? G‬إ دآ ن أ‪ 6‬ا ‪H 37"9 !J‬ول‪:‬‬
‫‪Probability‬‬
‫‪Time Between Arrivals‬‬
‫)‪(Minutes‬‬
‫‪0.23‬‬
‫‪1‬‬
‫‪0.37‬‬
‫‪2‬‬
‫‪0.28‬‬
‫‪3‬‬
‫‪0.12‬‬
‫‪4‬‬
‫)أ( و أز ‪ ! ,‬و'‪2‬ل "د ‪ 50‬ز ‪. 2‬‬
‫)ب( آ‪2‬ن رج ‪/I‬اري ‪q‬ز ‪ ,‬ا ‪2‬ة ;‪ 3‬ا`‪:‬ة ا ‪.,:‬‬
‫)ج( أ ‪2-‬دة ا‪q ;2‬ز ‪ ,‬ا ‪2‬ة ) ا ‪ O‬هة ‪ R ( O‬ا‪0‬ز ‪ ,‬ا "‪ 3; 5 7‬ا‪H‬ول‬
‫‪2‬‬
‫)ا ‪= 7.81 ) . α = 0.05 . .( E ,"J2‬‬
‫‪( χ 3,0.05‬‬
‫ا‪A‬ال ا[ ‪:3‬‬
‫‪q‬ر‪ J‬م ا ‪) :,‬إ‪J‬أ ! ا ر ! ‪7‬ا ‪(7‬‬
‫‪0.25 0.01 0.93 0.70 0.66 0.74 0.79 0.47 0.68 0.18 0.88 0.07 0.99 0.51 0.04 0.01‬‬
‫‪0.43 0.60 0.59 0.55 0.64 0.10 0.61 0.22 0.85 0.42 0.01 0.98 0.05 0.20 0.11 0.23‬‬
‫‪0.68 0.41 0.96 0.48 0.11 0.59 0.11 0.10‬‬
‫)أ( أم إ ر ا‪H‬ي ‪2; Runs Test‬ق و‪ W I‬ا ‪ @ w2‬ر ; إذا آ ‪ W‬ه‪ 5.‬ا‪0‬ر‪ J‬م‬
‫‪2O‬ا?‪. .,‬‬
‫‪b − ( 2n1n2 N ) − 1 2‬‬
‫) ‪2n1n2 1 2 2n1n2 ( 2n1n2 − N‬‬
‫= ‪+ ,σb‬‬
‫= ‪, Z0‬‬
‫‪12‬‬
‫‪2‬‬
‫‪N‬‬
‫‪2‬‬
‫)‪N ( N − 1‬‬
‫‪ 2n1n2 ( 2n1n2 − N ) ‬‬
‫‪‬‬
‫‪‬‬
‫‪N 2 ( N − 1) ‬‬
‫‪‬‬
‫‪α = 0.05, z0.025 = 1.96‬‬
‫= ‪µb‬‬
‫‪608‬‬
,‫ دا‬RI ,?‫ا‬2O ‫ات‬Y 8 ‫ ـ‬%J ‫ و‬,: ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ول ! ا‬0‫ ا‬7‫)ب( ام ا‬
:, ‫ ا‬R9‫ز‬2‫ا‬
0,
 2
x ,
2
F (x) = 
2
1 − ( 2 − x ) ,

2

1,

x≤0
0 < x ≤1
1< x ≤ 2
x>2
:P [‫ال ا‬A‫ا‬
‫ات‬Y 8 ‫ ـ‬%J ‫ و‬Acceptance-Rejection Technique ;‫ل وا‬2:‫ ا‬,:9C ‫ام‬
‫ إم‬. ( e −0.2 = 0.8187 ) λ = 0.2 w2 Poisson Variates ‫ن‬2‫ا‬2 R9‫ز‬2I RI ,?‫ا‬2O
:3‫ارزم ه‬2‫ات ا‬27 .7 ‫ا‬7 3 [‫ال ا‬A‫ ! ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ا‬
. P = 1 ‫ و‬n = 0 RV :1 ‫ة‬27‫ا‬
. P × Rn +1 ‫ ـ‬P ‫ و ل‬Rn+1 3?‫ا‬2O %J‫ و ر‬:2 ‫ة‬27‫ا‬
‫ و‬6‫ا‬2 n ‫ وزد‬, ‫ ا‬n ;‫ أر‬T‫ وإ‬N = n MJ‫ إ‬.? P < e − λ W ‫ إذا آ‬:3 ‫ة‬27‫ا‬
. 2 ‫ة‬27
609
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ا@ ر ا‬
( 1 ‫ق ا آ ة‬C ) P 241 ‫ دة‬
‫ت‬2' 3 #>‫ا‬
:, ‫ ا‬,b0‫ ا‬R - S-‫أ‬
:‫ول‬0‫ال ا‬A‫ا‬
:‫ول‬H 37"9 !J ‫ ا‬6‫ إ دآ ن أ‬,:J !? G ‫ل‬2'2‫ ز ! ! ا‬R9‫ز‬2I
Time Between Arrivals (Minutes)
1
2
3
4
Probability
0.23
0.37
0.28
0.12
. 2 ‫ ز‬50 ‫ل "د‬2'‫ ! و‬, ‫)أ( و أز‬
.,: ‫ة ا‬:`‫ ا‬3; ‫ة‬2 ‫ ا‬, ‫ز‬q ‫اري‬/I ‫ن رج‬2‫)ب( آ‬
‫ول‬H‫ ا‬3; 5 7" ‫ ا‬, ‫ز‬0‫ ا‬R ( O ‫ هة‬O ‫ة ) ا‬2 ‫ ا‬, ‫ز‬q ;2‫دة ا‬2- ‫)ج( أ‬
2
( χ 3,0.05
= 7.81 ) . α = 0.05 . .( E ,"J2 ‫)ا‬
:3 [‫ال ا‬A‫ا‬
(7 ‫ا‬7 ! ‫أ ! ا ر‬J‫ )إ‬:, ‫ م ا‬J‫ر‬q
0.25 0.01 0.93 0.70 0.66 0.74 0.79 0.47 0.68 0.18 0.88 0.07 0.99 0.51 0.04 0.01
0.43 0.60 0.59 0.55 0.64 0.10 0.61 0.22 0.85 0.42 0.01 0.98 0.05 0.20 0.11 0.23
0.68 0.41 0.96 0.48 0.11 0.59 0.11 0.10
‫ م‬J‫ر‬0‫ ا‬5.‫ ه‬W ‫ @ ر ; إذا آ‬w2 ‫ ا‬W I‫ق و‬2; Runs Test ‫ي‬H‫)أ( أم إ ر ا‬
. .,?‫ا‬2O
µb =
b − ( 2n1n2 N ) − 1 2
2n1n2 1 2 2n1n2 ( 2n1n2 − N )
+ ,σb =
, Z0 =
12
2
N
2
N ( N − 1)
 2n1n2 ( 2n1n2 − N ) 


N 2 ( N − 1) 

α = 0.05, z0.025 = 1.96
R7: 3?‫ا‬2OY ! %J 6 ‫ و‬,: ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ول ! ا‬0‫ ا‬7‫)ب( ام ا‬
:, ‫ ا‬R9‫ز‬2‫ ا‬,‫ دا‬R9 (M ` )
x
, x = 1, 2,⋯ , 6
6
Y'‫ أي أ‬ x  = smallest integer ≥ x ,J"‫م ا‬I , ' ‫ م‬J‫ أر‬3 ‫ل‬2
F (x) =
:,N6 )
. x ‫ وي‬9 ‫ أآ ! أو‬a ' ‫د‬
610
! %J 4 ‫ و‬Acceptance-Rejection Technique ;‫ل وا‬2:‫ ا‬,:9C ‫)ج( ام‬
. ( e −0.2 = 0.8187 ) λ = 0.2 w2 Poisson Variates ‫ن‬2‫ا‬2 R9‫ز‬2I R9 3?‫ا‬2OY
:3‫ارزم ه‬2‫ات ا‬27 .7 ‫ا‬7 3 [‫ال ا‬A‫ ! ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫إم ا‬
. P = 1 ‫ و‬n = 0 RV :1 ‫ة‬27‫ا‬
. P × Rn +1 ‫ ـ‬P ‫ و ل‬Rn+1 3?‫ا‬2O %J‫ و ر‬:2 ‫ة‬27‫ا‬
‫ و‬6‫ا‬2 n ‫ وزد‬, ‫ ا‬n ;‫ أر‬T‫ وإ‬N = n MJ‫ إ‬.? P < e − λ W ‫ إذا آ‬:3 ‫ة‬27‫ا‬
. 2 ‫ة‬27
:P [‫ال ا‬A‫ا‬
‫ "د‬3 [email protected]‫ أ‬R9‫ز‬2‫ ا‬. 29 ‫"ه‬9 3‫ ا‬G‫ أ‬,`^‫ د أر‬w2 9 I !9‫ ا ز‬6‫ أ‬99
:‫ول‬H 7"9 29 !? G‫ا‬
Number of Customers/Day
Probability
8
0.35
10
0.30
12
0.25
14
0.10
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬S6 ,`^‫ر‬0‫ي د ! ا‬O9 ‫ن‬2 ‫ ز‬M‫آ‬
Number of Loafs/Customer
Probability
4
0.4
8
0.3
12
0.2
16
0.1
. 29 ‫"ه ا ز‬9 3‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫د‬6‫ و‬M ‫ م‬9‫ أ‬, 9‫و‬9 3‫ آ‬6
‫" د‬I‫ ة و‬M‫ آ‬3; ‫ا‬9- J‫ ام ر‬.3 [‫ال ا‬A‫ ! ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ام ا‬:,N6
.(3U9 M‫ول آ‬H‫ م ! أول ا‬J‫ر‬0‫ ا‬,?‫ا‬J
611
%6‫ ! ا‬6‫ ا ا‬%
‫هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ ر ا‬z , ‫ ت‬-‫إ‬
P 241 ‫ا دة‬
:‫ول‬0‫ال ا‬A , -‫إ‬
( ‫)أ‬
1
2
3
1
2
2
1
2
1
4
1
2
4
3
1
4
3
2
2
3
2
3
3
1
3
2
2
3
2
1
2
2
2
1
2
2
1
4
1
1
2
2
1
3
2
3
2
3
2
3
(‫)ب‬
Count ( Oi )
13
21
12
4
x
1
2
3
4
p (x)
0.26
0.42
0.24
0.80
Frequency
20
10
0
1
2
3
4
C8
Ei ,"J2 ‫ ا‬%:‫ ا‬S (‫)ج‬
E1 = 50 × 0.23 = 11.5
E2 = 50 × 0.37 = 18.5
E3 = 50 × 0.28 = 14
E4 = 50 × 0.12 = 6
‫ آ ي‬R , J S ‫و‬
k
(Oi − Ei )
i =1
Ei
χ =∑
2
0
2
(13 − 11.5)
=
11.5
2
( 21 − 18.5)
+
18.5
2
(12 − 14 )
+
2
14
= 0.195652 + 0.337838 + 0.285714 + 0.666666 = 1.4859
2
∵ χ 02 = 1.4859 < 7.81 = χ 3,0.05
612
( 4 − 6)
+
6
2
.‫ول‬H 7" ‫ ا‬R9‫ز‬2‫ ا‬RI ‫ة‬2 ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ن ا‬e ,? :‫ ا‬,V`‫; ا‬T
w2 ‫ ا‬:3 [‫ال ا‬A , -‫إ‬
µ = 0.4485
w2 ‫ ا‬W I‫ق و‬2; ‫ي‬H‫ ا‬-2
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
b = 21 , n1 = 21 , n2 = 19 , N = 40
2 × 21 × 19 1
µb =
+ = 20.45
40
2
2 × 21 × 19 × ( 2 × 21 × 19 − 40 ) 604884
=
= 9.693654
σ b2 =
2
62400
( 40 ) ( 40 − 1)
21 − 20.45
0.55
Z0 =
=
= 0.17665
9.693654 3.11346
∵ Z 0 = 0.17665 < 1.96 = z0.025
+
-
-
+
+
+
-
-
.,?‫ا‬2O ‫ م‬J‫ر‬0‫ ا‬5.‫ أن ه‬,? :‫ ا‬,V`‫; ا‬T ;
(‫)ب‬
F (x) =
x
= R, x = 1, 2,...,6; R ∼ U ( 0,1)
6
X
=R
6
X = 6 R, R ∼ U ( 0,1)
∴
.e 6 ‫ و‬1 ! X 3?‫ا‬2O"‫ ا‬Y , ' ‫ م‬J‫ أر‬M
X =  6 R  , R ∼ U ( 0,1)
3/‫و‬
:3‫ ه‬, 27 ‫ ا‬%:‫ا‬
X 1 =  6 × 0.25 = 1.5 = 2,
X 4 =  6 × 0.70 =  4.2  = 5,
X 2 = 6 × 0.01 = 0.06 = 1, X 3 = 6 × 0.93 = 5.58 = 6
X 5 = 6 × 0.66 = 3.96 = 4, X 6 = 6 × 0.74  =  4.44  = 5
2,1,6,5,4,5 ‫أي‬
(‫)ج‬
step 1: set n = 0, P = 1
step 2 : R1 = 0.25, P → P × R1 , P = 1 × 0.25 = 0.25
step 3 : Sice P = 0.25 < e − λ = 0.8187, accept N = 0.
step 1: set n = 0, P = 1
step 2 : R1 = 0.01, P → P × R1 , P = 1 × 0.01 = 0.01
step 3 : Sice P = 0.01 < e − λ = 0.8187, accept N = 0.
step 1: set n = 0, P = 1
step 2 : R1 = 0.93, P → P × R1 , P = 1 × 0.93 = 0.93
step 3 : Sice P = 0.93 ≥ e − λ = 0.8187, reject n = 0, and return to step 2 with n = 1.
step 2 : R2 = 0.70, P → P × R2 , P = 0.93 × 0.70 = 0.65
step 3 : Sice P = 0.65 < e − λ = 0.8187, accept N = 1.
613
step 1: set n = 0, P = 1
step 2 : R1 = 0.66, P → P × R1 , P = 1 × 0.66 = 0.66
step 3 : Sice P = 0.66 < e − λ = 0.8187, accept N = 0.
0,0,1,0 :3‫ب ه‬27 ‫ ا‬3?‫ا‬2O"‫ ا‬Y ‫ ! ا‬%J 4 ‫إذا‬
:P [‫ال ا‬A , -‫إ‬
‫م‬29 M/ !? G‫( "د ا‬1) ‫ول‬- "
Number of Customers
8
10
12
14
CDF
0.35
0.65
0.90
1
Random Number
0.01 - 0.35
0.36 - 0.65
0.66 – 0.90
0.91 - 1
‫ن‬2 ‫ ز‬M/ ,`^‫ر‬0‫( "د ا‬2) ‫ول‬- "
Number of Loafs
4
8
12
16
CDF
0.40
0.70
0.90
1
Random Number
0.01 - 0.40
0.41 - 0.70
0.71 – 0.90
0.91 - 1
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.25 :‫ول‬0‫م ا‬2‫ا‬
Customer Number
1
2
3
4
5
6
7
8
R
0.01
0.93
0.70
0.66
0.74
0.79
0.47
0.68
Number of Loafs
04
16
08
08
12
12
08
08
Total = 76
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.18 :3 [‫م ا‬2‫ا‬
Customer Number
1
2
3
4
5
6
7
8
R
0.88
0.07
0.99
0.51
0.04
0.01
0.43
0.60
Number of Loafs
12
04
16
08
04
04
08
08
Total = 64
10 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.59 :P [‫م ا‬2‫ا‬
614
Customer Number
1
2
3
4
5
6
7
8
9
10
R
0.55
0.64
0.10
0.61
0.22
0.85
0.42
0.01
0.98
0.05
Number of Loafs
08
08
04
08
04
12
08
04
16
04 Total = 76
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.20 :R ‫م اا‬2‫ا‬
Customer Number
1
2
3
4
5
6
7
8
R
0.11
0.23
0.68
0.41
0.96
0.48
0.11
0.59
Number of Loafs
04
04
08
08
16
08
04
08
Total = 60
8 !? G‫ د ا‬H (1) ‫ول‬- ! ‫ و‬R = 0.11 :ˆ ‫م ا‬2‫ا‬
Customer Number
1
2
3
4
5
6
7
8
R
0.10
0.25
0.01
0.93
0.70
0.66
0.74
0.79
Number of Loafs
04
04
04
16
08
08
12
12
Total = 64
w2 ‫ إذا‬. `^‫ ر‬76,64,76,60,64 :3‫ م ه‬9‫ أ‬, 3; , ‫ ا‬,`^‫ر‬0‫ا ;ن د أ‬./‫وه‬
. `^‫ ر‬68 2‫ ه‬,`^‫ر‬0‫د ا‬
615
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ا@ ر ا‬
( 1 ‫ق ا آ ة‬C ) P 241 ‫ دة‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
2 ‫ ز‬50 ‫ م "د‬N ‫ا‬2C 6‫ أ‬3; , ‫ ! ا‬G , ‫ ا ت ا‬WH
5
7
5
8
5
7
8
6
8
6
7
8
7
8
6
9
8
6
8
8
8
9
9
7
6
9
6
9
6
7
7
8
5
9
6
7
9
5
9
5
6
6
8
5
6
9
7
9
7
5
.‫ هات‬O ‫ ا‬5.U S 3 6‫ إ‬R9‫ز‬2I C
(‫أ‬
.‫ م‬N‫ا ا‬.U , ! ‫ ز‬20 ‫و‬
(‫ب‬
:‫ا ‚ال ا‬
:, ‫ ا‬R9‫ز‬2‫ ا‬,‫ دا‬R9 (M ` ) R7: 3?‫ا‬2OY ! , J 20 ‫و‬
x
, x = 1, 2,⋯ ,6
6
Y'‫ أي أ‬ x  = smallest integer ≥ x ,J"‫م ا‬I , ' ‫ م‬J‫ أر‬3 ‫ل‬2
F (x) =
:,N6 )
. x ‫ وي‬9 ‫ أآ ! أو‬a ' ‫د‬
: ‫ا ‚ال ا‬
‫ "د‬3 [email protected]‫ أ‬R9‫ز‬2‫ ا‬. 29 ‫"ه‬9 3‫ ا‬G‫ أ‬,`^‫ د أر‬w2 9 I !9‫ ا ز‬6‫ أ‬99
:‫ول‬H 7"9 29 !? G‫ا‬
Number of Customers/Day
Probability
8
0.35
10
0.30
12
0.25
14
0.10
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬S6 ,`^‫ر‬0‫ي د ! ا‬O9 ‫ن‬2 ‫ ز‬M‫آ‬
Number of Loafs/Customer
Probability
4
0.4
8
0.3
12
0.2
16
0.1
. 29 ‫"ه ا ز‬9 3‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫د‬6‫ و‬M ‫ م‬9‫ أ‬10 9‫و‬9 3‫ آ‬6
616
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ا@ ر ا‬
( 1 ‫ق ا آ ة‬C ) P 241 ‫ دة‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
2 ‫ ز‬50 ‫ م "د‬N ‫ا‬2C 6‫ أ‬3; , ‫ ! ا‬G , ‫ ا ت ا‬WH
5
6
5
7
8
7
6
5
8
7
5
7
6
7
9
9
7
5
9
6
9
6
5
8
7
5
9
8
7
6
8
8
9
8
8
7
9
6
9
9
6
9
6
8
5
8
7
8
6
6
.‫ هات‬O ‫ ا‬5.U S 3 6‫ إ‬R9‫ز‬2I C (‫ت‬
.‫ م‬N‫ا ا‬.U , ! ‫ ز‬20 ‫ث( و‬
:‫ا ‚ال ا‬
:, ‫ ا‬R9‫ز‬2‫ ا‬,‫ دا‬R9 (M ` ) R7: 3?‫ا‬2OY ! , J 20 ‫و‬
x
, x = 1, 2,⋯ ,6
6
‫ د‬Y'‫ أي أ‬ x  = smallest integer ≥ x ,J"‫م ا‬I , ' ‫ م‬J‫ أر‬3 ‫ل‬2
F (x) =
:,N6 )
. x ‫ وي‬9 ‫ أآ ! أو‬a '
: ‫ا ‚ال ا‬
! %J 5 ‫ و‬Acceptance-Rejection Technique ;‫ل وا‬2:‫ ا‬,:9C ‫ام‬
. λ = 0.5 w2 Poisson Variates ‫ن‬2‫ا‬2 R9‫ز‬2I R9 3?‫ا‬2OY
:3‫ارزم ه‬2‫ات ا‬27
. P = 1 ‫ و‬n = 0 RV :1 ‫ة‬27‫ا‬
. P × Rn +1 ‫ ـ‬P ‫ و ل‬Rn+1 3?‫ا‬2O %J‫ و ر‬:2 ‫ة‬27‫ا‬
‫ و‬6‫ا‬2 n ‫ وزد‬, ‫ ا‬n ;‫ أر‬T‫ وإ‬N = n MJ‫ إ‬.? P < e − λ W ‫ إذا آ‬:3 ‫ة‬27‫ا‬
. 2 ‫ة‬27
:! ‫ا ‚ال اا‬
!? G‫ "د ا‬3 [email protected]‫ أ‬R9‫ز‬2‫ ا‬. 29 ‫"ه‬9 3‫ ا‬G‫ أ‬,`^‫ د أر‬w2 9 I !9‫ ا ز‬6‫ أ‬99
:‫ول‬H 7"9 29
Number of Customers/Day
Probability
8
0.35
10
0.30
12
0.25
14
0.10
:3 ‫ ا‬3 [email protected]‫ ا‬R9‫ز‬2‫ ا‬S6 ,`^‫ر‬0‫ي د ! ا‬O9 ‫ن‬2 ‫ ز‬M‫آ‬
Number of Loafs/Customer
Probability
4
0.4
8
0.3
12
0.2
16
0.1
. 29 ‫"ه ا ز‬9 3‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫د‬6‫ و‬M ‫ م‬9‫ أ‬, 9‫و‬9 3‫ آ‬6
617
%6‫ ! ا‬6‫ ا ا‬%
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ ا@ ر ا‬,b0 ,-‫ذ‬2 ‫ ت‬-‫إ‬
( 1 ‫ ة‬/ ‫ق ا‬C ) P 241 ‫ دة‬
:‫ ‚ال اول‬/ =‫إ‬
H Minitab ‫)أ( ام‬
MTB > Tally C1;
SUBC>
Counts;
SUBC>
CumCounts;
SUBC>
Percents;
SUBC>
CumPercents.
Summary Statistics for Discrete Variables
SerTime Count CumCnt Percent CumPct
5
8
8
16.00 16.00
6
11
19
22.00 38.00
7
10
29
20.00 58.00
8
11
40
22.00 80.00
9
10
50
20.00 100.00
N=
50
Input ‫ ا ت‬M ‫ آ ي أو م‬R ‫م إ ر‬
‫ إ‬S 3 6‫ إ‬R9‫ز‬2I 7
Analyzer
Distribution Summary
Distribution: Discrete
Expression: Disc(5, 9)
Square Error: 0.002400
Chi Square Test
Number of intervals = 5
Degrees of freedom = 4
Test Statistic
= 0.6
Corresponding p-value
> 0.75
Data Summary
Number of Data Points
= 50
Min Data Value
=5
Max Data Value
=9
Sample Mean
= 7.08
Sample Std Dev
= 1.38
Histogram Summary
Histogram Range
= 4.5 to 9.5
618
Number of Intervals = 5
‫ ا ت‬79 9 ‫ و‬5 ! Discrete R7: ‫ ا‬R9‫ز‬2‫ أن ا‬H
:3IT ‫ آ‬Minitab 3; ‫ل‬6 ,9 " ‫ م أ ا‬, ! ‫ ز‬20 2 (‫)ب‬
MTB > Sample 20 C1 c4;
SUBC>
Replace.
MTB > print c4
Data Display
C4
6
9
8
5
8
8
8
6
6
6
8
8
8
9
5
7
6
8
6
5
:‫ ‚ال ا‬/ =‫إ‬
R9‫ز‬2‫ ا‬,‫ دا‬R9 3?‫ا‬2O Y %J 2
F (x ) =
x
, x = 1,2,..., 6
6
:3 ‫ ا‬M "
x
R = F (x ) = , x = 1,2,..., 6
6
∴ x = 6R, R ∈ (0,1)
,J"‫ م ا‬, ' ‫ م‬J‫ل ار‬2
‫ و‬, ' ^ %J 7"9 ‫ا‬.‫وه‬
x  = smallest integer ≥ x
H Minitab ‫ام‬
MTB >
SUBC>
MTB >
MTB >
MTB >
MTB >
Random 20 c1;
Uniform 0.0 1.0.
let c2=6*c1
let c3=c2+0.5
round c3 c4
print c4
Data Display
C4
5
5
3
2
6
6
1
6
5
4
6
3
4
4
5
4
1
5
1
5
MTB >
: ‫ ‚ال ا‬/ =‫إ‬
e
−0.5
= 0.606531
619
1)n = 0, P = 1
2)R1 = 0.771828 ⇒ P → PR1 = 0.771828
3)0.771828<0.606531 ⇒ NO → reject n = 0 ⇒ n = 1
2)R2 = 0.428251 ⇒ P → PR2 = 0.3305361
3)0.3305361 < 0.606531 ⇒ YES → N = 1
1)n = 0, P = 1
2)R1 = 0.995495 ⇒ P → PR1 = 0.995495
3)0.995495<0.606531 ⇒ NO → reject n = 0 ⇒ n = 1
2)R2 = 0.067969 ⇒ P → PR2 = 0.067663
3)0.067663 < 0.606531 ⇒ YES → N = 1
1)n = 0, P = 1
2)R1 = 0.815945 ⇒ P → PR1 = 0.815945
3)0.815945<0.606531 ⇒ NO → reject n = 0 ⇒ n = 1
2)R2 = 0.833423 ⇒ P → PR2 = 0.680027
3)0.680027 < 0.606531 ⇒ NO → reject n = 1 ⇒ n = 2
2)R3 = 0.344675 ⇒ P → PR3 = 0.234388
3)0.234388 < 0.606531 ⇒ YES → N = 2
1)n = 0, P = 1
2)R1 = 0.565971 ⇒ P → PR1 = 0.565971
3)0.565971<0.606531 ⇒ NO → reject n = 0 ⇒ n = 1
2)R2 = 0.560698 ⇒ P → PR2 = 0.317339
3)0.317339 < 0.606531 ⇒ YES → N = 1
1)n = 0, P = 1
2)R1 = 0.718902 ⇒ P → PR1 = 0.718902
3)0.718902<0.606531 ⇒ NO → reject n = 0 ⇒ n = 1
2)R2 = 0.631130 ⇒ PR2 = 0.453721
3)0.453721<0.606531 ⇒ YES → N = 1
1,1,2,1,1 :3‫ ه‬%:‫ا‬
:! ‫ ‚ال اا‬/ =‫إ‬
:3 ‫ آ‬,9 " ‫اول‬- ‫ن‬2/ ,9‫اء ا آ ة او‬[email protected]
‫م‬29 M/ !? G‫ د ا‬,9 " ‫ول‬Number of Customers/Day
8
10
Probability
0.35
0.30
620
Cumulative Probability
0.35
0.65
12
14
0.25
0.10
0.90
1.00
‫ن‬2 ‫ ز‬M/ ,`^‫ر‬0‫ د ا‬,9 " ‫ول‬Number of Loafs/Customer
4
8
12
16
Probability
0.4
0.3
0.2
0.1
‫ إذا د‬0.35 ‫ و‬0 ! %J‫ا ا‬.‫أن ه‬
Number of Customer
1
2
3
4
5
6
7
8
Total
:‫ول‬0‫م ا‬2‫ا‬
‫ و‬0.125002 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
8 = ‫ول‬0‫م ا‬2 !? G‫ا‬
8 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Random Number
0.747727
0.165930
0.807279
0.691822
0.332073
0.865662
0.954414
0.605033
‫ إذا‬0.65‫ و‬0.35 ! %J‫ا ا‬.‫أن ه‬
Cumulative Probability
0.4
0.7
0.9
1.0
Number of Loafs
12
04
12
08
04
12
16
08
76
`^‫ ر‬76 = ‫ول‬0‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:3 [‫م ا‬2‫ا‬
‫ و‬0.436581 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
10 = 3 [‫م ا‬2 !? G‫د ا‬
10 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
1
0.795704
2
3
4
5
6
7
8
9
10
Total
0.191331
0.326339
0.760580
0.232169
0.766908
0.897992
0.498371
0.593898
0.917927
Number of Loafs
12
04
04
12
04
12
12
08
08
16
92
`^‫ ر‬92 = 3 [‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:P [‫م ا‬2‫ا‬
621
‫ إذا‬1.00‫ و‬0.90 ! %J‫ا ا‬.‫أن ه‬
‫ و‬0.975134 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
14 = 3 [‫م ا‬2 !? G‫د ا‬
14 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Number of Customer
Random Number
1
0.500345
2
3
4
5
6
7
8
9
10
11
12
13
14
Total
0.377338
0.497917
0.560237
0.742156
0.066540
0.953874
0.048342
0.133688
0.145730
0.313932
0.656628
0.146369
0.688054
‫ إذا‬0.90 ‫ و‬0.65 ! %J‫ا ا‬.‫أن ه‬
Number of Customer
`^‫ ر‬96 = P [‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:R ‫م اا‬2‫ا‬
‫ و‬0.852771 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
12 = 3 [‫م ا‬2 !? G‫د ا‬
12 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Random Number
1
0.102021
2
3
4
5
6
7
8
9
10
11
12
Total
0.352606
0.739246
0.278503
0.495604
0.471064
0.214966
0.784797
0.922574
0.011573
0.530562
0.811989
‫ إذا‬0.90 ‫ و‬0.65 ! %J‫ا ا‬.‫أن ه‬
Number of Customer
Number of Loafs
08
04
08
08
12
04
16
04
04
04
04
08
04
08
96
Number of Loafs
04
04
12
08
08
08
04
12
16
04
08
12
100
`^‫ ر‬100 = R ‫م اا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
:ˆ ‫م ا‬2‫ا‬
‫ و‬0.676495 3?‫ا‬2O %J‫ ر‬S !? G‫ د ا‬-2
12 = 3 [‫م ا‬2 !? G‫د ا‬
12 ‫ ?! اـ‬G‫ن ! ا‬2 ‫ ز‬M/ ,`^‫ر‬0‫ن د ا‬h‫ د ا‬
Random Number
622
Number of Loafs
1
0.113377
2
3
4
5
6
7
8
9
10
11
12
Total
0.682001
0.860924
0.616596
0.670505
0.996726
0.203282
0.616869
0.337997
0.273178
0.832140
0.575714
04
08
12
08
08
16
04
08
04
04
12
08
96
`^‫ ر‬96 = ˆ ‫م ا‬2 , ‫ ا‬,`^‫ر‬0‫إذا د ا‬
2‫ ه‬29 , ‫ ا‬,`^‫ر‬0‫ د ا‬w2 ‫إذا‬
Average Number of Loafs =
76 + 92 + 96 + 100 + 96
460
=
= 92
5
5
. 29 `^‫ ر‬92 ‫ ز إاد‬Mf;0‫ ! ا‬g.‫و‬
623
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫‪#‬دة ‪C) 241‬ق اآة ‪( 1‬‬
‫ا@ ر ا‪ M ` 3? U‬ا[ ‪ 1423/1422 3‬هـ‬
‫ا‪ 3 ! G‬ت‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫‪ SC‬ا‪O‬اء ا‪ R9 !" ] 3 2‬ا‪2‬ز‪ R9‬ا@‪ 3 6‬ا ‪:3‬‬
‫‪4‬‬
‫‪0.10‬‬
‫‪2‬‬
‫‪0.20‬‬
‫‪3‬‬
‫‪0.12‬‬
‫‪1‬‬
‫‪0.25‬‬
‫‪Daily Demand‬‬
‫‪Probability‬‬
‫‪0‬‬
‫‪0.33‬‬
‫‪ ‹ `9‬ا ‪G‬ون ! ه‪.‬ا ا ] آ‪ ," M‬ا‪ 9‬م ;ذا و‪ -‬ا& ا‪ ! MJ‬او ‪ 9‬وي ‪ 6‬و‪6‬ات ‪SC %9‬‬
‫‪ 10‬و‪6‬ات‪ .‬أي ‪: : I ,C‬را ‪G‬ون ا ‪2-2‬د و‪ C .AIT‬ت ‪) ,f92"I‬أي ‪" : I‬‬
‫و'‪2‬ل ‪G‬ون ‪ .(9-‬ز ! ا‪:‬م ‪) Lead Time‬وه‪ 2‬ا‪ ! G‬ا ‪27:‬ع ! ‪ !6‬و‪ RV‬ا‪S7‬‬
‫‪ 6‬و'‪ R9 (&2‬ا‪2‬ز‪ R9‬ا@‪ 3 6‬ا ‪:3‬‬
‫‪3‬‬
‫‪0.2‬‬
‫‪1‬‬
‫‪0.3‬‬
‫‪2‬‬
‫‪0.5‬‬
‫)‪Lead Time (Days‬‬
‫‪Probability‬‬
‫ا ! اول ا‪20‬ع إذا آ ن ا ‪G‬ون اا?‪ 12 3‬و‪6‬ة و‪ C -2IT‬ت ;‪ R‬ا ‪G‬ون "‬
‫; آ‪9 3‬و‪ 6 9‬أ ‪.U R‬ا ا‪ N‬م ‪6 .‬د ‪ ,‬ا‪ 90‬م ا‪6 3‬ث ;‪ ,C : I 3; ‹: U‬و‪,‬‬
‫ا‪62‬ات ا‪ WC 3‬و‪ : I %‬و ‪ w2‬د ا‪62‬ات ا ‪O , 27‬اء ا‪. 2‬‬
‫ا ‚ال ا‪:‬‬
‫ز ! ا ة ‪2 Lifetime‬ات ‪ 3 ' :‬و‪ 3; RV‬ار ‪26‬ل ا‪0‬رض ‪ R9‬ا‪2‬ز‪ R9‬ا ‪:3‬‬
‫‪0.4e−0.4 x ,‬‬
‫‪x≥0‬‬
‫‪f ( x) = ‬‬
‫‪otherwise‬‬
‫‪ 0,‬‬
‫ام ‪ MINITAB‬أو ‪ EXCEL‬و ‪ 1000‬أز ‪ 6 ,‬ة وأ‪ S-‬ا ‪:3‬‬
‫‪ -1‬ه‪ 2‬إ‪ 6‬ل أن ا‪ :‬ا ‪G9T 3‬ال ‪2 5 " M "9‬ات؟‬
‫‪ -2‬ه‪ 2‬إ‪ 6‬ل أن ا‪ :‬ا ‪ 3 ! M "9 3‬و ‪2 6‬ات " إ‪&JC‬؟‬
‫‪) I gH? :6 -3‬ا@‪ , -‬ه‪ 5.‬ا`‪:‬ة إ ر‪.( 9‬‬
‫ا ‚ال ا ‪:‬‬
‫‪624‬‬
xi 3?‫ا‬2O Y ‫ هات‬O M[ 9 3 ‫اري ا‬/‫ول ا‬H‫ا‬
xi
Observed
Frequency
0
118
1
274
2
298
3
169
4
105
5
25
6
8
7
1
8
2
. α = 0.05 . 2 w2 ‫ن‬2‫ا‬2 R9‫ز‬2I & 3?‫ا‬2O Y xi ‫ ان‬,? :‫ ا‬,V`‫أ ا‬
625
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫إ= ت ‪60ƒ /#‬ر ا‪ / W1‬ا ‪ 1423/1422‬هـ‬
‫‪#‬دة ‪C) 241‬ق اآة ‪( 1‬‬
‫إ= ‪‚ /‬ال اول‪:‬‬
‫ آ ة او‪2/ ,9‬ن ا‪H‬اول ا ‪:,‬‬
‫ول " ‪ ,9‬ا‪ S7‬ا‪:3 2‬‬‫‪Random Number‬‬
‫‪0.00 – 0.33‬‬
‫‪0.34 – 0.58‬‬
‫‪0.59 – 0.78‬‬
‫‪0.79 – 0.90‬‬
‫‪0.91 – 1.00‬‬
‫‪Cumulative Probability‬‬
‫‪0.33‬‬
‫‪0.58‬‬
‫‪0.78‬‬
‫‪0.90‬‬
‫‪1.00‬‬
‫‪Probability‬‬
‫‪0.33‬‬
‫‪0.25‬‬
‫‪0.20‬‬
‫‪0.12‬‬
‫‪0.10‬‬
‫‪Demand‬‬
‫‪0‬‬
‫‪1‬‬
‫‪2‬‬
‫‪3‬‬
‫‪4‬‬
‫‪Cumulative Probability‬‬
‫‪0.3‬‬
‫‪0.8‬‬
‫‪1.0‬‬
‫‪Probability‬‬
‫‪0.3‬‬
‫‪0.5‬‬
‫‪0.2‬‬
‫‪Lead Time‬‬
‫‪1‬‬
‫‪2‬‬
‫‪3‬‬
‫ول " ‪ ,9‬ز ! ا‪:‬م‪:‬‬‫‪Random Number‬‬
‫‪0.00 – 0.30‬‬
‫‪0.31 – 0.80‬‬
‫‪0.81 – 1.00‬‬
‫ا آ ة‪:‬‬
‫ا‪6'f‬ع اول‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 12 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪0.419225 3‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 11 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪0.672281 3‬‬
‫ا‪2‬م ا[ ‪:P‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 9 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪0.556692 3‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪0.179291 3‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪0.066128 3‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪0.136442 3‬‬
‫ا‪2‬م ا ‪:R‬‬
‫! ‪-‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫! ‪-‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫! ‪-‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫! ‪-‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫! ‪-‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫! ‪-‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫‪626‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.219630 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا‪0‬ول ‪ ! :I‬ا ‪G‬ون ‪ 8‬و‪6‬ات‬
‫‪ ,H‬ا` ‹‪.,C RfIT :‬‬
‫ا'‪6‬ع ا‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.345517 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 7 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.520493 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:P‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.616346 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 4 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.639711 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 2 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.330888 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 2 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.949622 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫)‪ ‹: , 6‬و‪(!I6‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.640219 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫)‪ ‹: , 6‬و‪(!I6‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا[ ‪ ! :9 % 3‬ا ‪G‬ون † و‪6‬ث ‪ 4 ‹:‬و‪6‬ات‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.315576 3‬ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫ا'‪6‬ع ا ‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.753165 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫)‪ ‹: , 6‬و‪(!I6‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.132686 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪) :P‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.203047 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫‪627‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.592781 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.641142 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.711578 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 4 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.976901 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا[ ‪ ! :9 % P‬ا ‪G‬ون † و‪ 9 %‬ث ‪.‹:‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.612898 3‬ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫ا'‪6‬ع اا !‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.940874 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫)‪ 4 ‹: , 6‬و‪6‬ات(‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.830444 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 3‬و‪6‬ة‪.‬‬
‫)‪ 3 ‹: , 6‬و‪6‬ات(‬
‫ا‪2‬م ا[ ‪) :P‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.761498 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.823155 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 3‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 5 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.996509 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 1 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.382630 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.018751 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع اا ‪ ! :9 % R‬ا ‪G‬ون † و‪6‬ث ‪ 7 ‹:‬و‪6‬ات‪.‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.015373 3‬ز ! ا‪:‬م ‪29 1‬م‪.‬‬
‫ا'‪6‬ع ا‪:"#$‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫‪628‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 0 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.599484 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫)‪ 2 ‹: , 6‬و‪6‬ات(‬
‫ا‪2‬م ا[ ‪) :3‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 10 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.583797 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:P‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 9 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.835045 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 3‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.362963 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 5 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.699827 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 3 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.089972 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 3 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.155004 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا ˆ ‪ ! :I‬ا ‪G‬ون ‪ 3‬و‪6‬ات و‪6‬ث ‪ 2 ‹:‬و‪6‬ة ;‪ 3‬ا‪ ,9‬ا‪20‬ع‪.‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.424699 3‬ز ! ا‪:‬م ‪29 2‬م‪.‬‬
‫ا'‪6‬ع ا دس‪:‬‬
‫ا‪2‬م ا‪0‬ول‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 3 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م ‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.373323 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪:3‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 2 :‬و‪6‬ة‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.379252 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا[ ‪) :P‬و'‪ W‬ا‪ ,7‬ا‪9H‬ة(‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 11 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.630487 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫ا‪2‬م اا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 9 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.584059 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 1‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا ˆ‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.138283 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 0‬و‪6‬ة‪.‬‬
‫ا‪2‬م ا دس‪:‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 8 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.615948 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 2‬و‪6‬ة‪.‬‬
‫‪629‬‬
‫ا‪2‬م ا ‪:R‬‬
‫ا ‪G‬ون ا ‪2-2‬د‪ 6 :‬و‪6‬ات‪.‬‬
‫ا‪.U S7‬ا ا‪2‬م‪ :‬ا‪ %J‬ا"‪2O‬ا?‪- ! 0.928577 3‬ول ا " ‪ ,9‬ا‪2/9 S7‬ن ‪ 4‬و‪6‬ة‪.‬‬
‫;‪ ,9 U 3‬ا‪20‬ع ا دس ‪ ! :I‬ا ‪G‬ون ‪ 2‬و‪6‬ات و‪ 9 %‬ث ‪.‹:‬‬
‫‪ ,H‬ا` ‹‪ 10 ,C RV :‬و‪6‬ات‪.‬‬
‫‪ 2‬و'‪2‬ل ا‪ :,7‬ا‪ %J‬ا"‪2O‬ا?‪ 0.892844 3‬ز ! ا‪:‬م ‪ 3‬ا‪ 9‬م‪.‬‬
‫)‪ ,9 U‬ا آ ة(‬
‫و‪ Rf‬ا ?] ;‪- 3‬ول آ ‪:3‬‬
‫ا ‪G‬ون‬
‫ا ‪2-2‬د‬
‫ا‪%J‬‬
‫ا"‪2O‬ا?‪3‬‬
‫‪S7‬‬
‫ا‪S7‬‬
‫‪12‬‬
‫‪11‬‬
‫‪9‬‬
‫‪8‬‬
‫‪8‬‬
‫‪8‬‬
‫‪8‬‬
‫‪8‬‬
‫‪0.419225‬‬
‫‪0.672281‬‬
‫‪0.556692‬‬
‫‪0.179291‬‬
‫‪0.066128‬‬
‫‪0.136442‬‬
‫‪0.219630‬‬
‫‪1‬‬
‫‪2‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪4‬‬
‫‪8‬‬
‫‪0.345517‬‬
‫‪0.520493‬‬
‫‪0.616346‬‬
‫‪0.639711‬‬
‫‪0.330888‬‬
‫‪0.949622‬‬
‫‪0.640219‬‬
‫‪1‬‬
‫‪1‬‬
‫‪2‬‬
‫‪2‬‬
‫‪0‬‬
‫‪4‬‬
‫‪2‬‬
‫‪12‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪10‬‬
‫‪0.753165‬‬
‫‪0.132686‬‬
‫‪0.203047‬‬
‫‪2‬‬
‫‪0‬‬
‫‪0‬‬
‫‪10‬‬
‫‪8‬‬
‫‪6‬‬
‫‪4‬‬
‫‪0‬‬
‫‪0.592781‬‬
‫‪0.641142‬‬
‫‪0.711578‬‬
‫‪0.976901‬‬
‫‪2‬‬
‫‪2‬‬
‫‪2‬‬
‫‪4‬‬
‫‪12‬‬
‫‪0‬‬
‫‪0‬‬
‫‪10‬‬
‫‪0.940874‬‬
‫‪0.830444‬‬
‫‪0.761498‬‬
‫‪4‬‬
‫‪3‬‬
‫‪2‬‬
‫‪8‬‬
‫‪5‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0.823155‬‬
‫‪0.996509‬‬
‫‪0.382630‬‬
‫‪0.018751‬‬
‫‪3‬‬
‫‪4‬‬
‫‪1‬‬
‫‪0‬‬
‫‪17‬‬
‫ا‪20‬ع)‪(5‬‬
‫ا‪2‬م ا‪0‬ول‬
‫ا‪2‬م ا[ ‪3‬‬
‫‪0‬‬
‫‪10‬‬
‫‪0.599484‬‬
‫‪0.583797‬‬
‫‪2‬‬
‫‪1‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫‪9‬‬
‫‪0.835045‬‬
‫‪3‬‬
‫ا‪ 90‬م‬
‫ا‪20‬ع )‪(1‬‬
‫ا‪2‬م ا‪0‬ول‬
‫ا‪2‬م ا[ ‪3‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫ا‪2‬م اا ‪R‬‬
‫ا‪2‬م ا ˆ‬
‫ا‪2‬م ا دس‬
‫ا‪2‬م ا ‪R‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫ا‪20‬ع)‪(2‬‬
‫ا‪2‬م ا‪0‬ول‬
‫ا‪2‬م ا[ ‪3‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫ا‪2‬م اا ‪R‬‬
‫ا‪2‬م ا ˆ‬
‫ا‪2‬م ا دس‬
‫ا‪2‬م ا ‪R‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫ا‪20‬ع)‪(3‬‬
‫ا‪2‬م ا‪0‬ول‬
‫ا‪2‬م ا[ ‪3‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫ا‪2‬م اا ‪R‬‬
‫ا‪2‬م ا ˆ‬
‫ا‪2‬م ا دس‬
‫ا‪2‬م ا ‪R‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫ا‪20‬ع)‪(4‬‬
‫ا‪2‬م ا‪0‬ول‬
‫ا‪2‬م ا[ ‪3‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫ا‪2‬م اا ‪R‬‬
‫ا‪2‬م ا ˆ‬
‫ا‪2‬م ا دس‬
‫ا‪2‬م ا ‪R‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪8‬‬
‫‪7‬‬
‫‪6‬‬
‫‪4‬‬
‫‪2‬‬
‫‪2‬‬
‫‪0‬‬
‫‪0‬‬
‫‪! :I‬‬
‫ا ‪G‬ون‬
‫‪,H‬‬
‫ا` ‹‬
‫‪,C RfIT‬‬
‫‪10,C RV‬‬
‫ا‪‹:‬‬
‫ا‪%J‬‬
‫ا"‪2O‬ا?‪3‬‬
‫‪2'2‬ل‬
‫ا‪,7‬‬
‫ز!‬
‫ا‪:‬م‬
‫‪0‬‬
‫‪2‬‬
‫‪2‬‬
‫‪4‬‬
‫‪0.315576‬‬
‫‪2‬‬
‫‪2‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪0‬‬
‫‪10,C RV‬‬
‫‪2‬‬
‫‪0.612898‬‬
‫‪2‬‬
‫‪4‬‬
‫‪3‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪0‬‬
‫‪10,C RV‬‬
‫‪7‬‬
‫‪0.015373‬‬
‫‪1‬‬
‫‪2‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪630‬‬
‫ا‪2‬م اا ‪R‬‬
‫ا‪2‬م ا ˆ‬
‫ا‪2‬م ا دس‬
‫ا‪2‬م ا ‪R‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫ا‪20‬ع)‪(6‬‬
‫ا‪2‬م ا‪0‬ول‬
‫ا‪2‬م ا[ ‪3‬‬
‫ا‪2‬م ا[ ‪P‬‬
‫ا‪2‬م اا ‪R‬‬
‫ا‪2‬م ا ˆ‬
‫ا‪2‬م ا دس‬
‫ا‪2‬م ا ‪R‬‬
‫‪ ,9 U‬ا‪20‬ع‬
‫‪0.362963‬‬
‫‪0.699827‬‬
‫‪0.089972‬‬
‫‪0.155004‬‬
‫‪1‬‬
‫‪2‬‬
‫‪0‬‬
‫‪0‬‬
‫‪9‬‬
‫‪6‬‬
‫‪5‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪2‬‬
‫‪11‬‬
‫‪0.373323‬‬
‫‪0.379252‬‬
‫‪0.630487‬‬
‫‪1‬‬
‫‪1‬‬
‫‪2‬‬
‫‪9‬‬
‫‪8‬‬
‫‪8‬‬
‫‪6‬‬
‫‪2‬‬
‫‪0.584059‬‬
‫‪0.138283‬‬
‫‪0.615948‬‬
‫‪0.928577‬‬
‫‪1‬‬
‫‪0‬‬
‫‪2‬‬
‫‪4‬‬
‫‪11‬‬
‫‪3‬‬
‫‪2‬‬
‫‪10,C RV‬‬
‫‪0.424699‬‬
‫‪2‬‬
‫و'‪2‬ل‬
‫ا‪,7‬‬
‫‪2‬‬
‫‪0‬‬
‫‪10,C RV‬‬
‫‪0.892844‬‬
‫‪3‬‬
‫ا‪:g1‬‬
‫ا‪20‬ع‬
‫‪1‬‬
‫‪2‬‬
‫‪3‬‬
‫‪4‬‬
‫‪5‬‬
‫‪6‬‬
‫ا‪S7‬‬
‫‪4‬‬
‫‪12‬‬
‫‪12‬‬
‫‪17‬‬
‫‪9‬‬
‫‪11‬‬
‫ا ‪2 H‬ع‬
‫‪65‬‬
‫د ا‪ 90‬م ا‪6 3‬ث ;‪‹: U‬‬
‫‪0‬‬
‫‪2‬‬
‫‪1‬‬
‫‪2‬‬
‫‪1‬‬
‫‪0‬‬
‫‪6‬‬
‫ا‪ ) ‹:‬ا‪ S7‬ا‪(R? f‬‬
‫‪0‬‬
‫‪4‬‬
‫‪2‬‬
‫‪7‬‬
‫‪2‬‬
‫‪0‬‬
‫‪15‬‬
‫ه ك ‪ 6‬أ‪ 9‬م ‪6‬ث ;‪ ‹: U‬اي ‪ ! 14.3%‬ا‪ 90‬م‪.‬‬
‫د ا‪62‬ات ا‪ WC 3‬و‪ : I %‬ه‪ 15 3‬و‪6‬ة أي ‪ , 23.07%‬ا‪ S7‬ا‪.R? f‬‬
‫‪ w2‬د ا‪62‬ات ا ‪O , 27‬اء ا‪ 10.83 2‬و‪6‬ة وه‪ 3‬ا ! د ا‪62‬ات ا‪3‬‬
‫‪. UC %9‬‬
‫‪631‬‬
:‫ ‚ال ا‬/ =‫إ‬
µ=
1
= 2.5 w2 ‫ أي أن ا‬λ = 0.4 H , [email protected]‫ ا‬,; [/‫ ا‬,‫! دا‬
0.4
:3 ‫وا آ‬0‫ وا‬MINITAB T‫ م او‬, J 1000 2
MTB > RANDOM 1000 C1;
SUBC> EXPO 2.5.
MTB >
‫ى‬Y ‫ ا‬%:‫ ا‬-‫ او‬%X A ‫د‬2 "‫ ا‬3; EXCEL ! , `' 3; U: ‫ة وا‬2 ‫ ا‬%:‫ ا‬d‫ا‬
‫ول‬H‫ن ا‬2‫ وآ‬U 6 ‫ ا اد‬%:‫ ا‬UI 9 U 7I P ‫ ت‬b`‫ن ا‬2‫ى ت وآ‬/‫وا‬
:3 ‫ا‬
Class Interval
xi ≤ 0
Relative Frequency
0
0 < xi ≤ 1
0.331
1 < xi ≤ 2
0.224
2 < xi ≤ 3
0.144
3 < xi ≤ 4
0.101
4 < xi ≤ 5
0.056
5 < xi ≤ 6
0.049
6 < xi ≤ 7
0.035
7 < xi ≤ 8
0.018
8 < xi ≤ 9
0.012
9 < xi ≤ 10
0.006
10 < xi ≤ 11
0.007
11 < xi ≤ 12
0.006
12 < xi ≤ 13
0.006
13 < xi ≤ 14
0.001
14 < xi ≤ 15
0.003
15 < xi ≤ 16
0
16 < xi ≤ 17
0.001
17 < xi
0
Cumulative Relative Frequency
0 = P ( X ≤ 0)
0.331 = P ( X ≤ 1)
0.555 = P ( X ≤ 2 )
0.699 = P ( X ≤ 3)
0.800 = P ( X ≤ 4 )
0.856 = P ( X ≤ 5 )
0.905 = P ( X ≤ 6 )
0.940 = P ( X ≤ 7 )
0.958 = P ( X ≤ 8 )
0.970 = P ( X ≤ 9 )
0.976 = P ( X ≤ 10 )
0.983 = P ( X ≤ 11)
0.989 = P ( X ≤ 12 )
0.995 = P ( X ≤ 13)
0.996 = P ( X ≤ 14 )
0.999 = P ( X ≤ 15 )
0.999 = P ( X ≤ 16 )
1.000 = P ( X ≤ 17 )
:‫ول‬H‫! ا‬
‫ات‬2 5 " M "9 ‫ال‬G9T 3 ‫ ا‬:‫ ل ان ا‬6‫ إ‬-1
P ( X ≥ 5 ) = 1 − P ( X < 5 ) = 1 − 0.856=0.144
.‫ول‬H P [‫د ا‬2 "‫ ! ا‬g‫وذ‬
‫ات‬2 6 ‫ و‬3 ! M "9 3 ‫ ا‬:‫ ل ان ا‬6‫ إ‬-2
P ( 3 ≤ X ≤ 6 ) = P ( X ≤ 6 ) − P ( X ≤ 3) = 0.905 - 0.699 = 0.206
.‫ول‬H‫ ا‬3; P [‫د ا‬2 "‫ ام ا‬f9‫ا‬
-3
632
1)
P ( X ≤ 5 ) = ∫ 0.4e−0.4 x = 1 − e −0.4(5) = 0.864664717
5
0
1-P ( X ≤ 5 ) = 0.1353353
2) P ( 3 ≤ X ≤ 6 ) = ∫ 0.4e −0.4 x = e −0.4(3) − e −0.4( 6) = 0.210476259
6
3
(, ! [‫ اآ‬.AI ‫ل ?] أدق‬2
633
) ]? ‫ ا‬3; ‫ رب‬:I ‫“ ان ه ك‬6
: ‫ ‚ال ا‬/ =‫إ‬
:3 ‫ آ‬,"J2 ‫ارات ا‬/‫ ا‬S E3 = 1000 P ( X
E4 = 1000 P ( X
E5 = 1000 P ( X
E6 = 1000 P ( X
E7 = 1000 P ( X
E8 = 1000 P ( X
E9 = 1000 P ( X
0
e 2
= 135.335283
0!
e −2 21
= 1) = 100
= 270.6705665
1!
e −2 2 2
= 2 ) = 100
= 270.6705665
2!
e −2 23
= 3) = 100
= 180.4470443
3!
e −2 2 4
= 4 ) = 100
= 90.22352216
4!
e −2 25
= 5 ) = 100
= 36.08940886
5!
e −2 26
= 6 ) = 100
= 12.02980295
6!
e −2 27
= 7 ) = 100
= 3.43708656
7!
e − 2 28
= 8 ) = 100
= 0.85927164
8!
E1 = 1000 P ( X = 0 ) = 100
E2 = 1000 P ( X
−2
:‫ول‬- ‫ن‬2/‫و‬
i
xi
Observed Oi
Expected Ei
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
Total
118
274
298
169
105
25
8
1
2
1000
135.3353
270.6706
270.6706
180.447
90.22352
36.08941
12.0298
3.437087
0.859272
999.7626
U ,: ‫ ا‬,‫ ا‬R !‫ ; ] ا‬5 ! MJ‫ة أ‬0‫ ا! ا‬3; ,"J2 ‫ ا‬, :‫“ أن ا‬6
xi
Observed Oi
Expected Ei
( Oi − Ei )
0
1
2
3
4
118
274
298
169
105
135.3353
270.6706
270.6706
180.447
90.22352
2.220504
0.040953
2.759428
0.726162
2.420038
634
2
Ei
‫‪3.40751‬‬
‫‪1.737578‬‬
‫‪13.31217‬‬
‫‪36.08941‬‬
‫‪16.32616‬‬
‫‪999.7626‬‬
‫‪χ 62 = 13.31217 , 2‬‬
‫‪25‬‬
‫‪11‬‬
‫‪1000‬‬
‫آ ي ‪ R I‬ا‬
‫‪χ‬‬
‫وآ ي ‪ R I‬ا‪H‬و‪= 12.5916 ,‬‬
‫ان ا‪ , :‬ا ‪ , 2‬اآ ! ا‪ , :‬ا‪H‬و‪ ; ; ,‬ا`‪ ,V‬ا‪ ,? :‬ان ‪Y xi‬‬
‫‪2O‬ا?‪2I & 3‬ز‪2 R9‬ا‪2‬ن ‪. α = 0.05 2 w2‬‬
‫‪2‬‬
‫‪0.05,6‬‬
‫‪635‬‬
‫‪5‬‬
‫‪≥6‬‬
‫‪Total‬‬
‫ا ا ا‬
‫‪ %J‬ا@‪ 6‬ء و ‪2‬ث ا" ت‬
‫دة ‪C ) P 342‬ق ا آ ة ‪( 2‬‬
‫إ ر ا` ‪ M‬ا‪0‬ول ‪ 1421‬هـ‪ 1422/‬هـ‬
‫ا‪ 3 ! G‬ت‬
‫أ‪ R - S-‬ا‪ ,b0‬ا ‪:,‬‬
‫ا ‚ال اول‪:‬‬
‫ا( ف ‪ ,:9C‬آ ة ا‪60‬اث ا ` ‪ Discrete-event simulation method ,‬و أذآ‬
‫أ [‪U ,‬‬
‫ب( ‪ J‬رن ! ‪- ,:9C‬و‪ ,‬ا‪60‬اث ‪ Event schedualing‬و‪ M `I ,:9C‬ا" ت ‪Process‬‬
‫‪ 3; interaction‬ا آ ة‬
‫ج( ‪ J‬رن ! ‪:I ,/ /‬م ز ! ا آ ة ا " ة ا‪60‬اث ‪Next event time‬‬
‫‪ advance‬و ا[ ‪Fixed increment time advance ,‬‬
‫ا ‚ال ا‪:‬‬
‫آ‪2/9 , G‬ن ! د ! ا‪2‬ا‪ 3‬آ‪ N & %U M‬م ‪2 C‬ر ‪ ، FIFO‬أي ز ‪2‬ن ‪M /9‬‬
‫ا ‪ R ,‬ا دم ا‪0‬ول ‪ &H9‬إ ا دم ا[ ‪ 3‬و ! " إآ & ا ‪ R ,‬ا دم ا[ ‪ Y9 3‬در‬
‫ا‪ N‬م‪` .‬ض أن ز ! ! ا‪2'2‬ل ‪ !? G‬دم ا‪0‬ول & ‪2I‬ز‪ R9‬ا‪ w2 3‬د‪,:J‬‬
‫وا‪6‬ة‪ .‬ز ! ا ‪ ,‬ا دم ا‪0‬ول ‪ U‬أ‪2I f9‬ز‪ R9‬ا‪ 0,7 w2 3‬د‪ ,:J‬و ا دم‬
‫ا[ ‪2I U 3‬ز‪ R9‬ا‪ 0،9 w2 3‬د‪ .,:J‬أو‪ -‬ا ‪: GPSS 3‬‬
‫أ( أ‪-‬ي آ ة ‪ N‬م "د ‪ 100‬ز ‪2‬ن و‪J‬ر ‪ w2‬ز ! ا@‪ N‬ر ‪ w2 ، !? G‬د‬
‫ا‪ 3; ،!? G‬آ‪2 C ! M‬ر ا د ! و‪J‬ر ;" ‪ ,‬آ‪ ! M‬ا د !‪.‬‬
‫ب( `ض أ& ‪; -29‬ة ز ‪ ! &-2 ,‬ا دم ا‪0‬ول إ ا دم ا[ ‪ 3‬وا‪2I U 3‬ز‪R9‬‬
‫ ‪ ! MX‬د‪ ,:J‬و‪X‬ث د‪ .? J‬أ إ‪-‬اء ا آ ة ‪ W I‬ه‪ 5.‬ا‪N‬وف وأو‪ -‬ا‪9:‬ات‬
‫ا ‪.,:‬‬
‫ج( `ض أن ‪ ! %20‬ا‪ 9T !? G‬ج إ ‪ ,‬ا دم ا[ ‪ Y9 M 3‬در ا‪ N‬م " إآ ل‬
‫ا ‪ R ,‬ا دم ا‪T‬ول‪ .‬أ‪ -‬ا آ ة ‪ W I‬ه‪ 5.‬ا‪N‬وف وأو‪ -‬ا‪9:‬ات ا ‪.,:‬‬
‫‪636‬‬
‫‪ %‬ا ا‪ ! 6‬ا‪%6‬‬
‫ء و ‪2‬ث ا" ت‬
‫‪ %J‬ا@‪6‬‬
‫آ‪ ,‬ا"‪2‬م‬
‫‪ ," -‬ا ‪2" g‬د‬
‫ا@ ر ا[ ‪ 0 3‬ل ا` ‪ M‬ا[ ‪ 1422/1421 3‬هـ‬
‫ دة ‪ ) P 342‬ا آ ة ‪( 2‬‬
‫ا‪, 2 :! G‬‬
‫أ‪ 3 S-‬وا‪ ! w:; 6‬ا‪ ,b0‬ا ‪:GPSS WORLD ,‬‬
‫)أ( ‪ ! ," 9C ! ,"7J R I‬ا" ت‪ ،‬آ‪ .‹ ` !:J RI U M‬ا" ‪ ,‬ا‪0‬و‬
‫‪ I‬ج إ ‪ ! 20%‬ا‪ " R7:‬د ‪ . U" I‬ا" ! ا[ ‪ ,‬وا[ [‪ I ,‬ج آ‪ U M‬إ ‪ 15%‬و‬
‫‪ ! 5%‬ا‪ " R7:‬د ‪ U" I‬ا‪2‬ا‪ ! 60% .3‬ا‪ R7:‬ا " د ‪2/I U" I‬ن ‪ &` I‬و ‪.I‬‬
‫‪ ، scrapped‬واـ ‪ 40%‬ا ‪ I ,J‬ج ا‪ 3‬إ دة " ‪ ! ,H‬ا" ‪ ,‬ا‪ U %I 3‬ا;‪.‬‬
‫' ‪9- ,"7J ,‬ة ‪ 3; %9‬ا ‪ w2‬آ‪ 30 M‬د‪2 ,:J‬ز‪ R9‬ا‪ .3‬ا‪ , " ! G‬ا‪T‬و ‪7"9‬‬
‫‪H‬ول ا ‪:3‬‬
‫‪Time For First Process‬‬
‫‪0.15‬‬
‫‪0.29‬‬
‫‪0.22‬‬
‫‪0.16‬‬
‫‪0.13‬‬
‫‪0.05‬‬
‫‪45‬‬
‫‪38‬‬
‫‪32‬‬
‫‪21‬‬
‫‪14‬‬
‫‪10‬‬
‫‪Frequency‬‬
‫)‪Process time (mins‬‬
‫ا" ‪ ,‬ا[ ‪YI ,‬ق ‪ 15±6‬د‪ ? J‬وز ! ا" ‪ ,‬ا‪0‬ة & ‪2I‬ز‪ 24 w2 3"C R9‬د‪ ,:J‬و‬
‫إ اف " ري ‪ 4‬د‪ 6 .? J‬آ‪ 3‬ت ا ‪ R‬ـ ‪ ! ., / ,"7J 100‬ا‪ ! G‬ا‪h‬زم ‪g.‬‬
‫ود ا‪ R7:‬ا ;‪.,V2‬‬
‫أو‬
‫)ب( ‪G‬ون ] ‪2 & %/ 9 3? U‬ا‪ ,7‬ا‪ ,"-‬دور‪ ,9‬ا‪ . 2‬ا ‪G‬ون ا@ ا?‪2/9 3‬ن‬
‫! ‪ 1000‬و‪6‬ة‪ .‬ا‪ S7‬ا‪ 40 ! Y9 3 2‬و ‪ 63‬و‪6‬ة و ‪ 6‬ل وي‪ .‬ا ‪G‬ون‬
‫ا ‪U‬ف ه‪ 1000 2‬و‪6‬ة‪ ،‬اي ان ‪ M9"I‬ا ‪G‬ون ‪ S7 %9‬ا`ق ! ا ‪G‬ون ا ‪2-2‬د و‬
‫‪1000‬و‪6‬ة‪; .‬ذا آ ن ا ‪G‬ون ا ‪2-2‬د ه‪ 800 2‬و‪6‬ة او اآ[ ;! ‪"9‬ل ا ‪G‬ون ‪g.‬‬
‫ا‪2T‬ع‪ .‬ا‪O‬آ‪ N M "I ,‬م ‪ ,‬ا‪ 9‬م ‪2z‬ع‪ .‬ز ! ا‪:‬م ‪ M'2 lead time‬ا‪ ,7‬ه‪2‬‬
‫ا‪2‬ع وا‪ 6 .6‬آ‪ N 3‬م ا ‪G‬ون ة ‪29 200‬م و‪ ; I‬إذا آ ن ه ك اي ‪G ‹:‬ون‬
‫‪.stockouts‬‬
‫‪637‬‬
‫ا ا ا‬
‫ هـ‬1422/1421 3 [‫ ا‬M `‫ ل ا‬0 3 [‫ ر ا‬z , ‫ ت‬-‫إ‬
(2 ‫ ) آ ة‬P 342 ‫ا ة‬
(, ‫ ا‬,?‫ا‬2O"‫اد ا‬0‫ ا‬,H _I ]? ‫ ا‬:,N6 ) (‫ال )أ‬A , -‫إ‬
*****************************************************************
*
Quality Control Program
*
*
Time units are in minutes
*
*****************************************************************
RMULT
93211
* Definitions
Transit
TABLE
M1,100,100,20
;Transit Time
Process
FUNCTION
RN1,D7
0,0/.05,10/.18,14/.34,21/.56,32/.85,38/1.0,45
*****************************************************************
GENERATE
(Exponential(1,0,30))
ASSIGN
1,FN$Process
;Process time in P1
Stage1
SEIZE
Machine1
ADVANCE
P1
;Process 1
RELEASE
Machine1
ADVANCE
2
;Inspection
TRANSFER
.200,,Rework1
;20% Need rework
*****************************************************************
Stage2
SEIZE
Machine2
ADVANCE
15,6
;Process 2
RELEASE
Machine2
ADVANCE
2
;Inspection
TRANSFER
.150,,Rework2
;15% Need rework
*****************************************************************
Stage3
SEIZE
Machine3
ADVANCE
(Normal(1,24,4))
;Process 3
RELEASE
Machine3
ADVANCE
2
;Inspection 3
TRANSFER
.050,,Rework3
;5% need rework
TABULATE
Transit
;Record transit time
TERMINATE
1
*****************************************************************
Rework1
TRANSFER
.400,,Stage1
TERMINATE
Rework2
TRANSFER
.400,,Stage2
TERMINATE
Rework3
TRANSFER
.400,,Stage3
TERMINATE
(, ‫ ا‬,?‫ا‬2O"‫اد ا‬0‫ ا‬,H _I ]? ‫ ا‬:,N6 ) (‫ال )ب‬A , -‫إ‬
*********************************************************************
*
*
Periodic Review Inventory Model
*
*
Time units are in days
*********************************************************************
* Definitions of non block entities
638
RMULT
39941
Stock
STORAGE
10000
;Warehouse can hold 10000
Stock
TABLE
S$Stock,100,100,20
;Table for inventory amts
Orderqty VARIABLE
Target-S$Stock
;Order quantity
Demand
VARIABLE
[email protected]+40
;Daily demand
Target
EQU
1000
;Initial stock level
Reorder EQU
800
;Reorder point
*********************************************************************
* The reorder process
GENERATE
5,,,,1
;Review xact, Priority=1
TEST L
S$Stock,Reorder,Skip ;Is stock < Reorderpt
ASSIGN
2,V$Orderqty
;Parameter 2=Order quantity
Custwait ADVANCE
5
;Lead time is 5 days
ENTER
Stock,P2
;Stock increases by P2
Skip
TERMINATE
;Ordering xact is finished
*********************************************************************
* The daily demand decrements quantity on hand
GENERATE
1
;Daily demand transaction
ASSIGN
1,V$Demand
;Parameter 1(P1)=daily
demand
TABULATE
Stock
;Record daily stock
TEST GE
S$Stock,P1,Stockout ;Can order be filled
LEAVE
Stock,P1
;Remove demand from stock
TERMINATE 1
;Daily timer
Stockout TERMINATE 1
;Daily timer
*********************************************************************
* Initialize the inventory
GENERATE
,,,1,10
;Set initial stock
ENTER
Stock,Target
;Set init stock level=target
TERMINATE
;Xact is terminated
639
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ا@ را‬
( 2 ‫ ) ا آ ة‬P 342 ‫ دة‬
‫ ت‬3 :! G‫ا‬
:3 ‫ال ا‬A‫ ا‬3 S-‫أ‬
” ‫ة‬6‫ا‬2‫ة ا‬9H‫ي ا‬O9 ،&? U" ?‫ا‬H‫ د ! ا‬29 ?‫ا‬- R? ‫ي‬O9
” ˆC‫ا‬J R ‫ ع‬I ‫م‬2‫ ا‬,9 U 3; 3:I 3‫ا? ا‬H‫ ا‬.‫ ل‬9‫ ر‬2 ” U"9‫ ل و‬9‫ ر‬1.50
‫ا ;ن‬./‫ وه‬،?‫ا‬- 10 ! ‫ن‬2/I ‫م‬G6 3; ‫ي ! ا‬OI ?‫ا‬H‫ ا‬.‫ة‬6‫ا‬2‫ة ا‬9H ,‫ ه‬20
‫ ه ك‬-2I R? ‫ ! ة ا‬. 29 ‫ة‬9- d‫ ا‬... ‫ او‬70 ‫ او‬60 ‫ او‬50 ‫ي إ‬O9 ?‫ا‬H‫ ا‬R?
‫ت‬T 6 ‫م "†" و‬29‫س &" و‬e T" ‫م‬29‫" و‬-" ‫م‬29 ،‫ ر‬q ‫ م‬90‫اع ! ا‬2‫ أ‬,XX
‫ع‬2 S6 ?‫ا‬H‫ ا‬3 S7‫ ا‬R9‫ز‬2I .(! ‫أ ! ا ر‬J‫ )إ‬3‫ا‬2‫ ا‬0.35,0.45,0.25
:3 ‫ول ا‬H 7"9 ‫م‬2‫ا‬
Demand Probability Distribution
Demand
40
50
60
70
80
90
100
Good
Fair
0.03
0.05
0.15
0.20
0.35
0.15
0.07
0.10
0.18
0.40
0.20
0.08
0.04
0.00
Poor
0.44
0.22
0.16
0.12
0.06
0.00
0.00
.a ‫ أ ر‬: 9 36 29 ?‫ا‬H‫ ا‬R? U9O9 3‫ا? ا‬H‫ ! ا‬M[ 0‫ ا"د ا‬9 I ‫ب‬27 ‫ا‬
.‫ب‬27 ‫ د ا‬[email protected] 9‫و‬9 ‫ م‬9‫ أ‬10 3‫ آ‬6 (‫)أ‬
.‫ب‬27 ‫ د ا‬[email protected] ‫م‬29 100 ‫ م ة‬N‫ ا‬3‫ آ‬6‫ و‬GPSS WORLD ‫ذج ام‬2 ‫ن‬2‫)ب( آ‬
:,Y ‫ر ح ! ا‬0‫ ا‬S I :,N6
P=R–C–L+S
:3"I ‫ز‬2 ‫ ا‬P6
P = Profit (‫ر ح‬0‫)ا‬
R = Revenue from sales (3/‫) ” ا " ت ا‬
C = Cost of newspapers (?‫ا‬H‫ ا‬,`/I)
L = Lost profit from excess demand (SC : I ‫دة ! م‬2:` ‫ر ح ا‬0‫)ا‬
S = salvage from sale of scrap papers (,: ‫ا? ا‬H‫ ا‬R ! R- ‫)ا ” ا‬
640
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ا@ را‬
( 2 ‫ ) ا آ ة‬P 342 ‫ دة‬
‫ ت‬3 :! G‫ا‬
:, ‫ ا‬,b0‫ ا‬3 S-‫أ‬
:‫ول‬0‫ال أ‬A‫ا‬
” ‫ة‬6‫ا‬2‫ة ا‬9H‫ي ا‬O9 ،&? U" ?‫ا‬H‫ د ! ا‬29 ?‫ا‬- R? ‫ي‬O9
” ˆC‫ا‬J R ‫ ع‬I ‫م‬2‫ ا‬,9 U 3; 3:I 3‫ا? ا‬H‫ ا‬.‫ ل‬9‫ ر‬2 ” U"9‫ ل و‬9‫ ر‬1.50
‫ا ;ن‬./‫ وه‬،?‫ا‬- 10 ! ‫ن‬2/I ‫م‬G6 3; ‫ي ! ا‬OI ?‫ا‬H‫ ا‬.‫ة‬6‫ا‬2‫ة ا‬9H ,‫ ه‬20
‫ ه ك‬-2I R? ‫ ! ة ا‬. 29 ‫ة‬9- d‫ ا‬... ‫ او‬70 ‫ او‬60 ‫ او‬50 ‫ي إ‬O9 ?‫ا‬H‫ ا‬R?
‫ت‬T 6 ‫م "†" و‬29‫س &" و‬e T" ‫م‬29‫" و‬-" ‫م‬29 ،‫ ر‬q ‫ م‬90‫اع ! ا‬2‫ أ‬,XX
‫ع‬2 S6 ?‫ا‬H‫ ا‬3 S7‫ ا‬R9‫ز‬2I .(! ‫أ ! ا ر‬J‫ )إ‬3‫ا‬2‫ ا‬0.35,0.45,0.20
:3 ‫ول ا‬H 7"9 ‫م‬2‫ا‬
Demand Probability Distribution
Demand
40
50
60
70
80
90
100
Good
Fair
0.03
0.05
0.15
0.20
0.35
0.15
0.07
0.10
0.18
0.40
0.20
0.08
0.04
0.00
Poor
0.44
0.22
0.16
0.12
0.06
0.00
0.00
.a ‫ أ ر‬: 9 36 29 ?‫ا‬H‫ ا‬R? U9O9 3‫ا? ا‬H‫ ! ا‬M[ 0‫ ا"د ا‬9 I ‫ب‬27 ‫ا‬
. 29 ‫ة‬9- 80,70,60,50 R? ‫ب ; إذا أى ا‬27 ‫ د ا‬[email protected] 9‫و‬9 ‫ م‬9‫ أ‬10 3‫ آ‬6
:,Y ‫ر ح ! ا‬0‫ ا‬S I :,N6
P=R–C–L+S
:3"I ‫ز‬2 ‫ ا‬P6
P = Profit (‫ر ح‬0‫)ا‬
R = Revenue from sales (3/‫) ” ا " ت ا‬
C = Cost of newspapers (?‫ا‬H‫ ا‬,`/I)
L = Lost profit from excess demand (SC : I ‫دة ! م‬2:` ‫ر ح ا‬0‫)ا‬
S = salvage from sale of scrap papers (,: ‫ا? ا‬H‫ ا‬R ! R- ‫)ا ” ا‬
641
:3 [‫ال ا‬A‫ا‬
R9‫ز‬2‫ ا‬%J 3; ‫ ا ت‬e"I ., J‫ ت ر‬, ‫و ت‬/‫ إ‬,‫ آ‬3; R ‫ ا‬%J ‫م‬2:9
%H6 .‫ن‬2‫ز‬2 ‫ ا‬U79 3‫ ت ا‬/ ‫ة "ض‬G‫ ه‬- S 3; ,b"I ,( ,7‫ا‬2 3? :I M/O
:, ‫ ا‬,‫ ا‬7"9 S7‫ا‬
Order Size
6
Frequency 0.10
12
0.25
18
0.30
24
0.15
30
0.12
36
0.05
48
0.03
, X 120 SC M/ ,b"‫ ز ! ا‬. ‫زع أ‬2 ,:J‫ د‬15 ‫ ت‬7‫ل ا‬2'‫ ! ! و‬G‫ ا‬w2
3; , J‫] ا ت ا‬9 R ‫ ا‬%J .S7‫ ا‬3; e"I , J‫ ر‬, M/ ‫ان‬2X 10 ‫ إ‬,; [email protected]
.,:J‫ د‬455 3; ‫ة‬6‫ و‬60 %H ‫ ت‬2 H
:, ‫ ت ا‬2" ‫ ا‬37"I 3/ ,‫آ‬O‫ ط ا‬O ! ‫ م‬9‫ أ‬10 3‫ آ‬6 GPSS ‫ام‬
,b"‫ ا‬%J 3; ‫ة‬N ‫ ت ا‬7‫ د ا‬w2 -4
‫م‬29 M‫ آ‬,‫ز‬2 ‫ ا‬, J‫ ا ت ا‬, ‫ آ‬-5
‫ ت‬7 transit times , :@‫ ت ا‬J‫و‬0‫ ا‬R9‫ز‬2I -6
642
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2
‫ءو‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ ر ا‬z , ‫ ت‬-‫إ‬
( 2 ‫ ) ا آ ة‬P 342 ‫دة‬
:‫ول‬0‫ال ا‬A‫ ا‬, -‫إ‬
:‫ ري‬0‫م ا‬2‫ع ا‬2 (1) ‫ول‬- ‫ن‬2/
News Day
Prob.
Cum. Prob
Random Digit
Good
0.35
0.35
01-35
Fair
0.45
0.80
36-80
Poor
0.25
1
81-00
:H‫ ري ا‬0‫م ا‬2 S7 (2) ‫ول‬- ‫ن‬2/
Demand
Prob.
Cum. Prob.
Random Dig.
40
0.03
0.03
01-03
50
0.05
0.08
04-08
60
0.15
0.23
09-23
70
0.20
0.43
24-43
80
0.35
0.78
44-78
90
0.15
0.93
79-93
100
0.7
1
94-00
:& ‫س‬e T ‫ ري‬0‫م ا‬2 S7 (3) ‫ول‬- ‫ن‬2/
Demand
Prob.
Cum. Prob.
Random Dig.
40
0.10
0.10
01-10
643
50
0.18
0.28
11-28
60
0.40
0.68
29-68
70
0.20
0.88
69-88
80
0.08
0.96
89-96
90
0.04
1
97-00
: †‫ ري ا‬0‫م ا‬2 S7 (4) ‫ول‬- ‫ن‬2/
Demand
Prob.
Cum. Prob.
Random Dig.
40
0.44
0.44
01-44
50
0.22
0.66
45-66
60
0.16
0.82
67-82
70
0.12
0.94
83-94
80
0.06
1
95-00
:‫ول‬0‫م ا‬2 ‫ ة‬/ ‫أ ا‬
(C = 75 SR ) ‫ ل‬9‫ ر‬75 " ‫ة‬9- 50 = ‫اة‬O ‫ا? ا‬H‫د ا‬
& ‫س‬e T 64 = A.1. ‫ول‬- ! 3?‫ا‬2O %J‫ ر‬S :‫ ري‬0‫م ا‬2‫ع ا‬2
50 = S7‫( ا‬3) ‫ول‬- ! ‫ و‬13 = 3?‫ا‬2O %J‫ ر‬S :‫ول‬0‫م ا‬2 S7‫ا‬
P=R–C–L+S
= 2x50 – 1.5x 50 – 0 + 0 = 25 SR
:3 [‫م ا‬2‫ا‬
‫ة‬9- 50 = ‫اة‬O ‫ا? ا‬H‫د ا‬
† 82 = A.1. ‫ول‬- ! 3?‫ا‬2O %J‫ ر‬S :‫ ري‬0‫م ا‬2‫ع ا‬2
50 = S7‫( ا‬4) ‫ول‬- ! ‫ و‬45 3?‫ا‬2O"‫ ا‬%J‫ ا‬:3 [‫م ا‬2 S7‫ا‬
P=R–C–L+S
= 2x50 – 1.5x 50 – 0 + 0 = 25 SR
:3 ‫ول آ‬- ‫ن‬2/‫ا و‬./‫وه‬
Day
R.D.
Newsday
Newsday
R.D.
Demand
Demand
R L
S
P
1
2
64
82
Fair
Poor
13
45
50
50
100
100
0
0
0
0
25
25
3
4
26
35
Good
Good
93
80
90
90
100
100
20
20
0
0
5
5
644
5
17
Good
04
50
100
0
0
25
6
45
Fair
20
50
100
0
0
25
7
03
Good
88
90
100
20
0
5
8
72
Fair
03
40
80
0
2
7
9
83
Poor
78
60
100
5
0
20
10
69
Fair
03
40
80
0
2
7
‫ ل‬9‫ ر‬14.5 2‫م ه‬2‫ ا‬3; ‫ة‬9- 50 R? ‫ ; إذا اي ا‬3 2‫ ا‬a ‫ ا‬w2 ‫ ان‬H ‫ول‬H‫! ا‬
.3 2‫ ا‬a ‫ ا‬w2 S ‫ و‬29 ‫ة‬9- 80 ‫ و‬70 ‫ و‬60 ‫ر ا ـ‬/
:3 [‫ال ا‬A‫ ا‬, -‫إ‬
:3 ‫ آ‬GPSS ‫ذج ام‬2 ‫ن‬2/
*
Time Unit is one hour
*
Sizeorder FUNCTION
RN1,D7
;Order size
.10,6/.35,12/.65,18/.80,24/.92,30/.97,36/1.0,48
Transit
TABLE
M1,.015,.015,20
;Transit time
Number
TABLE
X1,100,100,20
;No. packed each day
Ptime
VARIABLE
.0028#P1+0.0334
;Packing time
Amount
EQU
1000
;Initial stock amount
Stock
STORAGE
4000
;Warehouse holds
; 4000 units
*********************************************************************
GENERATE
(Exponential(1,0,0.25)) ;Order arrives
ASSIGN
1,1,Sizeorder
;P1=order size
TEST GE
S$Stock,P1,Stockout
;Is stock sufficient?
LEAVE
Stock,P1
;Remove P1 from stock
QUEUE
Packing
SEIZE
Machine
;Get a machine
DEPART
Packing
ADVANCE
V$Ptime
;Packing time
RELEASE
Machine
;Free the machine
SAVEVALUE 1+,P1
;Accumulate no. packed
TABULATE
Transit
;Record transit time
TERMINATE
Stockout TERMINATE
*********************************************************************
GENERATE
0.75,0.08334,1
;Xact every 40+/-5 mins
ENTER
Stock,60
;Make 60, Stock
*
increased by 60
Stockad
TERMINATE
*********************************************************************
GENERATE
8
;Xact every day
TABULATE
Number
SAVEVALUE 1,0
TERMINATE 1
*********************************************************************
GENERATE
,,,1,10
;Initial stock xact
ENTER
Stock,Amount
;Set initial stock
TERMINATE
]? 9‫ ر‬:I ‫ ! ة‬6‫ وا‬:]? ‫ا‬
645
GPSS World Simulation Report - Manufact.1.1
Saturday, May 19, 2001 17:49:40
START TIME
END TIME
0.000
80.000
BLOCKS
FACILITIES
STORAGES
NAME
AMOUNT
MACHINE
NUMBER
PACKING
PTIME
SIZEORDER
STOCK
STOCKAD
STOCKOUT
TRANSIT
LABEL
RETRY
23
1
1
VALUE
1000.000
10009.000
10003.000
10008.000
10004.000
10000.000
10006.000
16.000
13.000
10002.000
LOC
BLOCK TYPE
ENTRY COUNT CURRENT COUNT
1
GENERATE
325
0
2
ASSIGN
325
0
3
TEST
325
0
4
LEAVE
325
0
5
QUEUE
325
0
6
SEIZE
325
0
7
DEPART
325
0
8
ADVANCE
325
0
9
RELEASE
325
0
10
SAVEVALUE
325
0
11
TABULATE
325
0
12
TERMINATE
325
0
13
TERMINATE
0
0
14
GENERATE
105
0
15
ENTER
105
0
16
TERMINATE
105
0
17
GENERATE
10
0
18
TABULATE
10
0
0
0
0
0
0
0
0
0
0
0
0
0
STOCKOUT
0
0
0
STOCKAD
0
0
0
646
19
SAVEVALUE
10
0
20
TERMINATE
10
0
21
GENERATE
1
0
22
ENTER
1
0
23
TERMINATE
1
0
0
0
0
0
0
FACILITY
MACHINE
ENTRIES UTIL. AVE. TIME AVAIL. OWNER PEND INTER RETRY DELAY
325
0.354
0.087 1
0
0
0
0
0
MAX CONT.ENTRY ENTRY(0)AVE.CONT. AVE.TIME AVE.(-0)RETR PACKING
4
0
325
208
0.104
0.026
0.071
0
QUEUE
STORAGE
STOCK
TABLE
TRANSIT
CAP. REM. MIN. MAX.
4000 2928
0 1378
MEAN
0.113
22
6.77
52
22.77
66
43.08
51
58.77
43
72.00
20
78.15
17
83.38
7
STD.DEV.
0.055
ENTRIES AVL. AVE.C. UTIL. RETRY DELAY
7300
1 1132.973 0.283
0
0
RANGE
0.045
RETRY FREQUENCY CUM.%
0
0.060
0.060
-
0.075
0.075
-
0.090
0.090
-
0.105
0.105
-
0.120
0.120
-
0.135
0.135
-
0.150
0.150
-
0.165
0.165
-
0.180
0.180
-
0.195
0.195
-
0.210
0.210
-
0.225
0.225
-
0.240
0.240
-
0.255
0.255
-
0.270
0.270
-
0.285
0.285
-
85.54
17
90.77
8
93.23
2
93.85
3
94.77
3
95.69
2
96.31
1
96.62
5
98.15
6
100.00
NUMBER
622.800
156.046
647
_
0
1
10.00
1
20.00
1
30.00
4
70.00
2
90.00
1
100.00
SAVEVALUE
1
FEC XN
VALUE
443
442
444
300.000
-
400.000
400.000
-
500.000
500.000
-
600.000
600.000
-
700.000
700.000
-
800.000
800.000
-
900.000
RETRY
0
PRI
0
0
0
BDT
80.090
80.343
88.000
VALUE
0
ASSEM
CURRENT
443
442
444
0
0
0
648
NEXT
1
14
17
PARAMETER
649
Ave. , J ! 2‫ وه‬. 0.12 w:; 2‫ ه‬,b"‫ ا‬%J 3; ‫ة‬N ‫ ت ا‬7‫ د ا‬w2 •
.Queue Entity Packing W I 9:‫ ا‬3; Cont.
. Table Number 3; 7" 29 ,‫ز‬2 ‫ ا‬, J‫ ا ت ا‬R9‫ز‬2I •
. ‫ ا‬% , V2 ‫ و‬TRANSIT ‫ول‬H‫ ا‬3; ‫ ت‬7 , :@‫ ت ا‬J‫و‬0‫ ا‬R9‫ز‬2I •
650
‫ا ا ا‬
‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
‫ هـ‬1421-1420 ‫ول‬0‫ ا‬M ` 3? U‫ ر ا‬T‫ا‬
(2 ‫ق ا آ ة‬C ) P 342 ‫ا دة‬
‫ت‬2' ‫ث‬r` ! G‫ا‬
:, ‫ ا‬/K'‫ = ! ا‬3 S-‫ا‬
:‫ا ‚ال اول‬
: U ,[ ‫ أ‬37‫ و أ‬, ‫ ت ا‬7 ‫ف ا‬
(a) System state (b) Entity
Simulation clock.
(c) Attributes
(d) List
(e) Event
(f) Event list
(g) Activity (h)
:‫ا ‚ال ا‬
A taxicab company operates one vehicle during the 9:00 A.M. to 5:00 P.M. period. Currently,
consideration is being given to the addition of a second vehicle to the fleet. The demand for taxi
follows the distribution shown:
Time between Calls (Minutes)
Probability
15
0.14
20
0.22
25
0.43
30
0.17
35
0.04
The distribution of time to complete a service is as follows:
Service Time (Minute)
Probability
5
0.12
15
0.35
25
0.43
35
0.06
45
0.04
a) Simulate the operation of the system for one day by hand.
b) Using ARENA simulate five individual days of operation of the current system and
the system with an additional taxicab. Compare the two systems with respect to the
waiting times of the customers and any other measures that might shed light on the
situation ( like vehicle utilization etc.)
651
‫ا ا ا‬
: ‫ت * ا‬17 /BJ#
w7 37"9 ‫ ا‬M/O‫ ا‬.‫ رات‬7:‫ ا‬,7
‫ ا‬%H ! % `‫ ا‬M: ‫م‬I ‫ ت‬6 6 9
.g.
Station
Travelig
text
Loading
text
Scale
Weighing
text
Queue
Loader Queue
text
_'‫ إ ر‬,6 O‫ ك ا‬I M ‫ ر'`! و " ا‬6‫ ! ا‬6‫ ! ر'_ وا‬M I ,6 M‫آ‬
‫زن‬2‫ " ا‬،,:J‫ د‬2 ± 1 ‫ق‬YI ‫ان‬G ! O‫ ا‬,`'‫ ! ار‬,6‫ ز ! ا‬،‫زن‬2I 3/ ‫وزن‬
., X ‫ ! ة‬O‫ ا‬,`'‫د ا ار‬2"I‫ و‬U ‫`غ‬I‫ رات و‬7:‫ ا‬,7 ‫ ا‬,6 O‫ ك ا‬I
‫ ة‬7" ‫ رات‬7:‫ ا‬,7 ‫دة ! وا‬2"‫ه ب وا‬.‫زن وز ! ا‬2‫ ت ا‬J‫ ! واو‬O‫ ت ا‬J‫" ت او‬9‫ز‬2I
:, ‫اول ا‬H‫ ا‬3;
.M ‫ ا‬, ‫ول از‬- -1
Loading Time
5
10
15
Probability
0.3
0.5
0.2
.‫زن‬2‫ ا‬, ‫ول از‬- -2
Weighing Time
12
16
Probability
0.7
0.3
.‫ رات‬7:‫ ا‬,7
652
‫دة إ‬2"‫ه ب وا‬.‫ ا‬, ‫ول از‬- -3
‫‪Probability‬‬
‫‪0.4‬‬
‫‪0.3‬‬
‫‪0.2‬‬
‫‪0.1‬‬
‫‪Travel Time‬‬
‫‪40‬‬
‫‪60‬‬
‫‪80‬‬
‫‪100‬‬
‫ ‪ R‬ا‪0‬و‪ J‬ت ‪ :I‬س ‪.? J‬‬‫ا ‪27‬ب ‪ , "; 9:I‬آ‪ ! M‬ار'`‪ ,‬ا‪ ! O‬ور'_ ا‪2‬زن و ‪ w2‬ز ! ا@‪ N‬ر ;‪ 3‬آ‪M‬‬
‫‪2 C‬ر‪.‬‬
‫‪ 6 -1‬آ‪ 3‬ا‪ N‬م ا ‪9‬و‪ 9‬ـ ‪ 5‬ر‪6‬ت ‪.,6 M/‬‬
‫‪. -2‬ج ا‪ N‬م ] ا آ ة ‪ GPSS‬ـ ‪ 100‬ر‪.,6 M/ ,6‬‬
‫‪ -3‬آر ا`‪:‬ة ‪ ] 2‬ا آ ة ‪. ARENA‬‬
‫‪ N6‬ت‪:‬‬
‫‪ -1‬ا ‪ M‬ا ‪ ! , 30 9 a‬أ ل ا` ‪ 10 ) .M‬ت ‪:; M/‬ة(‬
‫‪ % 2 ( -2‬ا ‪ 10 M‬ر ‪ f‬ن ‪ 1422‬هـ ا ‪2‬ا; ‪; 25‬ا‪ 2001 9‬م‪.‬‬
‫‪ -3‬ا ‪ O‬رآ‪ ,‬ا‪ RHOI , H‬ا‪ 9G9T‬د ا ‪ O‬رآ! ! ‪. 2‬‬
‫وا ا ‪.;2‬‬
‫د‪ .‬ن ‪ -‬ي‬
‫‪653‬‬
‫ا ا ا‬
‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
( 2 ‫ق ا آ ة‬C) P 342 ‫دة‬
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ا@ ر ا‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
‫ و‬System states ‫ م‬N‫ت ا‬T 6 ‫ ذآ‬R , ‫ ا‬, N0‫ ا‬,‫ را‬,:9C Mf;‫أ( أو'_ أ‬
Activities ‫ م‬N‫ ا‬,7O‫ و أ‬Attributes ‫ ? ت‬/‫ و '` ت ا‬Entities ‫ ? ت‬/‫ا‬
‫` ت‬O ‫ ا‬6e ‫ارئ‬2C %J (3
!:9C RC :I (2 R ! Y' %J (1
Discrete-event Simulation Method , ` ‫اث ا‬60‫آ ة ا‬
,:97 ‫د‬2 : ‫ب( ا‬
,[ ‫ ذآ ا‬R
:‫ا ‚ال ا‬
:, ‫ ا‬GPSS S‫ا‬2J M ‫ ء [ ل‬7‫ إ‬R ‫ ز‬H9 ‫أ( أح‬
1) GENERATE
2) ADVANCE3) ASSIGN 4) TERMINATE
5) TRANSFER
6) TEST
‫ ء‬7‫ إ‬R GPSS ‫ ا آ ة‬,Y U M‫ ] آ‬I _‫ وآ‬Storage ‫ و‬Facility ! ‫ا`ق‬
(‫ب‬
,[ ‫أ‬
: ‫ا ‚ال ا‬
5:00 6‫ و‬6 ' 9:00 ‫ ا`ة‬3; ‫ة‬6‫ ء رة وا‬[email protected]‫ ا‬,[96 ‫ رات‬-eI ,‫ آ‬MYOI
,- ‫ ا‬W ‫ ; اذا آ‬,‫! " درا‬/‫ و‬, X ‫ رة‬,; V‫ إ‬3; ,‫آ‬O‫ ا‬S6 ' /`9 .‫ ا‬
:3‫ ه‬,‫آ‬O‫ ى ا‬," H ‫ ا ت ا‬S6 ‫ة‬-‫ رة ا‬S7‫ ا‬.g‫ ذ‬S7I
Time between calls (Minutes)
Probability
15
0.14
20
0.22
25
0.43
30
0.17
35
0.04
:3 ‫ن( آ‬2 G‫ ا‬M'2I) , ‫ إآ ل‬WJ‫ و‬R9‫ز‬2I‫و‬
Service Time (Minutes)
Probability
5
0.12
15
0.35
25
0.43
35
0.06
45
0.04
‫ ه ك‬W ‫ ; إذا آ‬5‫ار‬J ‫ ذ‬[email protected] ,‫آ‬O‫ ا‬S6 ' I 3/ ‫م‬29 100 ‫ ة‬,‫آ‬O‫ م ا‬N 3‫ آ‬6
., X ‫ رة‬,; [email protected] ,- 6
GPSS ‫ ا آ ة‬,Y ‫أ( ام‬
ARENA ,992 ‫ ا آ ة ا‬,Y ‫ب( و ام‬
654
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ ر ا‬z ,-‫ذ‬2 , -‫إ‬
(2 ‫ق آ ة‬C) P 342 ‫ا دة‬
:‫ول‬0‫ال ا‬A , -‫إ‬
(‫أ‬
R I R7J ‫ م ه ك‬M/O; R ‫ ا‬,"C‫ إ ا ] و‬N‫ ون ا‬:R ! %J (1
:3? U‫ل ا ] ا‬2 U" HI %9‫ إ ج و‬w 9 I
d‫ ا‬,"7J R HI ‫ ء‬U‫ إ‬,N ،‫ ا@ ج‬w ,"7J ‫ل‬2'‫ و‬,N :‫ م‬N‫ت ا‬T 6
R7:‫ ا‬:‫ ? ت‬/‫ا‬
(R H‫ )ز ! ا‬, ‫ ز ! ا‬،‫ل‬2'2‫ ز ! ا‬:‫ ? ت‬/‫'` ت ا‬
(, ‫ ا‬,"7: ‫ ر‬[email protected]‫ ز ! ا‬XAI ,"7J M‫ ر ) آ‬[email protected]‫ ت ا‬J‫ أو‬:‫ م‬N‫ ا‬,7O‫أ‬
:‫ إ رات ور‬U %/ I ‫ ه ت‬[email protected]‫ ا‬R - 3; ‫ ;ت‬6 ‫ ور‬G 9‫ و‬:!:9C RC :I (2
‫ إ رة ا ور‬YI ,N ،RC :‫ ا ا‬,; 6 ‫ل‬2'‫ و‬,N :‫ م‬N‫ت ا‬T 6
‫ ا ;ت‬:‫ ? ت‬/‫ا‬
‫ل‬2'2‫ ز ! ا‬:‫ ? ت‬/‫'` ت ا‬
( 3; 3‫ ا ;ت ا‬XA9 ‫ا‬.‫ )وه‬RC :‫ة ا‬N ‫ د ا ;ت ا‬:‫ م‬N‫ ا‬,7O‫أ‬
(‫ر‬2"‫ ا‬MJ ‫ ا@ رة‬U M`:I ‫ ا@ رة أو‬a; I ‫ر إ‬2 7‫ا‬
3: ‫ادث‬2 ‫ ا‬%J ‫ا إ‬2 9 ‫ادث او ^ه‬26 3; !
‫ ا‬:`O ‫ارئ‬2C %J (3
‫ا"ج‬
‫ ء ا"ج‬U‫ إ‬,N ،‫ل ا ب‬2'‫ و‬,N :‫ م‬N‫ت ا‬T 6 (4
!
‫ ا‬:‫ ? ت‬/‫ا‬
‫ ز ! ا"ج‬،‫ل‬2'2‫ ز ! ا‬:‫ ? ت‬/‫'` ت ا‬
(3 ‫ ر ب ا‬[email protected]‫ ز ! ا‬XA9 ‫ب‬
M‫ ر ا"ج ) آ‬N‫ ا‬WJ‫ و‬: ‫ م‬N‫ ا‬,7O‫أ‬
, ‫ ط ز‬: ‫ م‬N‫ت ا‬T 6 YI ,:97‫ ا‬5.‫ ه‬3; :, ` ‫اث ا‬60‫ آ ة ا‬,:9C (‫ب‬
, ‫ر‬2 C g‫ [ ل ذ‬.‫ث‬6 U; ‫ ث‬9 3‫ ( وا‬Discrete R7: ! G‫ )أي ان ا‬, `
‫ل ا ;ت إ‬2'‫ و‬.‫ن‬2‫ا‬2 , RI , ` , ‫ ?! أز‬G‫ ا‬M 9 ‫ إذ‬6‫ دم وا‬
.d‫! أ‬:9C RC :I
:3 [‫ال ا‬A , -‫إ‬
( ‫)أ‬
(1) GENERATE A,B,C,D,E
Future Events Chain 40!"(‫( ا) اث ا‬$; *+ j,B‫ و‬Transaction ,! Create A - Mean inter generation time.
B - Inter generation time half-range or Function Modifier.
C - Start delay time. Time increment for the first Transaction.
D - Creation limit.
E - Priority level.
Example: GENERATE 0.1
655
(2) ADVANCE A,B
Future Events Chain 40!"(‫( ا) اث ا‬$; * Transaction ,! ^B
A - The mean time increment.
B - The time half-range or, if a function, the function modifier.
Example: ADVANCE 101.6,50.3
(3) ASSIGN A,B,C
Transaction Parameter ,!(‫ ا‬X, ‫ ل‬,
A - Parameter number of the Active Transaction.
B - Value.
C - Function number.
Example: ASSIGN 2000,150.6
(4) TERMINATE A
‫ء‬8‫ اد ا‬O0‫ وا‬,! *‫ا‬
A - Termination Count decrement. Default is 0.
Example: TERMINATE 1
(5) TRANSFER A,B,C,D
‫] ا(@ د‬0‫ ا‬E‫ ا‬0‫&ك او ا‬
A - Transfer Block mode.
B - Block number or location.
C - Block number or location.
D - Block number increment for ALL Mode.
Examples:
(a) Unconditional Mode
TRANSFER ,New_Place
(b) Fractional Mode
TRANSFER .75,,New_Place
(c) Both Mode
656
TRANSFER BOTH,First_Place,Second_Place
(d) All Mode
TRANSFER ALL,First_Place,Last_Place,2
(e) Pick Mode
TRANSFER PICK,First_Place,Last_Place
(f) Function Mode
TRANSFER FN,Func1,5
(g) Parameter Mode
TRANSFER P,Placemarker,1
(h) Subroutine Mode
TRANSFER SBR,New_Place,Placemarker
(i) Simultaneous Mode
TRANSFER SIM,Nodelay_Place,Delay_Place
(6) TEST O A,B,C
,!(‫ و ل إ"ب ا‬arithmetic condition *%"@‫& ا[&ط ا‬4!G‫ا‬
O - Relational operator. Relationship of Operand A to Operand B for a successful test.
A - Test value.
B - Reference value.
C - Destination Block number.
Example: TEST G C1,70000
(‫)ب‬
,U‫ ا‬M[ ‫ ت و‬J‫و‬0‫ ! ا‬WJ‫ أي و‬w:; 6‫ وا‬M " S2I (,UI) Facility
RELEASE ‫ و‬SEIZE ! :‫م ا‬9
:‫[ ل‬
GPSS BLOCKS
SEIZE
Facility
GPSS BLOCKS
RELEASE Facility
GPSS BLOCKS
657
M[ ‫ و‬STORAGE 0 ," & ‫ د‬9‫ و‬6‫ وا‬M " ! [‫ اآ‬S29 (‫ن‬G ) Storage
LEAVE ‫ و‬ENTER ! :‫م ا‬9 ," 9 I " ‫ن‬G ‫ا‬
:‫[ ل‬
GPSS COMMANDS
SL STORAGE Capacity
GPSS COMMANDS
GPSS BLOCKS
ENTER
SL
GPSS BLOCKS
LEAVE SL
GPSS BLOCKS
:P [‫ال ا‬A , -‫إ‬
calls FUNCTION RN1,D5
0.14,15/0.36,20/0.79,25/0.96,30/1.0,35
sertime FUNCTION RN1,D5
0.12,5/0.47,15/0.9,25/0.96,35/1.0,45
callwait TABLE M1,10,10,20
*
GENERATE FN$calls
QUEUE
cabq
SEIZE
cab
DEPART
cabq
ADVANCE
FN$sertime
RELEASE
cab
TABULATE callwait
TERMINATE 1
GPSS World Simulation Report - Untitled Model 1.1.1
Sunday, January 13, 2002 00:06:22
START TIME
0.000
END TIME
2455.000
NAME
CAB
CABQ
CALLS
CALLWAIT
SERTIME
LABEL
FACILITY
CAB
BLOCKS
8
FACILITIES
1
STORAGES
0
VALUE
10006.000
10005.000
10000.000
10004.000
10002.000
LOC
1
2
3
4
5
6
7
8
ENTRIES
101
BLOCK TYPE
GENERATE
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TABULATE
TERMINATE
UTIL.
0.827
ENTRY COUNT CURRENT COUNT RETRY
101
0
0
101
0
0
101
1
0
100
0
0
100
0
0
100
0
0
100
0
0
100
0
0
AVE. TIME AVAIL. OWNER PEND INTER RETRY DELAY
20.099 1
101
0
0
0
0
658
QUEUE
CABQ
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
3
1
101
60
0.261
6.337
TABLE
CALLWAIT
MEAN
26.650
STD.DEV.
13.410
RANGE
_
10.000
20.000
30.000
40.000
50.000
60.000
-
10.000
20.000
30.000
40.000
50.000
60.000
70.000
AVE.(-0) RETRY
15.610
0
RETRY FREQUENCY CUM.%
0
7
7.00
27
34.00
39
73.00
13
86.00
9
95.00
3
98.00
2
100.00
CEC XN
101
PRI
0
M1
2450.000
ASSEM
101
CURRENT
3
NEXT
4
PARAMETER
VALUE
FEC XN
102
PRI
0
BDT
2475.000
ASSEM
102
CURRENT
0
NEXT
1
PARAMETER
VALUE
! ‫ أن ز‬H ‫ ر‬[email protected]‫ول ا‬- ! . 2 , 3‫ وه‬% 82.7 3‫ ا رة ه‬,9 "; ‫“ أن‬6
‫ا آ‬- 3 2‫ ? وه‬J‫ د‬26.65 w2 ‫ و‬,:J‫ د‬70 6 M 9 ‫ر رة‬2 7‫ ا‬3; ‫ ر‬[email protected]‫ا‬
:3 ‫اري ا‬/‫ ا رج ا‬3; aV2 2‫ه‬
ARENA ‫)ب( ام‬
659
ARENA Simulation Results
amb - License #9400000
Summary for Replication 1 of 1
Project:
Taxi Cab Problem
Analyst:
Replication ended at time
Run execution date :
1/12/2001
Model revision date:
1/12/2001
: 100.0
TALLY VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Observations
_______________________________________________________________________________
finish_Ta
25.750
(Insuf)
22.000
27.000
4
cab_R_Q Queue Time
1.0000
(Insuf)
.00000
5.0000
5
660
DISCRETE-CHANGE VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Final Value
_______________________________________________________________________________
# in cab_R_Q
.05000
(Insuf)
.00000
1.0000
.00000
cab_R Busy
.93000
(Insuf)
.00000
1.0000
1.0000
cab_R Available
1.0000
(Insuf)
1.0000
1.0000
1.0000
COUNTERS
Identifier
Count
Limit
_________________________________________
finish_C
4
Infinite
Simulation run time: 0.00 minutes.
Simulation run complete.
%93 ‫ ا رة‬, ";‫ و‬,:J‫ د‬25.75 ‫ ر‬[email protected]‫ ز ! ا‬w2 ‫ أن‬H 9:‫! ا‬
‫ ر‬N‫ از ن إ‬%U !9.‫ ?! ا‬G‫ ا‬:`9T 6 ‫ رة اى‬,‫آ‬O‫ ا‬S6 ' ‫ ج‬9 J :‫ار‬:‫ا‬
.,92C
SIMAN ,Y ] ‫ا‬
;
Model statements for module:
Arrive 1
42$
CREATE,
1:DISC( 0.14,15,0.36,20,0.79,25,0.96,30,1.0,35 );
3$
STATION,
calls;
51$
TRACE,
-1,"-Arrived to system at station calls\n":;
661
6$
ASSIGN:
Picture=Default;
27$
DELAY:
0.;
56$
TRACE,
-1,"-Transferred to station cab\n":;
29$
ROUTE:
2,cab;
;
;
Model statements for module:
Server 1
;
0$
STATION,
cab;
158$
TRACE,
-1,"-Arrived to station cab\n":;
121$
DELAY:
0.;
165$
TRACE,
-1,"-Waiting for resource cab_R\n":;
82$
QUEUE,
cab_R_Q:MARK(QueueTime);
83$
SEIZE,
1:
cab_R,1;
192$
BRANCH,
1:
If,RTYP(cab_R).eq.2,193$,Yes:
If,RTYP(cab_R).eq.1,95$,Yes;
193$
MOVE:
cab_R,cab;
95$
TALLY:
cab_R_Q Queue Time,INT(QueueTime),1;
202$
DELAY:
0.0;
TRACE,
-1,"-Delay for processing time DISC(
0.12,5,0.47,15,0.9,25,0.96,35,1.0,45 )\n":;
84$
DELAY:
DISC( 0.12,5,0.47,15,0.9,25,0.96,35,1.0,45 );
166$
TRACE,
-1,"-Releasing resource\n":;
85$
RELEASE:
cab_R,1;
149$
DELAY:
0.;
171$
TRACE,
-1,"-Transferred to station finish\n":;
89$
ROUTE:
0.,finish;
;
;
Model statements for module:
Depart 1
;
662
2$
STATION,
finish;
233$
TRACE,
-1,"-Arrived to station finish\n":;
203$
DELAY:
0.;
225$
COUNT:
finish_C,1;
230$
TALLY:
finish_Ta,Interval(QueueTime),1;
240$
TRACE,
-1,"-Disposing entity\n":;
232$
DISPOSE;
663
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
( 2 ‫ق اآة‬C) 342 ‫دة‬#
‫ هـ‬1423/1422 3 [‫ ا‬M ` 3? U‫ا@ ر ا‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
:3 ‫ ا ] ا‬3; S‫ا‬2:‫وا و ا‬0‫ ا‬M M ` ‫اح‬
SETS
TRANSIT
AGAIN
OCCUPIED
STORAGE
TABLE
GENERATE
GATE SNF
ENTER
ADVANCE
LEAVE
TABULATE
TERMINATE
ADVANCE
TRANSFER
2
M1,100,100,20
(Exponential(1,0,200))
SETS,OCCUPIED
SETS
180,60
SETS
TRANSIT
1
300,60
,AGAIN
:‫ا ‚ال ا‬
%"7 ‫ ?! إ ا‬G‫ ا‬M 9 ،!? G‫ ا‬, ,"9‫ ت ا‬-2 %"7 3; ‫ و‬/ ‫ و‬6‫ ا‬M "9
.? J‫ د‬10 ± 6 M‫ن آ‬2 ‫ ?! "ل ز‬G‫ و ا‬/ ‫ و‬6‫م ا‬9 .,:J‫ د‬5 ± 5 M‫ن آ‬2 ‫"ل ز‬
Mf` ‫ ا‬M "‫ن ان ا‬2 G‫ ا‬-‫ إذا و‬. ! / , ‫ و‬/ ! 6‫ ا‬, ‫ا‬2f`9 !? G‫ا‬
100 , ,9 U 6 3‫ آ‬6 GPSS ‫ ام‬.3 ‫ ا‬Mf` ‫ ا‬M "‫ ر ا‬9 &; ‫ل‬2YO &9
.‫ م‬N‫ ! ا‬, ‫ ءات ا‬[email protected]‫ ا‬M‫ آ‬-‫ أو‬.‫ن‬2 ‫ز‬
: ‫ا ‚ال ا‬
MH‫ ة و‬100 &?‫ا‬- %J‫ و‬GPSS 3; ‫ول‬0‫ال ا‬A‫ ا‬3; ‫ر‬2‫آ‬. ‫ ا ] ا‬M‫أ( أد‬
TRANSIT ‫ول‬H‫ا‬
ˆ` ‫ @ ج‬, ‫ ا‬,? [email protected]‫ ا‬R -‫ أ‬CLOSE ‫ و‬WRITE ‫ و‬OPEN S‫ا‬2:‫ب( ام ا‬
EXCEL ,7‫ا‬2 ‫ول‬H‫ا‬
664
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ هـ‬1423/1422 ‫ ا‬/ W1‫ر ا‬60ƒ /# ‫إ= ت‬
( 2 ‫ق اآة‬C) 342 ‫دة‬#
:‫إ= ا ‚ال اول‬
2
0‫ا‬
2 !I6‫ و‬," &7"9‫ن و‬G ‫ع‬2 ! SETS !? /‫"ف ا‬9
TRANSIT
TABLE
M1,100,100,20 0‫ا‬
M1 ‫ م‬N‫ ا‬3; ‫ ! ا ور‬G ‫اري‬/I ‫ول‬- 2‫ول وه‬- ‫ع‬2 ! TRANSIT !? /‫"ف ا‬9
20 ‫ ت‬b`‫ ود ا‬100 ,b`‫ ا‬,"‫ و‬100 ‫و‬0‫ ا‬,b`‫ ا‬,9‫ د & ا‬9‫ " ! و‬
GENERATE
(Exponential(1,0,200))S :‫ا‬
‫ل‬2'2‫ ! ! ا‬G , ‫ة ز‬6‫ و‬200 ‫ "ل‬3T‫ ا‬R9‫ز‬2‫ ا‬S6 ! " ‫ ا‬2 ‫م‬2:9
AGAIN
GATE SNF
SETS,OCCUPIED S :‫ا‬
, 6 3`; † ^ ‫ن‬G ‫ ط ان ا‬: 9 6 wO‫ ا‬M " ‫ ور ا‬a 9T S :‫ا ا‬.‫ه‬
‫ا‬.‫“ ان ه‬6T OCCUPIED %" ‫ ا‬S : wO‫ ا‬M " ‫ ا‬M:9 ‫ن‬G ‫ة ! ا‬6‫; و‬2I ‫م‬
AGAIN ‫ ـ‬%" S :‫ا‬
ENTER
SETS S :‫ا‬
,2YO a I 3 ‫ن و‬G ‫ ا‬3; ‫;ة‬2 ‫ات ا‬62‫ ا‬6‫ أ‬wO‫ ا‬M "‫ ا‬gّ 9ُ S :‫ا ا‬.‫ه‬
6‫ا‬2 !9G‫ات ا‬6‫‹ د و‬:I‫و‬
ADVANCE
180,60 S :‫ا‬
, ‫ ز ! ا‬M[ 9
LEAVE
SETS S :‫ا‬
‫;ة‬2 ‫ن‬G ‫ ا‬3; ,2YO ‫ات ا‬62‫ ا‬6‫ أ‬S :‫ا ا‬.‫ ه‬M"H9 wO‫ ا‬M " ‫ ا‬, ‫ ء‬U‫" إ‬
‫ام‬z
TABULATE
TRANSIT S :‫ا‬
TRANSIT ‫اري‬/‫ول ا‬H‫ إ ا‬wO‫ ا‬M " ‫ ز ! ا ور‬,; V S :‫ا ا‬.‫م ه‬2:9
TERMINATE
1 S :‫ا‬
6‫ا‬2 ‫ ص اد ا آ ة‬:‫ إ‬%9‫ م و‬N‫ ! ا‬wO‫ ا‬M " ‫وج ا‬
OCCUPIED ADVANCE
300,60 S :‫ا‬
M[ 9‫ و‬,2YO ‫ن‬G ‫ات ا‬6‫ و‬R - ‫ن‬2‫ آ‬, 6 3; wO‫ ا‬M " ‫ل ا& ا‬2 9 ‫ي‬.‫ ا‬S :‫ا ا‬.‫ه‬
‫ م ة اي‬N ‫ ور‬,‫ إ دة ا و‬MJ ‫ ر‬[email protected]‫ز ! ا‬
TRANSFER
,AGAIN S :‫ا‬
AGAIN ‫ ـ‬%" ‫ ا‬S: ‫ ري‬-‫ وإ‬3C ^ M92 I
SETS
STORAGE
:‫إ= ا ‚ال ا‬
(S 7‫ب ! ا‬27 ‫ ا‬MJ‫ & ) ا‬/‫ أ‬w ‫ ا‬3; ] ‫ا‬
GENERATE
TRANSFER
SEIZE
ADVANCE
RELEASE
5,5
BOTH,,BAKR
AHMD
10,6
AHMD
665
BAKR
KHLD
TERMINATE
TRANSFER
SEIZE
ADVANCE
RELEASE
TERMINATE
SEIZE
ADVANCE
RELEASE
TERMINATE
1
BOTH,,KHLD
BAKRS
10,6
BAKRS
1
KHLDS
10,6
KHLDS
1
:]? ‫ا‬
GPSS World Simulation Report - OR342F22223TEST.5.1
START TIME
END TIME BLOCKS FACILITIES STORAGES
0.000
527.111
15
3
0
NAME
AHMD
BAKR
BAKRS
KHLD
KHLDS
LABEL
LOC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
BAKR
KHLD
FACILITY
AHMD
BAKRS
KHLDS
VALUE
10001.000
7.000
10003.000
12.000
10004.000
BLOCK TYPE
GENERATE
TRANSFER
SEIZE
ADVANCE
RELEASE
TERMINATE
TRANSFER
SEIZE
ADVANCE
RELEASE
TERMINATE
SEIZE
ADVANCE
RELEASE
TERMINATE
ENTRIES UTIL.
38
0.742
33
0.625
29
0.538
ENTRY COUNT CURRENT COUNT RETRY
100
0
0
100
0
0
38
0
0
38
0
0
38
0
0
38
0
0
62
0
0
33
0
0
33
0
0
33
0
0
33
0
0
29
0
0
29
0
0
29
0
0
29
0
0
AVE. TIME
10.291
9.987
9.782
AVAIL. OWNER PEND INTER RETRY DELAY
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
:, ‫و‹ ا ?] ا‬
‫ن‬2 ‫ ز‬29 , ‫ن و‬2 ‫ ز‬33 , / ‫ن و‬2 ‫ ز‬38 , 6‫ م ا‬J ‫ن‬2 ‫ ز‬100 ! -1
% 53.8 ‫ و‬% 62.5 / ‫ و‬% 74.2 6‫ ا‬, "; -2
‫ة‬6‫ و‬9.78 ‫ و‬, ‫ة ز‬6‫ و‬9.99 /‫ و‬, ‫ة ز‬6‫ و‬10.29 60 , ‫ ز ! ا‬w2 -3
, ‫ز‬
: ‫ ‚ال ا‬/ =‫إ‬
SETS
TRANSIT
AGAIN
STORAGE
TABLE
GENERATE
GATE SNF
ENTER
2
M1,100,100,20
(Exponential(1,0,200))
SETS,OCCUPIED
SETS
666
OCCUPIED
ADVANCE
LEAVE
TABULATE
OPEN
WRITE
CLOSE
TERMINATE
ADVANCE
TRANSFER
180,60
SETS
TRANSIT
("OR342TEST.TXT")
M1
1
300,60
,AGAIN
GPSS ! ]? ‫ا‬
GPSS World Simulation Report - Untitled Model 3.1.1
START TIME
0.000
END TIME
20542.415
NAME
AGAIN
OCCUPIED
SETS
TRANSIT
LABEL
AGAIN
OCCUPIED
STORAGE
SETS
FACILITIES
0
STORAGES
1
VALUE
2.000
11.000
10000.000
10001.000
LOC
1
2
3
4
5
6
7
8
9
10
11
12
BLOCK TYPE
GENERATE
GATE
ENTER
ADVANCE
LEAVE
TABULATE
OPEN
WRITE
CLOSE
TERMINATE
ADVANCE
TRANSFER
ENTRY COUNT CURRENT COUNT RETRY
101
0
0
139
0
0
101
0
0
101
1
0
100
0
0
100
0
0
100
0
0
100
0
0
100
0
0
100
0
0
38
0
0
38
0
0
CAP. REM. MIN. MAX.
2
1
0
2
TABLE
TRANSIT
BLOCKS
12
MEAN
297.446
ENTRIES AVL.
101
1
STD.DEV.
218.612
100.000
200.000
300.000
400.000
500.000
600.000
700.000
800.000
900.000
1000.000
1100.000
AVE.C. UTIL. RETRY DELAY
0.880 0.440
0
0
RANGE
-
200.000
300.000
400.000
500.000
600.000
700.000
800.000
900.000
1000.000
1100.000
1200.000
RETRY FREQUENCY CUM.%
0
43
43.00
29
72.00
0
72.00
12
84.00
9
93.00
1
94.00
2
96.00
1
97.00
0
97.00
2
99.00
1
100.00
EXCEL ‫ا ?] ام‬
447.19104
120.9797
142.45752
1159.576
141.44256
100
Bin
Frequency
200
100
0
300
200
43
153.0858
400
300
29
224.15124
500
400
0
187.07448
600
500
12
473.57184
700
600
9
187.85268
800
700
1
667
138.25368
900
800
2
583.11864
1000
900
1
126.55968
1100
1000
0
210.52992
1200
1100
2
1200
1
166.04964
202.2108
More
221.46168
144.26412
170.22144
151.45536
564.96312
401.00184
168.51948
227.982
493.75908
645.29976
128.09292
172.87824
214.55064
134.52924
238.19016
523.35684
188.38032
156.58548
199.62912
225.40236
214.041
1098.33264
163.29384
709.89768
195.2046
212.42136
403.98228
207.80292
874.81932
223.1532
512.68284
210.61992
195.47808
230.361
170.83992
190.97136
166.10148
205.11792
528.2358
213.90372
668
0
124.18656
131.94768
232.80108
443.54328
441.855
579.49092
1159.57632
787.90956
234.73992
458.39088
217.89816
215.5128
234.14784
149.37048
120.97968
200.424
577.71828
122.3448
148.4562
214.66848
122.07684
169.5528
184.78092
225.53004
212.53392
153.53736
213.2232
128.63448
145.53648
206.16264
489.95664
560.03004
470.44152
125.72004
198.56412
1037.46348
513.23496
405.47844
135.97596
183.97836
485.02836
214.5666
161.3094
122.68596
175.62636
225.71892
669
‫و‪ 7I “6‬ا ?]‬
‫‪670‬‬
‫ا ا ا‬
‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
‫ هـ‬1421-1420 ‫ول‬0‫ ا‬M ` 3? U‫ ر ا‬T‫ا‬
(2 ‫ق ا آ ة‬C ) P 342 ‫ا دة‬
‫ت‬2' ‫ث‬r` ! G‫ا‬
:, ‫ ا‬/K'‫ = ! ا‬3 S-‫ا‬
:‫ا ‚ال اول‬
: U ,[ ‫ أ‬37‫ و أ‬, ‫ ت ا‬7 ‫ف ا‬
(a) System state (b) Entity
Simulation clock.
(c) Attributes
(d) List
(e) Event
(f) Event list
(g) Activity (h)
:‫ا ‚ال ا‬
A taxicab company operates one vehicle during the 9:00 A.M. to 5:00 P.M. period. Currently,
consideration is being given to the addition of a second vehicle to the fleet. The demand for taxi
follows the distribution shown:
Time between Calls (Minutes)
Probability
15
0.14
20
0.22
25
0.43
30
0.17
35
0.04
The distribution of time to complete a service is as follows:
Service Time (Minute)
Probability
5
0.12
15
0.35
25
0.43
35
0.06
45
0.04
a) Simulate the operation of the system for one day by hand.
b) Using ARENA simulate five individual days of operation of the current system and
the system with an additional taxicab. Compare the two systems with respect to the
waiting times of the customers and any other measures that might shed light on the
situation ( like vehicle utilization etc.)
671
‫ا ا ا‬
‫‪ %J‬ا@‪ 6‬ء و ‪2‬ث ا" ت‬
‫دة ‪C ) P 342‬ق ا آ ة ‪( 2‬‬
‫إ ر ا` ‪ M‬ا‪0‬ول ‪ 1421‬هـ‪ 1422/‬هـ‬
‫ا‪ 3 ! G‬ت‬
‫أ‪ R - S-‬ا‪ ,b0‬ا ‪:,‬‬
‫ا ‚ال اول‪:‬‬
‫ا( ف ‪ ,:9C‬آ ة ا‪60‬اث ا ` ‪ Discrete-event simulation method ,‬و أذآ‬
‫أ [‪U ,‬‬
‫ب( ‪ J‬رن ! ‪- ,:9C‬و‪ ,‬ا‪60‬اث ‪ Event schedualing‬و‪ M `I ,:9C‬ا" ت ‪Process‬‬
‫‪ 3; interaction‬ا آ ة‬
‫ح( ‪ J‬رن ! ‪:I ,/ /‬م ز ! ا آ ة ا " ة ا‪60‬اث ‪Next event time‬‬
‫‪ advance‬و ا[ ‪Fixed increment time advance ,‬‬
‫ا ‚ال ا‪:‬‬
‫آ‪2/9 , G‬ن ! د ! ا‪2‬ا‪ 3‬آ‪ N & %U M‬م ‪2 C‬ر ‪ ، FIFO‬أي ز ‪2‬ن ‪M /9‬‬
‫ا ‪ R ,‬ا دم ا‪0‬ول ‪ &H9‬إ ا دم ا[ ‪ 3‬و ! " إآ & ا ‪ R ,‬ا دم ا[ ‪ Y9 3‬در‬
‫ا‪ N‬م‪` .‬ض أن ز ! ! ا‪2'2‬ل ‪ !? G‬دم ا‪0‬ول & ‪2I‬ز‪ R9‬ا‪ w2 3‬د‪,:J‬‬
‫وا‪6‬ة‪ .‬ز ! ا ‪ ,‬ا دم ا‪0‬ول ‪ U‬أ‪2I f9‬ز‪ R9‬ا‪ 0,7 w2 3‬د‪ ,:J‬و ا دم‬
‫ا[ ‪2I U 3‬ز‪ R9‬ا‪ 0،9 w2 3‬د‪ .,:J‬أو‪ -‬ا ‪: GPSS 3‬‬
‫ت( أ‪-‬ي آ ة ‪ N‬م "د ‪ 100‬ز ‪2‬ن و‪J‬ر ‪ w2‬ز ! ا@‪ N‬ر ‪ w2 ، !? G‬د‬
‫ا‪ 3; ،!? G‬آ‪2 C ! M‬ر ا د ! و‪J‬ر ;" ‪ ,‬آ‪ ! M‬ا د !‪.‬‬
‫ث( `ض أ& ‪; -29‬ة ز ‪ ! &-2 ,‬ا دم ا‪0‬ول إ ا دم ا[ ‪ 3‬وا‪2I U 3‬ز‪R9‬‬
‫ ‪ ! MX‬د‪ ,:J‬و‪X‬ث د‪ .? J‬أ إ‪-‬اء ا آ ة ‪ W I‬ه‪ 5.‬ا‪N‬وف وأو‪ -‬ا‪9:‬ات‬
‫ا ‪.,:‬‬
‫ج( `ض أن ‪ ! %20‬ا‪ 9T !? G‬ج إ ‪ ,‬ا دم ا[ ‪ Y9 M 3‬در ا‪ N‬م " إآ ل‬
‫ا ‪ R ,‬ا دم ا‪T‬ول‪ .‬أ‪ -‬ا آ ة ‪ W I‬ه‪ 5.‬ا‪N‬وف وأو‪ -‬ا‪9:‬ات ا ‪.,:‬‬
‫‪672‬‬
‫‪ %‬ا ا‪ ! 6‬ا‪%6‬‬
‫ء و ‪2‬ث ا" ت‬
‫‪ %J‬ا@‪6‬‬
‫آ‪ ,‬ا"‪2‬م‬
‫‪ ," -‬ا ‪2" g‬د‬
‫ا@ ر ا[ ‪ 0 3‬ل ا` ‪ M‬ا[ ‪ 1422/1421 3‬هـ‬
‫ دة ‪ ) P 342‬ا آ ة ‪( 2‬‬
‫ا‪, 2 :! G‬‬
‫أ‪ 3 S-‬وا‪ ! w:; 6‬ا‪ ,b0‬ا ‪:GPSS WORLD ,‬‬
‫)أ( ‪ ! ," 9C ! ,"7J R I‬ا" ت‪ ،‬آ‪ .‹ ` !:J RI U M‬ا" ‪ ,‬ا‪0‬و‬
‫‪ I‬ج إ ‪ ! 20%‬ا‪ " R7:‬د ‪ . U" I‬ا" ! ا[ ‪ ,‬وا[ [‪ I ,‬ج آ‪ U M‬إ ‪ 15%‬و‬
‫‪ ! 5%‬ا‪ " R7:‬د ‪ U" I‬ا‪2‬ا‪ ! 60% .3‬ا‪ R7:‬ا " د ‪2/I U" I‬ن ‪ &` I‬و ‪.I‬‬
‫‪ ، scrapped‬واـ ‪ 40%‬ا ‪ I ,J‬ج ا‪ 3‬إ دة " ‪ ! ,H‬ا" ‪ ,‬ا‪ U %I 3‬ا;‪.‬‬
‫' ‪9- ,"7J ,‬ة ‪ 3; %9‬ا ‪ w2‬آ‪ 30 M‬د‪2 ,:J‬ز‪ R9‬ا‪ .3‬ا‪ , " ! G‬ا‪T‬و ‪7"9‬‬
‫‪H‬ول ا ‪:3‬‬
‫‪Time For First Process‬‬
‫‪0.15‬‬
‫‪0.29‬‬
‫‪0.22‬‬
‫‪0.16‬‬
‫‪0.13‬‬
‫‪0.05‬‬
‫‪45‬‬
‫‪38‬‬
‫‪32‬‬
‫‪21‬‬
‫‪14‬‬
‫‪10‬‬
‫‪Frequency‬‬
‫)‪Process time (mins‬‬
‫ا" ‪ ,‬ا[ ‪YI ,‬ق ‪ 15±6‬د‪ ? J‬وز ! ا" ‪ ,‬ا‪0‬ة & ‪2I‬ز‪ 24 w2 3"C R9‬د‪ ,:J‬و‬
‫إ اف " ري ‪ 4‬د‪ 6 .? J‬آ‪ 3‬ت ا ‪ R‬ـ ‪ ! ., / ,"7J 100‬ا‪ ! G‬ا‪h‬زم ‪g.‬‬
‫ود ا‪ R7:‬ا ;‪.,V2‬‬
‫أو‬
‫)ب( ‪G‬ون ] ‪2 & %/ 9 3? U‬ا‪ ,7‬ا‪ ,"-‬دور‪ ,9‬ا‪ . 2‬ا ‪G‬ون ا@ ا?‪2/9 3‬ن‬
‫! ‪ 1000‬و‪6‬ة‪ .‬ا‪ S7‬ا‪ 40 ! Y9 3 2‬و ‪ 63‬و‪6‬ة و ‪ 6‬ل وي‪ .‬ا ‪G‬ون‬
‫ا ‪U‬ف ه‪ 1000 2‬و‪6‬ة‪ ،‬اي ان ‪ M9"I‬ا ‪G‬ون ‪ S7 %9‬ا`ق ! ا ‪G‬ون ا ‪2-2‬د و‬
‫‪1000‬و‪6‬ة‪; .‬ذا آ ن ا ‪G‬ون ا ‪2-2‬د ه‪ 800 2‬و‪6‬ة او اآ[ ;! ‪"9‬ل ا ‪G‬ون ‪g.‬‬
‫ا‪2T‬ع‪ .‬ا‪O‬آ‪ N M "I ,‬م ‪ ,‬ا‪ 9‬م ‪2z‬ع‪ .‬ز ! ا‪:‬م ‪ M'2 lead time‬ا‪ ,7‬ه‪2‬‬
‫ا‪2‬ع وا‪ 6 .6‬آ‪ N 3‬م ا ‪G‬ون ة ‪29 200‬م و‪ ; I‬إذا آ ن ه ك اي ‪G ‹:‬ون‬
‫‪.stockouts‬‬
‫‪673‬‬
‫ا ا ا‬
‫ هـ‬1422/1421 3 [‫ ا‬M `‫ ل ا‬0 3 [‫ ر ا‬z , ‫ ت‬-‫إ‬
(2 ‫ ) آ ة‬P 342 ‫ا ة‬
(, ‫ ا‬,?‫ا‬2O"‫اد ا‬0‫ ا‬,H _I ]? ‫ ا‬:,N6 ) (‫ال )أ‬A , -‫إ‬
*****************************************************************
*
Quality Control Program
*
*
Time units are in minutes
*
*****************************************************************
RMULT
93211
* Definitions
Transit
TABLE
M1,100,100,20
;Transit Time
Process
FUNCTION
RN1,D7
0,0/.05,10/.18,14/.34,21/.56,32/.85,38/1.0,45
*****************************************************************
GENERATE
(Exponential(1,0,30))
ASSIGN
1,FN$Process
;Process time in P1
Stage1
SEIZE
Machine1
ADVANCE
P1
;Process 1
RELEASE
Machine1
ADVANCE
2
;Inspection
TRANSFER
.200,,Rework1
;20% Need rework
*****************************************************************
Stage2
SEIZE
Machine2
ADVANCE
15,6
;Process 2
RELEASE
Machine2
ADVANCE
2
;Inspection
TRANSFER
.150,,Rework2
;15% Need rework
*****************************************************************
Stage3
SEIZE
Machine3
ADVANCE
(Normal(1,24,4))
;Process 3
RELEASE
Machine3
ADVANCE
2
;Inspection 3
TRANSFER
.050,,Rework3
;5% need rework
TABULATE
Transit
;Record transit time
TERMINATE
1
*****************************************************************
Rework1
TRANSFER
.400,,Stage1
TERMINATE
Rework2
TRANSFER
.400,,Stage2
TERMINATE
Rework3
TRANSFER
.400,,Stage3
TERMINATE
(, ‫ ا‬,?‫ا‬2O"‫اد ا‬0‫ ا‬,H _I ]? ‫ ا‬:,N6 ) (‫ال )ب‬A , -‫إ‬
*********************************************************************
*
*
Periodic Review Inventory Model
*
*
Time units are in days
*********************************************************************
* Definitions of non block entities
674
RMULT
39941
Stock
STORAGE
10000
;Warehouse can hold 10000
Stock
TABLE
S$Stock,100,100,20
;Table for inventory amts
Orderqty VARIABLE
Target-S$Stock
;Order quantity
Demand
VARIABLE
[email protected]+40
;Daily demand
Target
EQU
1000
;Initial stock level
Reorder EQU
800
;Reorder point
*********************************************************************
* The reorder process
GENERATE
5,,,,1
;Review xact, Priority=1
TEST L
S$Stock,Reorder,Skip ;Is stock < Reorderpt
ASSIGN
2,V$Orderqty
;Parameter 2=Order quantity
Custwait ADVANCE
5
;Lead time is 5 days
ENTER
Stock,P2
;Stock increases by P2
Skip
TERMINATE
;Ordering xact is finished
*********************************************************************
* The daily demand decrements quantity on hand
GENERATE
1
;Daily demand transaction
ASSIGN
1,V$Demand
;Parameter 1(P1)=daily
demand
TABULATE
Stock
;Record daily stock
TEST GE
S$Stock,P1,Stockout ;Can order be filled
LEAVE
Stock,P1
;Remove demand from stock
TERMINATE 1
;Daily timer
Stockout TERMINATE 1
;Daily timer
*********************************************************************
* Initialize the inventory
GENERATE
,,,1,10
;Set initial stock
ENTER
Stock,Target
;Set init stock level=target
TERMINATE
;Xact is terminated
675
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ا@ را‬
( 2 ‫ ) ا آ ة‬P 342 ‫ دة‬
‫ ت‬3 :! G‫ا‬
:, ‫ ا‬,b0‫ ا‬3 S-‫أ‬
:‫ول‬0‫ال أ‬A‫ا‬
” ‫ة‬6‫ا‬2‫ة ا‬9H‫ي ا‬O9 ،&? U" ?‫ا‬H‫ د ! ا‬29 ?‫ا‬- R? ‫ي‬O9
” ˆC‫ا‬J R ‫ ع‬I ‫م‬2‫ ا‬,9 U 3; 3:I 3‫ا? ا‬H‫ ا‬.‫ ل‬9‫ ر‬2 ” U"9‫ ل و‬9‫ ر‬1.50
‫ا ;ن‬./‫ وه‬،?‫ا‬- 10 ! ‫ن‬2/I ‫م‬G6 3; ‫ي ! ا‬OI ?‫ا‬H‫ ا‬.‫ة‬6‫ا‬2‫ة ا‬9H ,‫ ه‬20
‫ ه ك‬-2I R? ‫ ! ة ا‬. 29 ‫ة‬9- d‫ ا‬... ‫ او‬70 ‫ او‬60 ‫ او‬50 ‫ي إ‬O9 ?‫ا‬H‫ ا‬R?
‫ت‬T 6 ‫م "†" و‬29‫س &" و‬e T" ‫م‬29‫" و‬-" ‫م‬29 ،‫ ر‬q ‫ م‬90‫اع ! ا‬2‫ أ‬,XX
‫ع‬2 S6 ?‫ا‬H‫ ا‬3 S7‫ ا‬R9‫ز‬2I .(! ‫أ ! ا ر‬J‫ )إ‬3‫ا‬2‫ ا‬0.35,0.45,0.20
:3 ‫ول ا‬H 7"9 ‫م‬2‫ا‬
Demand Probability Distribution
Demand
40
50
60
70
80
90
100
Good
Fair
0.03
0.05
0.15
0.20
0.35
0.15
0.07
0.10
0.18
0.40
0.20
0.08
0.04
0.00
Poor
0.44
0.22
0.16
0.12
0.06
0.00
0.00
.a ‫ أ ر‬: 9 36 29 ?‫ا‬H‫ ا‬R? U9O9 3‫ا? ا‬H‫ ! ا‬M[ 0‫ ا"د ا‬9 I ‫ب‬27 ‫ا‬
. 29 ‫ة‬9- 80,70,60,50 R? ‫ب ; إذا أى ا‬27 ‫ د ا‬[email protected] 9‫و‬9 ‫ م‬9‫ أ‬10 3‫ آ‬6
:,Y ‫ر ح ! ا‬0‫ ا‬S I :,N6
P=R–C–L+S
:3"I ‫ز‬2 ‫ ا‬P6
P = Profit (‫ر ح‬0‫)ا‬
R = Revenue from sales (3/‫) ” ا " ت ا‬
C = Cost of newspapers (?‫ا‬H‫ ا‬,`/I)
L = Lost profit from excess demand (SC : I ‫دة ! م‬2:` ‫ر ح ا‬0‫)ا‬
S = salvage from sale of scrap papers (,: ‫ا? ا‬H‫ ا‬R ! R- ‫)ا ” ا‬
676
:3 [‫ال ا‬A‫ا‬
R9‫ز‬2‫ ا‬%J 3; ‫ ا ت‬e"I ., J‫ ت ر‬, ‫و ت‬/‫ إ‬,‫ آ‬3; R ‫ ا‬%J ‫م‬2:9
%H6 .‫ن‬2‫ز‬2 ‫ ا‬U79 3‫ ت ا‬/ ‫ة "ض‬G‫ ه‬- S 3; ,b"I ,( ,7‫ا‬2 3? :I M/O
:, ‫ ا‬,‫ ا‬7"9 S7‫ا‬
Order Size
6
Frequency 0.10
12
0.25
18
0.30
24
0.15
30
0.12
36
0.05
48
0.03
, X 120 SC M/ ,b"‫ ز ! ا‬. ‫زع أ‬2 ,:J‫ د‬15 ‫ ت‬7‫ل ا‬2'‫ ! ! و‬G‫ ا‬w2
3; , J‫] ا ت ا‬9 R ‫ ا‬%J .S7‫ ا‬3; e"I , J‫ ر‬, M/ ‫ان‬2X 10 ‫ إ‬,; [email protected]
.,:J‫ د‬455 3; ‫ة‬6‫ و‬60 %H ‫ ت‬2 H
:, ‫ ت ا‬2" ‫ ا‬37"I 3/ ,‫آ‬O‫ ط ا‬O ! ‫ م‬9‫ أ‬10 3‫ آ‬6 GPSS ‫ام‬
,b"‫ ا‬%J 3; ‫ة‬N ‫ ت ا‬7‫ د ا‬w2 -7
‫م‬29 M‫ آ‬,‫ز‬2 ‫ ا‬, J‫ ا ت ا‬, ‫ آ‬-8
‫ ت‬7 transit times , :@‫ ت ا‬J‫و‬0‫ ا‬R9‫ز‬2I -9
677
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2
‫ءو‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1422/1421 3 [‫ ا‬M ` 3? U‫ ر ا‬z , ‫ ت‬-‫إ‬
( 2 ‫ ) ا آ ة‬P 342 ‫دة‬
:‫ول‬0‫ال ا‬A‫ ا‬, -‫إ‬
:‫ ري‬0‫م ا‬2‫ع ا‬2 (1) ‫ول‬- ‫ن‬2/
News Day
Prob.
Cum. Prob
Random Digit
Good
0.35
0.35
01-35
Fair
0.45
0.80
36-80
Poor
0.25
1
81-00
:H‫ ري ا‬0‫م ا‬2 S7 (2) ‫ول‬- ‫ن‬2/
Demand
Prob.
Cum. Prob.
Random Dig.
40
0.03
0.03
01-03
50
0.05
0.08
04-08
60
0.15
0.23
09-23
70
0.20
0.43
24-43
80
0.35
0.78
44-78
90
0.15
0.93
79-93
100
0.7
1
94-00
:& ‫س‬e T ‫ ري‬0‫م ا‬2 S7 (3) ‫ول‬- ‫ن‬2/
Demand
Prob.
Cum. Prob.
Random Dig.
40
0.10
0.10
01-10
678
50
0.18
0.28
11-28
60
0.40
0.68
29-68
70
0.20
0.88
69-88
80
0.08
0.96
89-96
90
0.04
1
97-00
: †‫ ري ا‬0‫م ا‬2 S7 (4) ‫ول‬- ‫ن‬2/
Demand
Prob.
Cum. Prob.
Random Dig.
40
0.44
0.44
01-44
50
0.22
0.66
45-66
60
0.16
0.82
67-82
70
0.12
0.94
83-94
80
0.06
1
95-00
:‫ول‬0‫م ا‬2 ‫ ة‬/ ‫أ ا‬
(C = 75 SR ) ‫ ل‬9‫ ر‬75 " ‫ة‬9- 50 = ‫اة‬O ‫ا? ا‬H‫د ا‬
& ‫س‬e T 64 = A.1. ‫ول‬- ! 3?‫ا‬2O %J‫ ر‬S :‫ ري‬0‫م ا‬2‫ع ا‬2
50 = S7‫( ا‬3) ‫ول‬- ! ‫ و‬13 = 3?‫ا‬2O %J‫ ر‬S :‫ول‬0‫م ا‬2 S7‫ا‬
P=R–C–L+S
= 2x50 – 1.5x 50 – 0 + 0 = 25 SR
:3 [‫م ا‬2‫ا‬
‫ة‬9- 50 = ‫اة‬O ‫ا? ا‬H‫د ا‬
† 82 = A.1. ‫ول‬- ! 3?‫ا‬2O %J‫ ر‬S :‫ ري‬0‫م ا‬2‫ع ا‬2
50 = S7‫( ا‬4) ‫ول‬- ! ‫ و‬45 3?‫ا‬2O"‫ ا‬%J‫ ا‬:3 [‫م ا‬2 S7‫ا‬
P=R–C–L+S
= 2x50 – 1.5x 50 – 0 + 0 = 25 SR
:3 ‫ول آ‬- ‫ن‬2/‫ا و‬./‫وه‬
Day
R.D.
Newsday
Newsday
R.D.
Demand
Demand
R L
S
P
1
2
64
82
Fair
Poor
13
45
50
50
100
100
0
0
0
0
25
25
3
4
26
35
Good
Good
93
80
90
90
100
100
20
20
0
0
5
5
679
5
17
Good
04
50
100
0
0
25
6
45
Fair
20
50
100
0
0
25
7
03
Good
88
90
100
20
0
5
8
72
Fair
03
40
80
0
2
7
9
83
Poor
78
60
100
5
0
20
10
69
Fair
03
40
80
0
2
7
‫ ل‬9‫ ر‬14.5 2‫م ه‬2‫ ا‬3; ‫ة‬9- 50 R? ‫ ; إذا اي ا‬3 2‫ ا‬a ‫ ا‬w2 ‫ ان‬H ‫ول‬H‫! ا‬
.3 2‫ ا‬a ‫ ا‬w2 S ‫ و‬29 ‫ة‬9- 80 ‫ و‬70 ‫ و‬60 ‫ر ا ـ‬/
:3 [‫ال ا‬A‫ ا‬, -‫إ‬
:3 ‫ آ‬GPSS ‫ذج ام‬2 ‫ن‬2/
*
Time Unit is one hour
*
Sizeorder FUNCTION
RN1,D7
;Order size
.10,6/.35,12/.65,18/.80,24/.92,30/.97,36/1.0,48
Transit
TABLE
M1,.015,.015,20
;Transit time
Number
TABLE
X1,100,100,20
;No. packed each day
Ptime
VARIABLE
.0028#P1+0.0334
;Packing time
Amount
EQU
1000
;Initial stock amount
Stock
STORAGE
4000
;Warehouse holds
; 4000 units
*********************************************************************
GENERATE
(Exponential(1,0,0.25)) ;Order arrives
ASSIGN
1,1,Sizeorder
;P1=order size
TEST GE
S$Stock,P1,Stockout
;Is stock sufficient?
LEAVE
Stock,P1
;Remove P1 from stock
QUEUE
Packing
SEIZE
Machine
;Get a machine
DEPART
Packing
ADVANCE
V$Ptime
;Packing time
RELEASE
Machine
;Free the machine
SAVEVALUE 1+,P1
;Accumulate no. packed
TABULATE
Transit
;Record transit time
TERMINATE
Stockout TERMINATE
*********************************************************************
GENERATE
0.75,0.08334,1
;Xact every 40+/-5 mins
ENTER
Stock,60
;Make 60, Stock
*
increased by 60
Stockad
TERMINATE
*********************************************************************
GENERATE
8
;Xact every day
TABULATE
Number
SAVEVALUE 1,0
TERMINATE 1
*********************************************************************
GENERATE
,,,1,10
;Initial stock xact
ENTER
Stock,Amount
;Set initial stock
TERMINATE
]? 9‫ ر‬:I ‫ ! ة‬6‫ وا‬:]? ‫ا‬
680
GPSS World Simulation Report - Manufact.1.1
Saturday, May 19, 2001 17:49:40
START TIME
END TIME
0.000
80.000
BLOCKS
FACILITIES
STORAGES
NAME
AMOUNT
MACHINE
NUMBER
PACKING
PTIME
SIZEORDER
STOCK
STOCKAD
STOCKOUT
TRANSIT
LABEL
RETRY
23
1
1
VALUE
1000.000
10009.000
10003.000
10008.000
10004.000
10000.000
10006.000
16.000
13.000
10002.000
LOC
BLOCK TYPE
ENTRY COUNT CURRENT COUNT
1
GENERATE
325
0
2
ASSIGN
325
0
3
TEST
325
0
4
LEAVE
325
0
5
QUEUE
325
0
6
SEIZE
325
0
7
DEPART
325
0
8
ADVANCE
325
0
9
RELEASE
325
0
10
SAVEVALUE
325
0
11
TABULATE
325
0
12
TERMINATE
325
0
13
TERMINATE
0
0
14
GENERATE
105
0
15
ENTER
105
0
16
TERMINATE
105
0
17
GENERATE
10
0
18
TABULATE
10
0
0
0
0
0
0
0
0
0
0
0
0
0
STOCKOUT
0
0
0
STOCKAD
0
0
0
681
19
SAVEVALUE
10
0
20
TERMINATE
10
0
21
GENERATE
1
0
22
ENTER
1
0
23
TERMINATE
1
0
0
0
0
0
0
FACILITY
MACHINE
ENTRIES UTIL. AVE. TIME AVAIL. OWNER PEND INTER RETRY DELAY
325
0.354
0.087 1
0
0
0
0
0
MAX CONT.ENTRY ENTRY(0)AVE.CONT. AVE.TIME AVE.(-0)RETR PACKING
4
0
325
208
0.104
0.026
0.071
0
QUEUE
STORAGE
STOCK
TABLE
TRANSIT
CAP. REM. MIN. MAX.
4000 2928
0 1378
MEAN
0.113
22
6.77
52
22.77
66
43.08
51
58.77
43
72.00
20
78.15
17
83.38
7
STD.DEV.
0.055
ENTRIES AVL. AVE.C. UTIL. RETRY DELAY
7300
1 1132.973 0.283
0
0
RANGE
0.045
RETRY FREQUENCY CUM.%
0
0.060
0.060
-
0.075
0.075
-
0.090
0.090
-
0.105
0.105
-
0.120
0.120
-
0.135
0.135
-
0.150
0.150
-
0.165
0.165
-
0.180
0.180
-
0.195
0.195
-
0.210
0.210
-
0.225
0.225
-
0.240
0.240
-
0.255
0.255
-
0.270
0.270
-
0.285
0.285
-
85.54
17
90.77
8
93.23
2
93.85
3
94.77
3
95.69
2
96.31
1
96.62
5
98.15
6
100.00
NUMBER
622.800
156.046
682
_
0
1
10.00
1
20.00
1
30.00
4
70.00
2
90.00
1
100.00
SAVEVALUE
1
FEC XN
VALUE
443
442
444
300.000
-
400.000
400.000
-
500.000
500.000
-
600.000
600.000
-
700.000
700.000
-
800.000
800.000
-
900.000
RETRY
0
PRI
0
0
0
BDT
80.090
80.343
88.000
VALUE
0
ASSEM
CURRENT
443
442
444
0
0
0
683
NEXT
1
14
17
PARAMETER
684
Ave. , J ! 2‫ وه‬. 0.12 w:; 2‫ ه‬,b"‫ ا‬%J 3; ‫ة‬N ‫ ت ا‬7‫ د ا‬w2 •
.Queue Entity Packing W I 9:‫ ا‬3; Cont.
. Table Number 3; 7" 29 ,‫ز‬2 ‫ ا‬, J‫ ا ت ا‬R9‫ز‬2I •
. ‫ ا‬% , V2 ‫ و‬TRANSIT ‫ول‬H‫ ا‬3; ‫ ت‬7 , :@‫ ت ا‬J‫و‬0‫ ا‬R9‫ز‬2I •
685
‫ا ا ا‬
: ‫ت * ا‬17 /BJ#
w7 37"9 ‫ ا‬M/O‫ ا‬.‫ رات‬7:‫ ا‬,7
‫ ا‬%H ! % `‫ ا‬M: ‫م‬I ‫ ت‬6 6 9
.g.
Station
Travelig
text
Loading
text
Scale
Weighing
text
Queue
Loader Queue
text
_'‫ إ ر‬,6 O‫ ك ا‬I M ‫ ر'`! و " ا‬6‫ ! ا‬6‫ ! ر'_ وا‬M I ,6 M‫آ‬
‫زن‬2‫ " ا‬،,:J‫ د‬2 ± 1 ‫ق‬YI ‫ان‬G ! O‫ ا‬,`'‫ ! ار‬,6‫ ز ! ا‬،‫زن‬2I 3/ ‫وزن‬
., X ‫ ! ة‬O‫ ا‬,`'‫د ا ار‬2"I‫ و‬U ‫`غ‬I‫ رات و‬7:‫ ا‬,7 ‫ ا‬,6 O‫ ك ا‬I
‫ ة‬7" ‫ رات‬7:‫ ا‬,7 ‫دة ! وا‬2"‫ه ب وا‬.‫زن وز ! ا‬2‫ ت ا‬J‫ ! واو‬O‫ ت ا‬J‫" ت او‬9‫ز‬2I
:, ‫اول ا‬H‫ ا‬3;
.M ‫ ا‬, ‫ول از‬- -1
Loading Time
5
10
15
Probability
0.3
0.5
0.2
.‫زن‬2‫ ا‬, ‫ول از‬- -2
Weighing Time
12
16
Probability
0.7
0.3
.‫ رات‬7:‫ ا‬,7
686
‫دة إ‬2"‫ه ب وا‬.‫ ا‬, ‫ول از‬- -3
‫‪Probability‬‬
‫‪0.4‬‬
‫‪0.3‬‬
‫‪0.2‬‬
‫‪0.1‬‬
‫‪Travel Time‬‬
‫‪40‬‬
‫‪60‬‬
‫‪80‬‬
‫‪100‬‬
‫ ‪ R‬ا‪0‬و‪ J‬ت ‪ :I‬س ‪.? J‬‬‫ا ‪27‬ب ‪ , "; 9:I‬آ‪ ! M‬ار'`‪ ,‬ا‪ ! O‬ور'_ ا‪2‬زن و ‪ w2‬ز ! ا@‪ N‬ر ;‪ 3‬آ‪M‬‬
‫‪2 C‬ر‪.‬‬
‫‪ 6 -4‬آ‪ 3‬ا‪ N‬م ا ‪9‬و‪ 9‬ـ ‪ 5‬ر‪6‬ت ‪.,6 M/‬‬
‫‪. -5‬ج ا‪ N‬م ] ا آ ة ‪ GPSS‬ـ ‪ 100‬ر‪.,6 M/ ,6‬‬
‫‪ -6‬آر ا`‪:‬ة ‪ ] 2‬ا آ ة ‪. ARENA‬‬
‫‪ N6‬ت‪:‬‬
‫‪ -4‬ا ‪ M‬ا ‪ ! , 30 9 a‬أ ل ا` ‪ 10 ) .M‬ت ‪:; M/‬ة(‬
‫‪ % 2 ( -5‬ا ‪ 10 M‬ر ‪ f‬ن ‪ 1422‬هـ ا ‪2‬ا; ‪; 25‬ا‪ 2001 9‬م‪.‬‬
‫‪ -6‬ا ‪ O‬رآ‪ ,‬ا‪ RHOI , H‬ا‪ 9G9T‬د ا ‪ O‬رآ! ! ‪. 2‬‬
‫وا ا ‪.;2‬‬
‫د‪ .‬ن ‪ -‬ي‬
‫‪687‬‬
‫ا ا ا‬
‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
( 2 ‫ق ا آ ة‬C) P 342 ‫دة‬
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ا@ ر ا‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
‫ و‬System states ‫ م‬N‫ت ا‬T 6 ‫ ذآ‬R , ‫ ا‬, N0‫ ا‬,‫ را‬,:9C Mf;‫ب( أو'_ أ‬
Activities ‫ م‬N‫ ا‬,7O‫ و أ‬Attributes ‫ ? ت‬/‫ و '` ت ا‬Entities ‫ ? ت‬/‫ا‬
‫` ت‬O ‫ ا‬6e ‫ارئ‬2C %J (3
!:9C RC :I (2 R ! Y' %J (1
Discrete-event Simulation Method , ` ‫اث ا‬60‫آ ة ا‬
,:97 ‫د‬2 : ‫ب( ا‬
,[ ‫ ذآ ا‬R
:‫ا ‚ال ا‬
:, ‫ ا‬GPSS S‫ا‬2J M ‫ ء [ ل‬7‫ إ‬R ‫ ز‬H9 ‫أ( أح‬
1) GENERATE
2) ADVANCE3) ASSIGN 4) TERMINATE
5) TRANSFER
6) TEST
‫ ء‬7‫ إ‬R GPSS ‫ ا آ ة‬,Y U M‫ ] آ‬I _‫ وآ‬Storage ‫ و‬Facility ! ‫ا`ق‬
(‫ب‬
,[ ‫أ‬
: ‫ا ‚ال ا‬
5:00 6‫ و‬6 ' 9:00 ‫ ا`ة‬3; ‫ة‬6‫ ء رة وا‬[email protected]‫ ا‬,[96 ‫ رات‬-eI ,‫ آ‬MYOI
,- ‫ ا‬W ‫ ; اذا آ‬,‫! " درا‬/‫ و‬, X ‫ رة‬,; V‫ إ‬3; ,‫آ‬O‫ ا‬S6 ' /`9 .‫ ا‬
:3‫ ه‬,‫آ‬O‫ ى ا‬," H ‫ ا ت ا‬S6 ‫ة‬-‫ رة ا‬S7‫ ا‬.g‫ ذ‬S7I
Time between calls (Minutes)
Probability
15
0.14
20
0.22
25
0.43
30
0.17
35
0.04
:3 ‫ن( آ‬2 G‫ ا‬M'2I) , ‫ إآ ل‬WJ‫ و‬R9‫ز‬2I‫و‬
Service Time (Minutes)
Probability
5
0.12
15
0.35
25
0.43
35
0.06
45
0.04
‫ ه ك‬W ‫ ; إذا آ‬5‫ار‬J ‫ ذ‬[email protected] ,‫آ‬O‫ ا‬S6 ' I 3/ ‫م‬29 100 ‫ ة‬,‫آ‬O‫ م ا‬N 3‫ آ‬6
., X ‫ رة‬,; [email protected] ,- 6
GPSS ‫ ا آ ة‬,Y ‫ت( ام‬
ARENA ,992 ‫ ا آ ة ا‬,Y ‫ث( و ام‬
688
‫ هـ‬1423/1422 ‫ول‬0‫ ا‬M ` 3? U‫ ر ا‬z ,-‫ذ‬2 , -‫إ‬
(2 ‫ق آ ة‬C) P 342 ‫ا دة‬
:‫ول‬0‫ال ا‬A , -‫إ‬
(‫أ‬
R I R7J ‫ م ه ك‬M/O; R ‫ ا‬,"C‫ إ ا ] و‬N‫ ون ا‬:R ! %J (5
:3? U‫ل ا ] ا‬2 U" HI %9‫ إ ج و‬w 9 I
d‫ ا‬,"7J R HI ‫ ء‬U‫ إ‬,N ،‫ ا@ ج‬w ,"7J ‫ل‬2'‫ و‬,N :‫ م‬N‫ت ا‬T 6
R7:‫ ا‬:‫ ? ت‬/‫ا‬
(R H‫ )ز ! ا‬, ‫ ز ! ا‬،‫ل‬2'2‫ ز ! ا‬:‫ ? ت‬/‫'` ت ا‬
(, ‫ ا‬,"7: ‫ ر‬[email protected]‫ ز ! ا‬XAI ,"7J M‫ ر ) آ‬[email protected]‫ ت ا‬J‫ أو‬:‫ م‬N‫ ا‬,7O‫أ‬
:‫ إ رات ور‬U %/ I ‫ ه ت‬[email protected]‫ ا‬R - 3; ‫ ;ت‬6 ‫ ور‬G 9‫ و‬:!:9C RC :I (6
‫ إ رة ا ور‬YI ,N ،RC :‫ ا ا‬,; 6 ‫ل‬2'‫ و‬,N :‫ م‬N‫ت ا‬T 6
‫ ا ;ت‬:‫ ? ت‬/‫ا‬
‫ل‬2'2‫ ز ! ا‬:‫ ? ت‬/‫'` ت ا‬
( 3; 3‫ ا ;ت ا‬XA9 ‫ا‬.‫ )وه‬RC :‫ة ا‬N ‫ د ا ;ت ا‬:‫ م‬N‫ ا‬,7O‫أ‬
(‫ر‬2"‫ ا‬MJ ‫ ا@ رة‬U M`:I ‫ ا@ رة أو‬a; I ‫ر إ‬2 7‫ا‬
3: ‫ادث‬2 ‫ ا‬%J ‫ا إ‬2 9 ‫ادث او ^ه‬26 3; !
‫ ا‬:`O ‫ارئ‬2C %J (7
‫ا"ج‬
‫ ء ا"ج‬U‫ إ‬,N ،‫ل ا ب‬2'‫ و‬,N :‫ م‬N‫ت ا‬T 6 (8
!
‫ ا‬:‫ ? ت‬/‫ا‬
‫ ز ! ا"ج‬،‫ل‬2'2‫ ز ! ا‬:‫ ? ت‬/‫'` ت ا‬
(3 ‫ ر ب ا‬[email protected]‫ ز ! ا‬XA9 ‫ب‬
M‫ ر ا"ج ) آ‬N‫ ا‬WJ‫ و‬: ‫ م‬N‫ ا‬,7O‫أ‬
, ‫ ط ز‬: ‫ م‬N‫ت ا‬T 6 YI ,:97‫ ا‬5.‫ ه‬3; :, ` ‫اث ا‬60‫ آ ة ا‬,:9C (‫ب‬
, ‫ر‬2 C g‫ [ ل ذ‬.‫ث‬6 U; ‫ ث‬9 3‫ ( وا‬Discrete R7: ! G‫ )أي ان ا‬, `
‫ل ا ;ت إ‬2'‫ و‬.‫ن‬2‫ا‬2 , RI , ` , ‫ ?! أز‬G‫ ا‬M 9 ‫ إذ‬6‫ دم وا‬
.d‫! أ‬:9C RC :I
:3 [‫ال ا‬A , -‫إ‬
( ‫)أ‬
(1) GENERATE A,B,C,D,E
Future Events Chain 40!"(‫( ا) اث ا‬$; *+ j,B‫ و‬Transaction ,! Create A - Mean inter generation time.
B - Inter generation time half-range or Function Modifier.
C - Start delay time. Time increment for the first Transaction.
D - Creation limit.
E - Priority level.
Example: GENERATE 0.1
689
(2) ADVANCE A,B
Future Events Chain 40!"(‫( ا) اث ا‬$; * Transaction ,! ^B
A - The mean time increment.
B - The time half-range or, if a function, the function modifier.
Example: ADVANCE 101.6,50.3
(3) ASSIGN A,B,C
Transaction Parameter ,!(‫ ا‬X, ‫ ل‬,
A - Parameter number of the Active Transaction.
B - Value.
C - Function number.
Example: ASSIGN 2000,150.6
(4) TERMINATE A
‫ء‬8‫ اد ا‬O0‫ وا‬,! *‫ا‬
A - Termination Count decrement. Default is 0.
Example: TERMINATE 1
(5) TRANSFER A,B,C,D
‫] ا(@ د‬0‫ ا‬E‫ ا‬0‫&ك او ا‬
A - Transfer Block mode.
B - Block number or location.
C - Block number or location.
D - Block number increment for ALL Mode.
Examples:
(a) Unconditional Mode
TRANSFER ,New_Place
(b) Fractional Mode
TRANSFER .75,,New_Place
(c) Both Mode
690
TRANSFER BOTH,First_Place,Second_Place
(d) All Mode
TRANSFER ALL,First_Place,Last_Place,2
(e) Pick Mode
TRANSFER PICK,First_Place,Last_Place
(f) Function Mode
TRANSFER FN,Func1,5
(g) Parameter Mode
TRANSFER P,Placemarker,1
(h) Subroutine Mode
TRANSFER SBR,New_Place,Placemarker
(i) Simultaneous Mode
TRANSFER SIM,Nodelay_Place,Delay_Place
(6) TEST O A,B,C
,!(‫ و ل إ"ب ا‬arithmetic condition *%"@‫& ا[&ط ا‬4!G‫ا‬
O - Relational operator. Relationship of Operand A to Operand B for a successful test.
A - Test value.
B - Reference value.
C - Destination Block number.
Example: TEST G C1,70000
(‫)ب‬
,U‫ ا‬M[ ‫ ت و‬J‫و‬0‫ ! ا‬WJ‫ أي و‬w:; 6‫ وا‬M " S2I (,UI) Facility
RELEASE ‫ و‬SEIZE ! :‫م ا‬9
:‫[ ل‬
GPSS BLOCKS
SEIZE
Facility
GPSS BLOCKS
RELEASE Facility
GPSS BLOCKS
691
M[ ‫ و‬STORAGE 0 ," & ‫ د‬9‫ و‬6‫ وا‬M " ! [‫ اآ‬S29 (‫ن‬G ) Storage
LEAVE ‫ و‬ENTER ! :‫م ا‬9 ," 9 I " ‫ن‬G ‫ا‬
:‫[ ل‬
GPSS COMMANDS
SL STORAGE Capacity
GPSS COMMANDS
GPSS BLOCKS
ENTER
SL
GPSS BLOCKS
LEAVE SL
GPSS BLOCKS
:P [‫ال ا‬A , -‫إ‬
calls FUNCTION RN1,D5
0.14,15/0.36,20/0.79,25/0.96,30/1.0,35
sertime FUNCTION RN1,D5
0.12,5/0.47,15/0.9,25/0.96,35/1.0,45
callwait TABLE M1,10,10,20
*
GENERATE FN$calls
QUEUE
cabq
SEIZE
cab
DEPART
cabq
ADVANCE
FN$sertime
RELEASE
cab
TABULATE callwait
TERMINATE 1
GPSS World Simulation Report - Untitled Model 1.1.1
Sunday, January 13, 2002 00:06:22
START TIME
0.000
END TIME
2455.000
NAME
CAB
CABQ
CALLS
CALLWAIT
SERTIME
LABEL
FACILITY
CAB
BLOCKS
8
FACILITIES
1
STORAGES
0
VALUE
10006.000
10005.000
10000.000
10004.000
10002.000
LOC
1
2
3
4
5
6
7
8
ENTRIES
101
BLOCK TYPE
GENERATE
QUEUE
SEIZE
DEPART
ADVANCE
RELEASE
TABULATE
TERMINATE
UTIL.
0.827
ENTRY COUNT CURRENT COUNT RETRY
101
0
0
101
0
0
101
1
0
100
0
0
100
0
0
100
0
0
100
0
0
100
0
0
AVE. TIME AVAIL. OWNER PEND INTER RETRY DELAY
20.099 1
101
0
0
0
0
692
QUEUE
CABQ
MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME
3
1
101
60
0.261
6.337
TABLE
CALLWAIT
MEAN
26.650
STD.DEV.
13.410
RANGE
_
10.000
20.000
30.000
40.000
50.000
60.000
-
10.000
20.000
30.000
40.000
50.000
60.000
70.000
AVE.(-0) RETRY
15.610
0
RETRY FREQUENCY CUM.%
0
7
7.00
27
34.00
39
73.00
13
86.00
9
95.00
3
98.00
2
100.00
CEC XN
101
PRI
0
M1
2450.000
ASSEM
101
CURRENT
3
NEXT
4
PARAMETER
VALUE
FEC XN
102
PRI
0
BDT
2475.000
ASSEM
102
CURRENT
0
NEXT
1
PARAMETER
VALUE
! ‫ أن ز‬H ‫ ر‬[email protected]‫ول ا‬- ! . 2 , 3‫ وه‬% 82.7 3‫ ا رة ه‬,9 "; ‫“ أن‬6
‫ا آ‬- 3 2‫ ? وه‬J‫ د‬26.65 w2 ‫ و‬,:J‫ د‬70 6 M 9 ‫ر رة‬2 7‫ ا‬3; ‫ ر‬[email protected]‫ا‬
:3 ‫اري ا‬/‫ ا رج ا‬3; aV2 2‫ه‬
ARENA ‫)ب( ام‬
693
ARENA Simulation Results
amb - License #9400000
Summary for Replication 1 of 1
Project:
Taxi Cab Problem
Analyst:
Replication ended at time
Run execution date :
1/12/2001
Model revision date:
1/12/2001
: 100.0
TALLY VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Observations
_______________________________________________________________________________
finish_Ta
25.750
(Insuf)
22.000
27.000
4
cab_R_Q Queue Time
1.0000
(Insuf)
.00000
5.0000
5
694
DISCRETE-CHANGE VARIABLES
Identifier
Average
Half Width
Minimum
Maximum
Final Value
_______________________________________________________________________________
# in cab_R_Q
.05000
(Insuf)
.00000
1.0000
.00000
cab_R Busy
.93000
(Insuf)
.00000
1.0000
1.0000
cab_R Available
1.0000
(Insuf)
1.0000
1.0000
1.0000
COUNTERS
Identifier
Count
Limit
_________________________________________
finish_C
4
Infinite
Simulation run time: 0.00 minutes.
Simulation run complete.
%93 ‫ ا رة‬, ";‫ و‬,:J‫ د‬25.75 ‫ ر‬[email protected]‫ ز ! ا‬w2 ‫ أن‬H 9:‫! ا‬
‫ ر‬N‫ از ن إ‬%U !9.‫ ?! ا‬G‫ ا‬:`9T 6 ‫ رة اى‬,‫آ‬O‫ ا‬S6 ' ‫ ج‬9 J :‫ار‬:‫ا‬
.,92C
SIMAN ,Y ] ‫ا‬
;
Model statements for module:
Arrive 1
42$
CREATE,
1:DISC( 0.14,15,0.36,20,0.79,25,0.96,30,1.0,35 );
3$
STATION,
calls;
51$
TRACE,
-1,"-Arrived to system at station calls\n":;
695
6$
ASSIGN:
Picture=Default;
27$
DELAY:
0.;
56$
TRACE,
-1,"-Transferred to station cab\n":;
29$
ROUTE:
2,cab;
;
;
Model statements for module:
Server 1
;
0$
STATION,
cab;
158$
TRACE,
-1,"-Arrived to station cab\n":;
121$
DELAY:
0.;
165$
TRACE,
-1,"-Waiting for resource cab_R\n":;
82$
QUEUE,
cab_R_Q:MARK(QueueTime);
83$
SEIZE,
1:
cab_R,1;
192$
BRANCH,
1:
If,RTYP(cab_R).eq.2,193$,Yes:
If,RTYP(cab_R).eq.1,95$,Yes;
193$
MOVE:
cab_R,cab;
95$
TALLY:
cab_R_Q Queue Time,INT(QueueTime),1;
202$
DELAY:
0.0;
TRACE,
-1,"-Delay for processing time DISC(
0.12,5,0.47,15,0.9,25,0.96,35,1.0,45 )\n":;
84$
DELAY:
DISC( 0.12,5,0.47,15,0.9,25,0.96,35,1.0,45 );
166$
TRACE,
-1,"-Releasing resource\n":;
85$
RELEASE:
cab_R,1;
149$
DELAY:
0.;
171$
TRACE,
-1,"-Transferred to station finish\n":;
89$
ROUTE:
0.,finish;
;
;
Model statements for module:
Depart 1
;
696
2$
STATION,
finish;
233$
TRACE,
-1,"-Arrived to station finish\n":;
203$
DELAY:
0.;
225$
COUNT:
finish_C,1;
230$
TALLY:
finish_Ta,Interval(QueueTime),1;
240$
TRACE,
-1,"-Disposing entity\n":;
232$
DISPOSE;
697
‫‪ %‬ا ا‪ ! 6‬ا‪%6‬‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫إ ر ا ل ا` ‪ M‬ا `‪ 1423/1422 3‬هـ‬
‫ دة ‪C ) P 241‬ق ا آ ة ‪( 1‬‬
‫ا‪, 2 ! G‬‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫‪2I‬ز‪ R9‬ز !‬
‫! ا‪2'2‬ل ‪ ,:J !? G‬إ دآ ن أ‪ 6‬ا ‪H 37"9 !J‬ول‪:‬‬
‫‪Time Between Arrivals‬‬
‫)‪(Minutes‬‬
‫‪1‬‬
‫‪2‬‬
‫‪3‬‬
‫‪4‬‬
‫‪Probability‬‬
‫‪0.23‬‬
‫‪0.37‬‬
‫‪0.28‬‬
‫‪0.12‬‬
‫)أ( و أز ‪ ! ,‬و'‪2‬ل "د ‪ 50‬ز ‪. 2‬‬
‫)ب( آ‪2‬ن رج ‪/I‬اري ‪q‬ز ‪ ,‬ا ‪2‬ة ;‪ 3‬ا`‪:‬ة ا ‪.,:‬‬
‫)ج( إم ‪ 1000 2 Excel‬أز ‪ ! ,‬و'‪2‬ل وآ‪2‬ن رج ‪/I‬اري ‪. U‬‬
‫ا ‚ال ا‪:‬‬
‫ت( ‪q‬اد ا"‪2O‬ا?‪ ,‬ا ‪:,‬‬
‫‪0.488 0.226 0.221 0.043 0.055 0.743 0.081 0.685 0.364 0.012‬‬
‫‪0.372 0.543 0.483 0.050 0.628 0.966 0.750 0.697 0.764 0.040‬‬
‫‪0.404 0.549 0.203 0.990 0.155 0.079 0.789 0.462 0.795 0.190‬‬
‫ إ ر ‪ R‬آ ي أ ا`‪ ,V‬ا ‪:,‬‬
‫‪H 0 : Ri ∼ U 0,1‬‬
‫‪H1 : Ri ≁ U 0,1‬‬
‫‪. α = 0.05 .‬‬
‫ب( إم إ ر آ‪2-2 2‬روف – ‪2‬ف ‪ @ Kolmogorov-Smirnov‬ر ا`‪; ,V‬‬
‫إذا آ ‪ W‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪,‬‬
‫‪0.136 0.513 0.844 0.681 0.154 0.239 0.888 0.090 0.631 0.245‬‬
‫‪0.394 0.531 0.715 0.276 0.880‬‬
‫‪2I U‬ز‪ %N R9‬ا`ة ]‪ . α = 0.05 . .[0,1‬ان ‪D0.05,15 = 0.338‬‬
‫إم ‪ 3; Excel‬إ‪ gI -‬آ أ ‪ !/‬ذ‪.g‬‬
‫‪698‬‬
%6‫ ! ا‬6‫ ا ا‬%
‫ هـ‬1423/1422 3` ‫ ا‬M `‫ @ ر ا ل ا‬, ‫ ت‬-‫إ‬
( 1 ‫ق ا آ ة‬C ) P 241 ‫ دة‬
:‫ ‚ال اول‬/ =‫إ‬
7" ‫ ا‬R9‫ز‬2‫ ! ا‬,9 " ‫ول‬- ‫ن‬2/
Time Between
Arrivals (Minutes)
1
2
3
4
Probability
0.23
0.37
0.28
0.12
Cumulative
Probability
0.23
0.60
0.88
1.00
Random Number
0.00 - 0.23
0.24 - 0.60
0.61 - 0.88
0.89 - 1.00
2 ‫ ز‬50 ‫ل "د‬2'‫! و‬
Customer
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Random Number
Time Between
Arrivals (Minutes)
3
2
4
4
2
4
1
1
3
1
3
1
3
3
2
2
1
2
3
3
4
1
1
1
4
4
3
3
2
2
1
2
3
0.625855
0.556581
0.945541
0.952997
0.420310
0.936866
0.107296
0.114627
0.740750
0.187467
0.755018
0.107803
0.778554
0.866096
0.504978
0.272018
0.040550
0.545166
0.880144
0.653542
0.950950
0.007961
0.059577
0.212337
0.959134
0.958470
0.493049
0.714507
0.247049
0.463654
0.224657
0.279055
0.629967
699
, ‫ أز‬2I (‫)أ‬
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.846872
0.269160
0.047683
0.744348
0.251238
0.884811
0.946383
0.116568
0.591652
0.086417
0.007588
0.206254
0.114240
0.242383
0.221609
0.017977
0.281981
3
2
1
3
2
3
4
1
2
1
1
1
1
2
1
1
2
.,: ‫ة ا‬:`‫ ا‬3; ‫ة‬2 ‫ ا‬, ‫ز‬q ‫اري‬/I ‫! رج‬92/I (‫)ب‬
Time Between Arrivals
(Minutes)
1
2
3
4
Frequency
Relative Frequency
17
13
13
7
0.34
0.26
0.26
0.14
3 ‫ ا‬M/O‫و& ا‬
Frequency
15
10
5
0
1
2
3
4
Time Between Arrivals (Minutes)
700
. ‫اري‬/I ‫! رج‬92/I‫ل و‬2'‫! و‬
, ‫ أز‬1000 2 Excel ‫)ح( إام‬
Excel ! , `' 3; 3 ‫ ا‬M‫أد‬
:]? ‫ ا‬M
;
:3 [‫ال ا‬A , -‫إ‬
:,?‫ا‬2O"‫اد ا‬q
0.488 0.226 0.221 0.043 0.055 0.743 0.081 0.685 0.364 0.012
0.372 0.543 0.483 0.050 0.628 0.966 0.750 0.697 0.764 0.040
0.404 0.549 0.203 0.990 0.155 0.079 0.789 0.462 0.795 0.190
:, ‫ ا‬,V`‫ف ا‬2
H 0 : Ri ∼ U 0,1
H1 : Ri ≁ U 0,1
‫ آ ي‬R ‫ ! إ ر‬
‫ ;ة‬M‫ آ‬3; R:I 3‫ ا‬,?‫ا‬2O"‫اد ا‬0‫ د ا‬MH‫ و‬,9‫ ;ات و‬10 ‫[ إ‬0,1] ‫ ا`ة‬%:
Interval
0.00 - 0.10
0.11 - 0.20
Observed
7
2
Expected
3
3
701
Chi Sq.
5.33
0.33
‫‪0‬‬
‫‪0.33‬‬
‫‪0.33‬‬
‫‪0.33‬‬
‫‪0‬‬
‫‪1.33‬‬
‫‪3‬‬
‫‪0.33‬‬
‫‪11.33‬‬
‫‪3‬‬
‫‪2‬‬
‫‪4‬‬
‫‪2‬‬
‫‪3‬‬
‫‪5‬‬
‫‪0‬‬
‫‪2‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪3‬‬
‫‪0.21 - 0.30‬‬
‫‪0.31 - 0.40‬‬
‫‪0.41 - 0.50‬‬
‫‪0.51 - 0.60‬‬
‫‪0.61 - 0.70‬‬
‫‪0.71 - 0.80‬‬
‫‪0.81 - 0.90‬‬
‫‪0.91 - 1.00‬‬
‫‪ , J‬آ ي ‪ R I‬ا ‪ , 2‬ه‪ 11.33 3‬و ر‪ -‬ت ‪9 ,96‬‬
‫‪ , J‬آ ي ‪ R I‬ا‪H‬و‪ α = 0.05 ,‬ودر‪ -‬ت ‪ 9 ,96‬ه‪ 16.9 3‬وه‪ 3‬أآ ! ا‪, :‬‬
‫ا ‪., 2‬‬
‫ا‪:‬ار‪ ;T :‬ا`‪ ,V‬ا `‪.,9‬‬
‫ا ‪ M‬ام ‪Excel‬‬
‫‪702‬‬
‫ @ ر‬Kolmogorov-Smirnov ‫ف‬2 – ‫روف‬2-2 2‫ف م إ ر آ‬2 (‫ب‬
,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ ا‬W ‫ ; إذا آ‬,V`‫ا‬
0.136 0.513 0.844 0.681 0.154 0.239 0.888 0.090 0.631 0.245
0.394 0.531 0.715 0.276 0.880
.[0,1] ‫ ا`ة‬%N R9‫ز‬2I U
9
I ‫اد‬0‫ ا‬SI T‫أو‬
0.09 0.136 0.154 0.239 0.245 0.276 0.394 0.513 0.531 0.631 0.681 0.715
0.844 0.88 0.888
‫ ت‬/‫ ا‬S i

D + = max  − R(i ) 
1≤ i ≤ N
N


i − 1

D − = max  R( i ) −

1≤i ≤ N
N 

3 ‫آ‬
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
R(i)
0.09
0.136
0.154
0.239
0.245
0.276
0.394
0.513
0.531
0.631
0.681
0.715
0.844
0.88
0.888
i/N
0.066
0.133
0.199
0.266
0.333
0.399
0.466
0.533
0.599
0.666
0.733
0.799
0.866
0.933
0.999
(i-1)/N
0
0.066
0.133
0.199
0.266
0.333
0.399
0.466
0.533
0.599
0.666
0.733
0.799
0.866
0.933
[i/N]-R(i)
-0.069
-0.379
-0.644
-0.414
+0.18
+0.16
-0.421
+0.44
-0.031
+0.42
+0.34
+0.27
+0.15
+0.65
+0.12
R(i)-[(i-1)/N]
+0.136
+0.446
+0.711
+0.481
-0.1127
-0.0943
+0.488
-0.3767
+0.098
-0.355
-0.2727
-0.2023
-0.085
-0.5907
-0.0533
D + = 0.657
D − = 0.711
D = 0.711
D0.05,15 = 0.338 ‫ أن‬H ‫اول‬H‫! ا‬
.,9` ‫ ا‬,V`‫ ; ; ا‬,‫و‬H ‫ ا‬, :‫ أآ ! ا‬, 2 ‫ ا‬, :‫ ان ا‬:‫ار‬:‫ا‬
Excel ‫ ام‬M ‫ا‬
703
704
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ا@ ر ا‪ M ` 3? U‬ا `‪ 1423/1422 3‬هـ‬
‫ دة ‪241‬‬
‫‪C ) P‬ق ا‬
‫آة‪(1‬‬
‫ا‪, 3 ! G‬‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫ "‪ W‬ا ت ا ‪ ,‬ـ ‪ 50‬ز ‪2 C 3; 2‬ر أ‪ 6‬ا‪2‬ك‪.‬‬‫أز ‪,‬‬
‫! ا‪2'2‬ل‪:‬‬
‫‪IAT‬‬
‫‪6.0‬‬
‫‪11.9‬‬
‫‪2.0‬‬
‫‪1.5‬‬
‫‪0.4‬‬
‫‪14.3‬‬
‫‪0.0‬‬
‫‪2.9‬‬
‫‪0.2‬‬
‫‪5.0‬‬
‫‪0.1‬‬
‫‪1.6‬‬
‫‪5.1‬‬
‫‪2.6‬‬
‫‪11.6‬‬
‫‪9.2‬‬
‫‪7.4‬‬
‫‪3.2‬‬
‫‪3.2‬‬
‫‪3.5‬‬
‫‪2.4‬‬
‫‪2.7‬‬
‫‪6.4‬‬
‫‪10.0‬‬
‫‪8.7‬‬
‫‪3.8‬‬
‫‪15.5‬‬
‫‪0.1‬‬
‫‪1.6‬‬
‫‪0.0‬‬
‫‪3.8‬‬
‫‪4.0‬‬
‫‪2.8‬‬
‫‪2.5‬‬
‫‪3.3‬‬
‫‪1.4‬‬
‫‪4.8‬‬
‫‪16.5‬‬
‫‪0.3‬‬
‫‪9.6‬‬
‫‪3.1‬‬
‫‪4.1‬‬
‫‪0.2‬‬
‫‪1.5‬‬
‫‪7.1‬‬
‫‪8.5‬‬
‫‪6.1‬‬
‫‪4.8‬‬
‫‪10.8‬‬
‫‪5.5‬‬
‫وأز ‪:, ,‬‬
‫‪ST‬‬
‫‪1.2‬‬
‫‪6.8‬‬
‫‪4.5‬‬
‫‪6.5‬‬
‫‪4.1‬‬
‫‪4.9‬‬
‫‪3.3‬‬
‫‪6.8‬‬
‫‪5.0‬‬
‫‪5.8‬‬
‫‪4.0‬‬
‫‪4.8‬‬
‫‪7.1‬‬
‫‪8.1‬‬
‫‪5.6‬‬
‫‪6.2‬‬
‫‪2.7‬‬
‫‪6.8‬‬
‫‪2.8‬‬
‫‪5.2‬‬
‫‪5.4‬‬
‫‪5.3‬‬
‫‪5.5‬‬
‫‪3.4‬‬
‫‪5.3‬‬
‫‪5.5‬‬
‫‪4.1‬‬
‫‪4.4‬‬
‫‪7.5‬‬
‫‪3.7‬‬
‫‪2.6‬‬
‫‪9.9‬‬
‫‪5.6‬‬
‫‪6.7‬‬
‫‪3.2‬‬
‫‪4.4‬‬
‫‪4.6‬‬
‫‪5.0‬‬
‫‪4.2‬‬
‫‪4.3‬‬
‫‪5.3‬‬
‫‪6.0‬‬
‫‪5.1‬‬
‫‪4.6‬‬
‫‪4.6‬‬
‫‪5.4‬‬
‫‪7.7‬‬
‫‪7.0‬‬
‫‪5.9‬‬
‫‪3.6‬‬
‫‪ -1‬أو‪ -‬دا‪ ,‬ا‪2‬ز‪ R9‬ا‪) 39H‬ا"‪ ! M/ (3‬أز ‪,‬‬
‫‪ -2‬أز ‪,‬‬
‫! ا‪2'2‬ل وأز ‪ ,‬ا ‪.,‬‬
‫! ا‪2'2‬ل وا ‪ ,‬ا "‪ 7‬ة‪ 6 ،‬آ‪9 3‬و‪ 9‬ا‪ N‬م وأو‪ , "; -‬ا دم‬
‫و ‪ w2‬ز ! ا@‪ N‬ر ! ا‪.N‬‬
‫ا ‚ال ا‪:‬‬
‫‪705‬‬
‫ ?! إ‬G‫ ا‬M 9 .!? G ‫ ت‬7‫ ا‬M'2I‫ و‬.0 6‫ ت ;& دم وا‬7‫ ا‬,I ‫م‬2:9 %"7
:, ‫اول ا‬H‫ ا‬3; ‫" ت‬9‫ز‬2 :C %U %I‫ل و‬2'‫! و‬
, ‫ از‬R9‫ز‬2I S6 %"7 ‫ا‬
:, ‫ل وا‬2'2‫! ا‬
IAT
(Minutes)
Probability
3
0.25
4
0.40
5
0.20
6
0.15
Service Time
(Minutes)
Probability
2
0.35
3
0.25
4
0.20
5
0.20
706
, ‫ أز‬R9‫ز‬2I ‫اول‬-
‫ ة‬31 ‫ ة‬/ ‫ن وآر ا‬2 ‫ ز‬100 , ‫ ء‬U‫ إ‬6 ‫ م‬N‫ا ا‬.‫ ه‬3‫ آ‬6 Excel ‫ام‬
:, ‫ ت ا‬V`‫وأ ا‬
H 0 : Server Utilization = 0.75
H1 : Server Utilization ≠ 0.75
: ‫ا ‚ال ا‬
, 6‫ إ‬,; [‫ آ‬,‫ & دا‬X 3?‫ا‬2O Y
2 x, 0 ≤ x ≤ 1
f ( x) = 
 0, otherwise
.3?‫ا‬2O"‫ ا‬Y ‫ا ا‬.‫ هة ! ه‬O 50 ‫ و‬-1
. α = 0.05 . .K-S Test ‫ ام إ ر‬7‫ة ! ا‬2 ‫ هات ا‬O ‫ أ ا‬-2
DN ,0.05 = 1.36
384
N ‫ن‬e
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫إ‪ -‬ت‬
‫ دة ‪241‬‬
‫ ‪ z ,‬ر ا‪ M ` 3? U‬ا `‪ 1423/1422 3‬هـ‬
‫‪C ) P‬ق ا‬
‫آة‪(1‬‬
‫إ= ‪‚ /‬ال اول‪:‬‬
‫‪-1‬‬
‫‪385‬‬
:3‫ ه‬, ‫ ا‬, ‫ل وأز‬2'2‫! ا‬
IAT
−∞ < x ≤ 0
, ‫ ! أز‬M/ (3"‫ )ا‬39H‫ ا‬R9‫ز‬2‫ ا‬,‫إذا دا‬
CDF
0.00
0 < x ≤ 3.3
0.04
3.3 < x ≤ 6.6
0.48
6.6 < x ≤ 9.9
0.74
9.9 < x ≤ 13.2
0.86
13.2 < x ≤ 16.5
0.94
16.5 < x < ∞
1.00
ST
−∞ < x ≤ 1.2
CDF
0.00
1.2 < x ≤ 2.94
0.02
2.94 < x ≤ 4.68
0.08
4.68 < x ≤ 6.42
0.40
6.42 < x ≤ 8.16
0.78
8.16 < x ≤ 9.9
0.98
9.9 < x < ∞
1.00
:3 ‫ول ا‬H‫ن ا‬2/ ,9‫آ ة او‬
:‫آ ة‬
Customer
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
-2
‫ول‬- ‫ن‬2/
IAT
Arrival
Time
ST
Service
Begin
Service
Ends
Wait?
Wait
Time
4.8
4.8
5.5
4.8
10.3
0
0.0
3.3
2.8
3.8
0.4
0.1
0.2
0.0
6.0
2.0
16.5
1.4
2.5
4.0
8.1
10.9
14.7
15.1
15.2
15.4
15.4
21.4
23.4
39.9
41.3
43.8
47.8
5.4
2.8
2.7
5.6
7.1
4.0
5.0
3.3
4.1
4.5
1.2
3.4
5.3
10.3
15.7
18.5
21.2
26.8
33.9
37.9
42.9
46.2
50.3
54.8
56.0
59.4
15.7
18.5
21.2
26.8
33.9
37.9
42.9
46.2
50.3
54.8
56.0
59.4
64.7
1
1
1
1
1
1
1
1
1
1
1
1
1
2.2
4.8
3.8
6.1
11.6
18.5
22.5
21.5
22.8
10.4
13.5
12.2
11.6
386
‫‪2.6‬‬
‫‪6.2‬‬
‫‪8.0‬‬
‫‪11.3‬‬
‫‪7.5‬‬
‫‪10.8‬‬
‫‪9.5‬‬
‫‪16.1‬‬
‫‪17.9‬‬
‫‪24.1‬‬
‫‪24.5‬‬
‫‪29.8‬‬
‫‪31.2‬‬
‫‪28.9‬‬
‫‪22.6‬‬
‫‪21.7‬‬
‫‪17.8‬‬
‫‪19.5‬‬
‫‪21.0‬‬
‫‪14.0‬‬
‫‪11.5‬‬
‫‪12.9‬‬
‫‪14.7‬‬
‫‪18.5‬‬
‫‪14.7‬‬
‫‪16.7‬‬
‫‪17.2‬‬
‫‪10.7‬‬
‫‪10.9‬‬
‫‪9.2‬‬
‫‪15.9‬‬
‫‪24.2‬‬
‫‪27.8‬‬
‫‪16.7‬‬
‫‪18.4‬‬
‫‪13.3‬‬
‫‪759.8‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪49‬‬
‫‪69.9‬‬
‫‪76.7‬‬
‫‪82.9‬‬
‫‪91.0‬‬
‫‪95.8‬‬
‫‪101.6‬‬
‫‪108.4‬‬
‫‪113.3‬‬
‫‪119.8‬‬
‫‪126.6‬‬
‫‪134.3‬‬
‫‪138.9‬‬
‫‪144.0‬‬
‫‪149.3‬‬
‫‪153.5‬‬
‫‪158.1‬‬
‫‪161.3‬‬
‫‪166.9‬‬
‫‪169.5‬‬
‫‪177.0‬‬
‫‪181.1‬‬
‫‪186.4‬‬
‫‪193.4‬‬
‫‪198.8‬‬
‫‪203.4‬‬
‫‪209.4‬‬
‫‪213.7‬‬
‫‪218.7‬‬
‫‪223.1‬‬
‫‪229.8‬‬
‫‪239.7‬‬
‫‪243.4‬‬
‫‪247.8‬‬
‫‪253.3‬‬
‫‪256.9‬‬
‫‪262.8‬‬
‫‪5.2‬‬
‫‪6.8‬‬
‫‪6.2‬‬
‫‪8.1‬‬
‫‪4.8‬‬
‫‪5.8‬‬
‫‪6.8‬‬
‫‪4.9‬‬
‫‪6.5‬‬
‫‪6.8‬‬
‫‪7.7‬‬
‫‪4.6‬‬
‫‪5.1‬‬
‫‪5.3‬‬
‫‪4.2‬‬
‫‪4.6‬‬
‫‪3.2‬‬
‫‪5.6‬‬
‫‪2.6‬‬
‫‪7.5‬‬
‫‪4.1‬‬
‫‪5.3‬‬
‫‪7.0‬‬
‫‪5.4‬‬
‫‪4.6‬‬
‫‪6.0‬‬
‫‪4.3‬‬
‫‪5.0‬‬
‫‪4.4‬‬
‫‪6.7‬‬
‫‪9.9‬‬
‫‪3.7‬‬
‫‪4.4‬‬
‫‪5.5‬‬
‫‪3.6‬‬
‫‪5.9‬‬
‫‪258‬‬
‫‪64.7‬‬
‫‪69.9‬‬
‫‪76.7‬‬
‫‪82.9‬‬
‫‪91.0‬‬
‫‪95.8‬‬
‫‪101.6‬‬
‫‪108.4‬‬
‫‪113.3‬‬
‫‪119.8‬‬
‫‪126.6‬‬
‫‪134.3‬‬
‫‪138.9‬‬
‫‪144.0‬‬
‫‪149.3‬‬
‫‪153.5‬‬
‫‪158.1‬‬
‫‪161.3‬‬
‫‪166.9‬‬
‫‪169.5‬‬
‫‪177.0‬‬
‫‪181.1‬‬
‫‪186.4‬‬
‫‪193.4‬‬
‫‪198.8‬‬
‫‪203.4‬‬
‫‪209.4‬‬
‫‪213.7‬‬
‫‪218.7‬‬
‫‪223.1‬‬
‫‪229.8‬‬
‫‪239.7‬‬
‫‪243.4‬‬
‫‪247.8‬‬
‫‪253.3‬‬
‫‪256.9‬‬
‫! ا‪H‬ول ‪:H‬‬
‫‪258‬‬
‫;" ‪ ,‬ا دم =‬
‫‪262.8‬‬
‫= ‪0.982‬‬
‫‪759.8‬‬
‫‪ w2‬ز ! ا@‪ N‬ر ! إ‪N‬وا =‬
‫‪49‬‬
‫= ‪ 15.51‬د‪,:J‬‬
‫‪387‬‬
‫‪62.1‬‬
‫‪63.7‬‬
‫‪68.7‬‬
‫‪71.6‬‬
‫‪83.5‬‬
‫‪85.0‬‬
‫‪92.1‬‬
‫‪92.3‬‬
‫‪95.4‬‬
‫‪95.7‬‬
‫‪102.1‬‬
‫‪104.5‬‬
‫‪107.7‬‬
‫‪115.1‬‬
‫‪126.7‬‬
‫‪131.8‬‬
‫‪140.3‬‬
‫‪141.8‬‬
‫‪145.9‬‬
‫‪155.5‬‬
‫‪165.5‬‬
‫‪168.2‬‬
‫‪171.7‬‬
‫‪174.9‬‬
‫‪184.1‬‬
‫‪186.7‬‬
‫‪192.2‬‬
‫‪203.0‬‬
‫‪207.8‬‬
‫‪213.9‬‬
‫‪213.9‬‬
‫‪215.5‬‬
‫‪215.6‬‬
‫‪231.1‬‬
‫‪234.9‬‬
‫‪243.6‬‬
‫‪14.3‬‬
‫‪1.6‬‬
‫‪5.0‬‬
‫‪2.9‬‬
‫‪11.9‬‬
‫‪1.5‬‬
‫‪7.1‬‬
‫‪0.2‬‬
‫‪3.1‬‬
‫‪0.3‬‬
‫‪6.4‬‬
‫‪2.4‬‬
‫‪3.2‬‬
‫‪7.4‬‬
‫‪11.6‬‬
‫‪5.1‬‬
‫‪8.5‬‬
‫‪1.5‬‬
‫‪4.1‬‬
‫‪9.6‬‬
‫‪10.0‬‬
‫‪2.7‬‬
‫‪3.5‬‬
‫‪3.2‬‬
‫‪9.2‬‬
‫‪2.6‬‬
‫‪5.5‬‬
‫‪10.8‬‬
‫‪4.8‬‬
‫‪6.1‬‬
‫‪0.0‬‬
‫‪1.6‬‬
‫‪0.1‬‬
‫‪15.5‬‬
‫‪3.8‬‬
‫‪8.7‬‬
‫‪15‬‬
‫‪16‬‬
‫‪17‬‬
‫‪18‬‬
‫‪19‬‬
‫‪20‬‬
‫‪21‬‬
‫‪22‬‬
‫‪23‬‬
‫‪24‬‬
‫‪25‬‬
‫‪26‬‬
‫‪27‬‬
‫‪28‬‬
‫‪28‬‬
‫‪30‬‬
‫‪31‬‬
‫‪32‬‬
‫‪33‬‬
‫‪34‬‬
‫‪35‬‬
‫‪36‬‬
‫‪37‬‬
‫‪38‬‬
‫‪39‬‬
‫‪40‬‬
‫‪41‬‬
‫‪42‬‬
‫‪43‬‬
‫‪44‬‬
‫‪45‬‬
‫‪46‬‬
‫‪47‬‬
‫‪48‬‬
‫‪49‬‬
‫‪50‬‬
‫‪Totals‬‬
‫إ= ‪‚ /‬ال ا‪:‬‬
‫;‪9- , `' 3‬ة ! ‪ Excel‬أد‪ M‬ا ت آ ه‪aV2 2‬‬
‫;‪ UN‬ا‪ ,H‬ا ‪:,‬‬
‫‪388‬‬
,V`‫ف ا‬2‫ ا دم و‬, "` , J 31 ‫ى‬2 9 (L) 0‫د ا‬2 "‫ا‬
H 0 : Server Utilization = 0.75
H1 : Server Utilization ≠ 0.75
t0 =
xUtil − 0.75
,?
sUtil
[email protected]‫ ا‬S ‫ و‬, "` ‫ وا@ اف ا " ري‬w2 ‫ ا‬-2
,V`‫ ر; ا‬R7T ‫ا‬.U ‫ و‬,‫و‬H ‫ ا‬, :‫ ! ا‬MJ‫ أ‬, 2 ‫ ا‬,?
[email protected]‫ ا‬, J ‫“ أن‬6
.,9` ‫ا‬
389
‫‪ “6T‬أ‪ f9‬ا‪ , :‬ا@‪ , : , 6‬ا ‪ , 2‬ه‪ 0.68288 3‬وه‪ 3‬أآ ! ‪. 0.05‬‬
‫‪390‬‬
: ‫ ‚ال ا‬/ =‫إ‬
, 6‫ إ‬,; [‫ آ‬,‫ & دا‬X 3?‫ا‬2O Y
 2 x, 0 ≤ x ≤ 1
f ( x) = 
 0, otherwise
3 ‫ ااآ‬R9‫ز‬2‫ ا‬,‫ دا‬-2
F ( x) = P ( X ≤ x) = ∫
x
−∞
f ( t ) dt
x
= ∫ 2t dt = x 2 , 0 ≤ x ≤ 1
−∞
‫أي‬
 0,
x<0
 2
F ( x) = x , 0 ≤ x ≤ 1
 1,
x >1

,J"‫ ! ا‬3?‫ا‬2O"‫ ا‬Y ‫ا ا‬.‫ هة ! ه‬O 50 2 -1
X i = F −1 ( Ri )
‫ أي‬Ri ∼ U ( 0,1) P6
X i = Ri
:]? ‫ول‬- ‫ن‬2/
R
0.714465
0.708959
0.267740
0.474856
0.005750
0.271049
0.736142
0.976983
0.269966
0.721422
0.174332
0.303994
0.530758
0.994646
0.648218
0.508599
0.841944
0.999339
0.160562
X
0.845260
0.841997
0.517436
0.689098
0.075830
0.520623
0.857987
0.988425
0.519583
0.849366
0.417530
0.551357
0.728531
0.997320
0.805120
0.713161
0.917575
0.999670
0.400701
391
‫‪0.615609‬‬
‫‪0.836656‬‬
‫‪0.197353‬‬
‫‪0.507724‬‬
‫‪0.989777‬‬
‫‪0.964941‬‬
‫‪0.583050‬‬
‫‪0.469857‬‬
‫‪0.470888‬‬
‫‪0.804164‬‬
‫‪0.637345‬‬
‫‪0.428227‬‬
‫‪0.964925‬‬
‫‪0.600677‬‬
‫‪0.646756‬‬
‫‪0.149989‬‬
‫‪0.619184‬‬
‫‪0.929395‬‬
‫‪0.629613‬‬
‫‪0.602700‬‬
‫‪0.880204‬‬
‫‪0.972109‬‬
‫‪0.588065‬‬
‫‪0.737051‬‬
‫‪0.772378‬‬
‫‪0.747966‬‬
‫‪0.321506‬‬
‫‪0.937846‬‬
‫‪0.619193‬‬
‫‪0.728816‬‬
‫‪0.322449‬‬
‫‪0.378975‬‬
‫‪0.699994‬‬
‫‪0.038948‬‬
‫‪0.257783‬‬
‫‪0.979658‬‬
‫‪0.931111‬‬
‫‪0.339948‬‬
‫‪0.220766‬‬
‫‪0.221735‬‬
‫‪0.646679‬‬
‫‪0.406209‬‬
‫‪0.183378‬‬
‫‪0.931081‬‬
‫‪0.360813‬‬
‫‪0.418293‬‬
‫‪0.022497‬‬
‫‪0.383389‬‬
‫‪0.863775‬‬
‫‪0.396413‬‬
‫‪0.363247‬‬
‫‪0.774759‬‬
‫‪0.944995‬‬
‫‪0.345821‬‬
‫‪0.543244‬‬
‫‪0.596568‬‬
‫‪0.559454‬‬
‫‪0.103366‬‬
‫‪0.879555‬‬
‫‪0.383400‬‬
‫‪0.531172‬‬
‫‪0.103973‬‬
‫‪ -2‬ا ‪ O‬هات ا ‪2‬ة ! ا‪ 7‬ام إ ر ‪α = 0.05 K-S Test‬‬
‫آ ‪:3‬‬
‫;‪9- , `' 3‬ة ! ‪ Excel‬أد‪ M‬ا ‪:3‬‬
‫;]‬
‫‪392‬‬
‫‪ “6‬أن ‪ D < D50,0.05‬أي ‪ ;T‬ا`‪ ,V‬ا `‪.,9‬‬
‫‪393‬‬
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫‪#‬دة ‪C) 241‬ق اآة ‪( 1‬‬
‫ا^‪60‬ر ا‪ / W1‬ا ‪ 1424/1423‬هـ‬
‫ا‪ 3 ! G‬ت‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫;‪ 3‬آ ب ‪27‬ع و‪ -‬أن د ا‪ 70‬ء ا ‪ 3; ,"7‬اـ ‪ , `' 50‬ا‪0‬و ه‪:3‬‬
‫‪3‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪3‬‬
‫‪1‬‬
‫‪1‬‬
‫‪4‬‬
‫‪2‬‬
‫‪2‬‬
‫‪0‬‬
‫‪3‬‬
‫‪1‬‬
‫‪2‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪1‬‬
‫‪1‬‬
‫‪0‬‬
‫‪2‬‬
‫‪1‬‬
‫‪1‬‬
‫‪2‬‬
‫‪2‬‬
‫‪1‬‬
‫‪2‬‬
‫‪1‬‬
‫‪1‬‬
‫‪4‬‬
‫‪0‬‬
‫‪0‬‬
‫‪0‬‬
‫‪3‬‬
‫‪0‬‬
‫‪1‬‬
‫‪3‬‬
‫‪2‬‬
‫‪1‬‬
‫)أ( أو‪ -‬ا‪2‬ز‪ R9‬ا‪) 39H‬ا"‪ (3‬ت ا ‪.,:‬‬
‫)ب( ‪.9‬آ ;‪ 3‬آ‪ S‬ا@‪ 6‬ء أن ا ‪ Y‬ا"‪2O‬ا?‪ " 3‬د ا‪ 70‬ء ا ‪",27 , `' 3; ,"7‬‬
‫& ‪2I‬ز‪2 R9‬ا‪2‬ن‪ .‬إ ه‪ 5.‬ا`‪ ,V‬ت ا ‪ ,:‬أ س أن ‪. λ = 1‬‬
‫)ج( ام ‪ , `' 50 !9 EXCEL‬أى ! ه‪.‬ا ا‪ /‬ب‪.‬‬
‫ا ‚ال ا‪:‬‬
‫إ ر "د ا@ رات ‪2/9‬ن ! ‪ 10‬أ‪ ،,b‬آ‪A M‬ال ‪ 4 ,‬إ‪ -‬ت )‪ (A‬و )‪ (B‬و )‪ (C‬و )‪(D‬‬
‫وا‪6‬ة ‪ J ., ' w:; U‬م ‪ S2 ^ S C‬دة ‪ , -‬ا‪ ,b0‬ر ‪A‬ال ‪M/O‬‬
‫‪2O‬ا?‪2/9 P 3‬ن إ ر‪0 5‬ي ‪A‬ال & `ˆ ا`'‪.,‬‬
‫ا‪/D‬ب‪:‬‬
‫)أ( ;ض أن آ‪A M‬ال & ‪ ,‬وا‪6‬ة‪ ،‬وأن ا‪ H‬ح ‪2/9‬ن أ س ا@‪ , -‬ا ‪,‬‬
‫ ‪ 10 ! 5‬أ‪J .,b‬ر ام ا آ ة او‪ ,9‬إ‪ 6‬ل ‪ H‬ح ه‪.‬ا ا‪20 S 7‬‬
‫‪/I‬ارا‪ .‬أن ا@‪ -‬ت ا ‪ ,‬ه‪ 3‬آ ;‪ 3‬ا‪H‬ول ا ‪:3‬‬
‫ا‪A‬ال‬
‫ا@‪ , -‬ا‬
‫ ‪,‬‬
‫‪1‬‬
‫‪2‬‬
‫‪3‬‬
‫‪4‬‬
‫‪5‬‬
‫‪6‬‬
‫‪7‬‬
‫‪8‬‬
‫‪9‬‬
‫‪10‬‬
‫‪B‬‬
‫‪A‬‬
‫‪A‬‬
‫‪C‬‬
‫‪B‬‬
‫‪D‬‬
‫‪C‬‬
‫‪D‬‬
‫‪B‬‬
‫‪D‬‬
‫)ب( ام ‪ EXCEL‬أ ا`‪:‬ة )أ( ‪/I 200‬ار‪.‬‬
‫)ج( أ ;‪:‬ة )ب( إذا آ ن ا‪ H‬ح أ س ا@‪ , -‬ا ‪ 10 ! 6 ,‬أ‪.,b‬‬
‫)د( ه‪ 5.‬ا`‪:‬ة إ ر‪ 9G ,9‬دة ‪ :gI‬أو‪ -‬ا‪ , :‬ا‪ [email protected] ,9N‬ل ‪ H‬ح ه‪.‬ا ا‪.S 7‬‬
‫‪394‬‬
‫ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫‪#‬دة ‪C) 241‬ق اآة ‪( 1‬‬
‫ا@ ر ا‪ M ` 3? U‬ا[ ‪ 1423/1422 3‬هـ‬
‫ا‪ 3 ! G‬ت‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫‪ SC‬ا‪O‬اء ا‪ R9 !" ] 3 2‬ا‪2‬ز‪ R9‬ا@‪ 3 6‬ا ‪:3‬‬
‫‪4‬‬
‫‪0.10‬‬
‫‪2‬‬
‫‪0.20‬‬
‫‪3‬‬
‫‪0.12‬‬
‫‪1‬‬
‫‪0.25‬‬
‫‪Daily Demand‬‬
‫‪Probability‬‬
‫‪0‬‬
‫‪0.33‬‬
‫‪ ‹ `9‬ا ‪G‬ون ! ه‪.‬ا ا ] آ‪ ," M‬ا‪ 9‬م ;ذا و‪ -‬ا& ا‪ ! MJ‬او ‪ 9‬وي ‪ 6‬و‪6‬ات ‪SC %9‬‬
‫‪ 10‬و‪6‬ات‪ .‬أي ‪: : I ,C‬را ‪G‬ون ا ‪2-2‬د و‪ C .AIT‬ت ‪) ,f92"I‬أي ‪" : I‬‬
‫و'‪2‬ل ‪G‬ون ‪ .(9-‬ز ! ا‪:‬م ‪) Lead Time‬وه‪ 2‬ا‪ ! G‬ا ‪27:‬ع ! ‪ !6‬و‪ RV‬ا‪S7‬‬
‫‪ 6‬و'‪ R9 (&2‬ا‪2‬ز‪ R9‬ا@‪ 3 6‬ا ‪:3‬‬
‫‪3‬‬
‫‪0.2‬‬
‫‪1‬‬
‫‪0.3‬‬
‫‪2‬‬
‫‪0.5‬‬
‫)‪Lead Time (Days‬‬
‫‪Probability‬‬
‫ا ! اول ا‪20‬ع إذا آ ن ا ‪G‬ون اا?‪ 12 3‬و‪6‬ة و‪ C -2IT‬ت ;‪ R‬ا ‪G‬ون "‬
‫; آ‪9 3‬و‪ 6 9‬أ ‪.U R‬ا ا‪ N‬م ‪6 .‬د ‪ ,‬ا‪ 90‬م ا‪6 3‬ث ;‪ ,C : I 3; ‹: U‬و‪,‬‬
‫ا‪62‬ات ا‪ WC 3‬و‪ : I %‬و ‪ w2‬د ا‪62‬ات ا ‪O , 27‬اء ا‪. 2‬‬
‫ا ‚ال ا‪:‬‬
‫ز ! ا ة ‪2 Lifetime‬ات ‪ 3 ' :‬و‪ 3; RV‬ار ‪26‬ل ا‪0‬رض ‪ R9‬ا‪2‬ز‪ R9‬ا ‪:3‬‬
‫‪0.4e−0.4 x ,‬‬
‫‪x≥0‬‬
‫‪f ( x) = ‬‬
‫‪otherwise‬‬
‫‪ 0,‬‬
‫ام ‪ MINITAB‬أو ‪ EXCEL‬و ‪ 1000‬أز ‪ 6 ,‬ة وأ‪ S-‬ا ‪:3‬‬
‫‪ -4‬ه‪ 2‬إ‪ 6‬ل أن ا‪ :‬ا ‪G9T 3‬ال ‪2 5 " M "9‬ات؟‬
‫‪ -5‬ه‪ 2‬إ‪ 6‬ل أن ا‪ :‬ا ‪ 3 ! M "9 3‬و ‪2 6‬ات " إ‪&JC‬؟‬
‫‪) I gH? :6 -6‬ا@‪ , -‬ه‪ 5.‬ا`‪:‬ة إ ر‪.( 9‬‬
‫‪395‬‬
: ‫ا ‚ال ا‬
xi 3?‫ا‬2O Y ‫ هات‬O M[ 9 3 ‫اري ا‬/‫ول ا‬H‫ا‬
xi
Observed
Frequency
0
118
1
274
2
298
3
169
4
105
5
25
6
8
7
1
8
2
. α = 0.05 . 2 w2 ‫ن‬2‫ا‬2 R9‫ز‬2I & 3?‫ا‬2O Y xi ‫ ان‬,? :‫ ا‬,V`‫أ ا‬
396
‫ا ا ا‬
‫ "‪ ,‬ا ‪2" g‬د‬‫‪ %J‬ا@‪ 6‬ء و ‪2‬ث ا" ت‬
‫دة ‪C) P 241‬ق ا آ ة ‪( 1‬‬
‫ا@ ر ا‪ M ` 3? U‬ا‪0‬ول ‪ 1424/1423‬هـ‬
‫ا‪ 3 ! G‬ت‬
‫أ=‪ ! = U/2 -‬ا'‪ /K‬ا ‪:‬‬
‫ا ‚ال اول‪:‬‬
‫‪R7J‬‬
‫"‪ M I ,‬إ ‪ ,7:‬ا‪e _Y‬ز ‪,‬‬
‫! و'‪2‬ل ‪ U‬ا‪2‬ز‪ R9‬ا ‪:3‬‬
‫‪Time Between Arrivals Probability‬‬
‫‪0‬‬
‫‪0.23‬‬
‫‪1‬‬
‫‪0.37‬‬
‫‪2‬‬
‫‪0.28‬‬
‫‪3‬‬
‫‪0.12‬‬
‫ ت ا‪YI _Y‬ق أز ‪ U ,‬ا‪2‬ز‪ R9‬ا وي ! ‪ 1‬و ‪ R - . 4‬ا‪0‬و‪ J‬ت ‪ :I‬س ‪.? J‬‬
‫أ( أ‪-‬ي آ ة ‪9‬و‪ N ,9‬م ‪ 6‬ا@‪ U‬ء ! ‪ .R7J 10 _YI‬و‪J‬ر‬
‫‪ w2 -1‬أز ‪ ,‬ا@‪ N‬ر ;‪2 C 3‬ر ا‪ R H _Y‬ا‪ R7:‬و‪ R7:‬ا‪ 3‬أ‪N‬ت ;"‪.‬‬
‫‪ , , "; -2‬ا‪ _Y‬وه‪ M‬ج إ ‪ _YI ,7:‬اى‪ -3 .‬أ‪2C J‬ل ‪2 7‬ر‪.‬‬
‫ب( ام ‪ EXCEL‬أ‪-‬ى‬
‫`‪:‬ة ا ‪.,:‬‬
‫آ ة ‪ N‬م ‪ 6‬ا@‪ U‬ء ! ‪J .,"7J 100 _YI‬ر ا ‪27‬ب ;‪ 1 3‬و ‪ 2‬و ‪3‬‬
‫ا ‚ال ا‪:‬‬
‫أ( ا ‪2O‬ا?‪ ,‬ا‪0‬ر‪ J‬م ا ‪ ,‬ام إ ر آ‪2-2 2‬روف‪2 -‬ف )‪:( K-S Test‬‬
‫‪0.0465‬‬
‫‪0.3435‬‬
‫‪0.9203‬‬
‫‪0.0988‬‬
‫‪0.9011‬‬
‫‪0.0824‬‬
‫‪0.7549‬‬
‫‪0.6749‬‬
‫‪0.3506‬‬
‫‪0.5310‬‬
‫‪0.2400‬‬
‫‪0.0689‬‬
‫‪0.3827‬‬
‫‪0.7177‬‬
‫‪0.3676‬‬
‫‪0.5087‬‬
‫‪0.0930‬‬
‫‪0.9542‬‬
‫‪0.0366‬‬
‫‪0.1155‬‬
‫‪0.2112‬‬
‫ب( ‪ EXCEL‬ا ‪2O‬ا?‪ ,‬ا‪0‬ر‪ J‬م ا ‪ ,:‬ام إ ر ا‪H‬ي ‪ M`0‬وأ ‪Runs Up and‬‬
‫‪.Runs Down Test‬‬
‫‪ :;r#‬إذا ;‪ V‬أن ‪ a‬ه‪ 2‬ا"د ا‪H 3/‬ي ;‪ ! ," 3‬ا‪0‬ر‪ J‬م ا"‪2O‬ا?‪ ,‬ا ‪; ,::‬ن ‪ w2‬و‪!9 I‬‬
‫‪2N −1‬‬
‫‪16 N − 29‬‬
‫= ‪, σ a2‬‬
‫‪ J" 7"I a‬ت‬
‫‪3‬‬
‫‪90‬‬
‫= ‪ %H6 N P6 µ a‬ا"‪; .,‬ذا آ ‪; N > 20 W‬ن ‪a‬‬
‫‪2/9‬ن ‪2I 9:I U‬ز‪. N ( µ a , σ a2 ) R9‬‬
‫‪397‬‬
%6‫ ! ا‬6‫ ا ا‬%
‫ث ا" ت‬2 ‫ء و‬
[email protected]‫ ا‬%J
‫م‬2"‫ ا‬,‫آ‬
‫د‬2" g ‫ ا‬," -
‫ هـ‬1424/1423 ‫ول‬0‫ ا‬M `‫إ ر أ ل ا‬
( 1 ‫ق ا آ ة‬C ) P 241 ‫ دة‬
2' 2 #>‫ا‬
:, ‫ ا‬,b0‫ ا‬R - S-‫أ‬
‫ ?! إ‬G‫ ا‬M 9 .!? G S7‫ ا‬M'2I‫ و‬.0 6‫ ت ;& دم وا‬7‫ ا‬,I ‫م‬2:9 %"7
:, ‫ل ا‬2'2‫! ا‬
, ‫ از‬R9‫ز‬2I S6 %"7 ‫ا‬
:‫ل‬2'2‫! ا‬
IAT
(Minutes)
1
2
3
4
, ‫ أز‬R9‫ز‬2I ‫ول‬-
Probability
0.25
0.40
0.20
0.15
:3 ‫ ر آ‬[email protected]‫ر ا‬2 C ‫ل‬2C S6 , ! N R9 ‫ا دم‬
:4 ! MJ‫ر أ‬2 7‫ل ا‬2C ‫ إذا آ ن‬, ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬-
Service Time
(Minutes)
4
5
6
7
Probability
0.35
0.25
0.20
0.20
:4 ‫ وي‬9 ‫ر أآ ! أو‬2 7‫ل ا‬2C ‫ إذا آ ن‬, ‫ ا‬, ‫ أز‬R9‫ز‬2I ‫ول‬Service Time
(Minutes)
2
3
4
5
Probability
0.30
0.28
0.25
0.17
398
‫ا ‚ال اول‪:‬‬
‫‪ 6‬آ‪9 3‬و‪ 9‬ه‪.‬ا ا‪ N‬م ‪ 6‬إ‪ U‬ء ‪ 20 ,‬ز ‪2‬ن‪ .‬وأو‪ , "; -‬ا دم وأ‪2C J‬ل ‪2 7‬ر‬
‫و ‪ w2‬ز ! ا@‪ N‬ر‪.‬‬
‫ا ‚ال ا‪:‬‬
‫أم ‪ Excel‬‬
‫آ ة ا‪ N‬م ‪ 36‬إ‪ U‬ء ‪ 200‬ز ‪2‬ن‪ .‬أو‪ ˆ9 : -‬ا‪0‬داء ‪ N‬م‪.‬‬
‫‪399‬‬
‫‪ %‬ا ا‪ ! 6‬ا‪%6‬‬
‫ء و ‪2‬ث ا" ت‬
‫‪ %J‬ا@‪6‬‬
‫آ‪ ,‬ا"‪2‬م‬
‫‪ ," -‬ا ‪2" g‬د‬
‫ا@ ر ا‪ M ` 3? U‬ا[ ‪ 1422/1421 3‬هـ‬
‫ دة ‪C ) P 241‬ق ا آ ة ‪( 1‬‬
‫ا>‪2' 3 #‬ت‬
‫أ‪ R - S-‬ا‪ ,b0‬ا ‪:,‬‬
‫ا‪A‬ال ا‪0‬ول‪:‬‬
‫‪2I‬ز‪ R9‬ز !‬
‫! ا‪2'2‬ل ‪ ,:J !? G‬إ دآ ن أ‪ 6‬ا ‪H 37"9 !J‬ول‪:‬‬
‫‪Probability‬‬
‫‪Time Between Arrivals‬‬
‫)‪(Minutes‬‬
‫‪0.23‬‬
‫‪1‬‬
‫‪0.37‬‬
‫‪2‬‬
‫‪0.28‬‬
‫‪3‬‬
‫‪0.12‬‬
‫‪4‬‬
‫)أ( و أز ‪ ! ,‬و'‪2‬ل "د ‪ 50‬ز ‪. 2‬‬
‫)ب( آ‪2‬ن رج ‪/I‬اري ‪q‬ز ‪ ,‬ا ‪2‬ة ;‪ 3‬ا`‪:‬ة ا ‪.,:‬‬
‫)ج( أ ‪2-‬دة ا‪q ;2‬ز ‪ ,‬ا ‪2‬ة ) ا ‪ O‬هة ‪ R ( O‬ا‪0‬ز ‪ ,‬ا "‪ 3; 5 7‬ا‪H‬ول‬
‫‪2‬‬
‫‪( χ 3,0.05‬‬
‫)ا ‪= 7.81 ) . α = 0.05 . .( E ,"J2‬‬
‫ا‪A‬ال ا[ ‪:3‬‬
‫‪q‬ر‪ J‬م ا ‪) :,‬إ‪J‬أ ! ا ر ! ‪7‬ا ‪(7‬‬
‫‪0.25 0.01 0.93 0.70 0.66 0.74 0.79 0.47 0.68 0.18 0.88 0.07 0.99 0.51 0.04 0.01‬‬
‫‪0.43 0.60 0.59 0.55 0.64 0.10 0.61 0.22 0.85 0.42 0.01 0.98 0.05 0.20 0.11 0.23‬‬
‫‪0.68 0.41 0.96 0.48 0.11 0.59 0.11 0.10‬‬
‫)أ( أم إ ر ا‪H‬ي ‪2; Runs Test‬ق و‪ W I‬ا ‪ @ w2‬ر ; إذا آ ‪ W‬ه‪ 5.‬ا‪0‬ر‪ J‬م‬
‫‪2O‬ا?‪. .,‬‬
‫‪b − ( 2n1n2 N ) − 1 2‬‬
‫) ‪2n1n2 1 2 2n1n2 ( 2n1n2 − N‬‬
‫= ‪+ ,σb‬‬
‫= ‪, Z0‬‬
‫‪12‬‬
‫‪2‬‬
‫‪N‬‬
‫‪2‬‬
‫)‪N ( N − 1‬‬
‫‪ 2n1n2 ( 2n1n2 − N ) ‬‬
‫‪‬‬
‫‪‬‬
‫‪N 2 ( N − 1) ‬‬
‫‪‬‬
‫‪α = 0.05, z0.025 = 1.96‬‬
‫= ‪µb‬‬
‫‪400‬‬
,‫ دا‬RI ,?‫ا‬2O ‫ات‬Y 8 ‫ ـ‬%J ‫ و‬,: ‫ ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ول ! ا‬0‫ ا‬7‫)ب( ام ا‬
:, ‫ ا‬R9‫ز‬2‫ا‬
0,
 2
x ,
2
F (x) = 
2
1 − ( 2 − x ) ,

2

1,

x≤0
0 < x ≤1
1< x ≤ 2
x>2
:P [‫ال ا‬A‫ا‬
‫ات‬Y 8 ‫ ـ‬%J ‫ و‬Acceptance-Rejection Technique ;‫ل وا‬2:‫ ا‬,:9C ‫ام‬
‫ إم‬. ( e −0.2 = 0.8187 ) λ = 0.2 w2 Poisson Variates ‫ن‬2‫ا‬2 R9‫ز‬2I RI ,?‫ا‬2O
:3‫ارزم ه‬2‫ات ا‬27 .7 ‫ا‬7 3 [‫ال ا‬A‫ ! ا‬,?‫ا‬2O"‫ م ا‬J‫ر‬0‫ا‬
. P = 1 ‫ و‬n = 0 RV :1 ‫ة‬27‫ا‬
. P × Rn +1 ‫ ـ‬P ‫ و ل‬Rn+1 3?‫ا‬2O %J‫ و ر‬:2 ‫ة‬27‫ا‬
‫ و‬6‫ا‬2 n ‫ وزد‬, ‫ ا‬n ;‫ أر‬T‫ وإ‬N = n MJ‫ إ‬.? P < e − λ W ‫ إذا آ‬:3 ‫ة‬27‫ا‬
. 2 ‫ة‬27
401
%6‫ ! ا‬6‫ ا ا‬%
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ هـ‬1424/1423 ‫ ا‬/ W1‫ر ا‬60^‫ا‬
(2 ‫آة‬#) 342 ‫ادة‬
‫ت‬2' 3 #>‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
:3 ‫ ا ] ا‬M M ` ‫أح‬
Space
*
*
*
Lost
*
*
*
STORAGE
3
Model Segment 1
GENERATE
TRANSFER
ENTER
SEIZE
LEAVE
ADVANCE
RELEASE
TERMINATE
(Exponential(1,0,500))
Both,,Lost
Space
Wash
Space
(Exponential(1,0,400))
Wash
Model Segment 2
GENERATE 48000
TERMINATE 1
:‫ا ‚ال ا‬
:GPSS ‫)ام‬$'_
:P ‫ر ا ] ا‬2C
.‫ م‬N‫ا ا‬2C ! ‫ ? ت‬6‫ إ‬R HI -1
.‫ م‬N %UX2/ , ‫ م وأز‬N ‫! و‬9.‫ "د ا " ! ا‬,9‫ار‬/I ‫اول‬- -2I -2
.Lost ‫ م‬N ‫ و‬9 % !9.‫ "د ا " ! ا‬,9‫ار‬/I ‫اول‬- -2I -3
.]I ‫ ا‬9:‫ و; ا‬RC‫ر وأ‬27 ‫ي ا ] ا‬-‫ أ‬-4
402
‫‪ %‬ا ا‪ ! 6‬ا‪%6‬‬
‫ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﺑﺤﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬
‫ﺟﺎﻣﻌﺔ ﺍﻟﻤﻠﻚ ﺳﻌﻮﺩ‬
‫ا^‪60‬ر ا‪ / W1‬ا ‪ 1424/1423‬هـ‬
‫ادة ‪#) 342‬آة ‪ (2‬ا>‪2' 3 #‬ت‬
‫أ=‪ U/2 -‬أ) ا'‪ /K‬ا _'‪)$‬ام ‪: GPSS‬‬
‫ا ‚ال اول‪:‬‬
‫‪ M I‬إ أ‪ 6‬ا ‪2‬ا† ‪ ! !2‬ا`! ‪`I 3/‬غ ‪ 3; -29 . U2 6‬ا ء زور‪7J !J‬‬
‫) ‪ S‬ا`! إ دا‪ M‬و رج ا‪0‬ر'`‪ (,‬ا‪2‬ع ا‪0‬ول ! ا`! '‪Y‬ة ا ‪ %H‬و‪ I‬ج إ‬
‫زورق ‪ 7J‬وا‪ U 6‬إ و ! ا'_ وا‪2‬ع ا[ ‪ 3‬آة ا ‪ %H‬و‪ I‬ج إ آ‪! M‬‬
‫ا‪G‬ور‪7: !J‬ه إ و ! ا'_‪ S .‬إف ‪ %H6‬ا`! ;‪`I U‬غ ‪ 3; U2 6‬أر'`‪,‬‬
‫`‪ ,‬و;‪ 3‬أز ‪ S6 ,` ,‬ا‪H‬ول ا ‪:3‬‬
‫‪2‬ع ا`‪,‬‬
‫آة‬
‫'‪Y‬ة‬
‫أز ‪ ! ,‬ا‪2'2‬ل)د‪(,:J‬‬
‫‪390 ± 60‬‬
‫‪130 ± 30‬‬
‫ز ! ا ‪)_' S‬د‪(,:J‬‬
‫‪45 ± 12‬‬
‫‪30 ± 7‬‬
‫‪3‬‬
‫‪6‬‬
‫د أر'`‪ ,‬ا`‪ ”9‬ا ‪,6‬‬
‫ز ! ا`‪(, )”9‬‬
‫‪18 ± 4‬‬
‫‪12 ± 2‬‬
‫ز ! ا ‪ ! S‬ا'_)د‪(,:J‬‬
‫‪35 ± 10‬‬
‫‪20 ± 5‬‬
‫ا`‪ S IT ,‬إ دا‪ M‬ا ء إ‪ T‬إذا آ ن ه ك ر'_ ح ‪ . U H S‬آ أن ا`!‬
‫! ا ‪ %H‬ا‪ S IT /‬إ‪ T‬إذا آ ن آ‪ ! M‬زور‪ 3J‬ا‪. U ,6 7:‬‬
‫‪ 6‬آ‪ N M 3‬م ا ء ة ا‪2‬ع وا‪ 6‬وأو‪ ˆ9 : R - -‬ا‪0‬داء ‪ N‬م‪.‬‬
‫ا ‚ال ا‪:‬‬
‫‪2/9 Y' , : M‬ن ! ‪ 3‬رات ! أر;_ ا‪ R? f‬و ‪ S‬وا‪ M 9 .6‬ا‪ !? G‬إ‬
‫ا ‪e M‬ز ‪ ! ,‬و'‪2‬ل ‪2‬ز‪ ,‬ا ‪ ., X 90 w2‬و'‪2‬ل ا‪2 G‬ن ‪! , .e9‬‬
‫آ‪2/I , 2‬ن ! ‪ , 20‬و;‪ , 6 3‬م و‪2-‬د ‪; ,‬ن ا‪2 G‬ن ‪ Y9‬در ا ‪ M‬أو ‪; N9 J‬اغ‬
‫‪ 6 ,‬ل ‪ ,H9 J %X 0.55‬إ رأو أآ[ ‪2‬ق ‪ S6‬ا‪H‬ول ا ‪:3‬‬
‫ا ر إ‪ 6‬ل د‪2‬ل ا ر ز ! ا‪2‬ق ;‪ 3‬ا ر د ا‪62‬ات ا ‪2e‬ذة ;‪ 3‬ا ر‬
‫‪, X 120 ± 60‬‬
‫‪0.75‬‬
‫‪1‬‬
‫‪3 ±1‬‬
‫‪, X 150 ± 30‬‬
‫‪0.55‬‬
‫‪2‬‬
‫‪4 ±1‬‬
‫‪, X 120 ± 45‬‬
‫‪0.82‬‬
‫‪3‬‬
‫‪5 ±1‬‬
‫ ا@‪ U‬ء ! ا‪2‬ق ‪ &H9‬ا‪2 G‬ن ‪ ,7:‬ا ‪ S‬و‪2 C 3; N9‬ر ‪ S6‬أو‪ ,92‬ا‪2'2‬ل‪.‬‬
‫ ‪ ,7:‬ا ‪ -29 S‬رف & " ا‪ R? f‬ا `‪ ,f‬وا‪ 9 J 3‬ر ‪ U‬ا‪2 G‬ن د‬
‫‪ ! 2 ± 1‬ا‪62‬ات ‪ 6‬ل ‪ . 0.25‬ز ! ا ‪ M/ ,‬ز ‪2‬ن ‪ "9‬د ا‪62‬ات ا‪99 3‬‬
‫ا?‪ U‬وه‪2X 3 2‬ان ‪ M/‬و‪6‬ة‪ " .‬إ‪ U‬ء د;‪ R‬ا ب ‪9‬ك ا‪2 G‬ن ا‪ ,‬و‪ Y9‬در‪.‬‬
‫‪ 6‬آ‪ 3‬ه‪.‬ا ا‪ N‬م ة ا‪2‬ع وا‪29 P6 6‬م ا" ‪ 8 M‬ت وأو‪ w2 -‬د ا‪ !? G‬ا‪!9.‬‬
‫^ درو ا ‪ M‬ون ‪2I‬ق "م ‪ ;2I‬ل‪- .‬ول ز ! ا ‪2/‬ث ‪ N‬م ‪ !? G‬ا ‪،!J2‬‬
‫ه‪ , "; 3‬ال وا ‪ S‬ه‪ 2‬د ال ا‪ M[ 0‬ا‪.‬ي ‪ SH9‬ان ‪ S6 ' 5;29‬ا ‪M‬‬
‫‪ :`9T 6‬أي ز ‪2‬ن؟‬
‫‪403‬‬
‫ا ا ا‬
‫د‬2" g ‫ ا‬," ‫ث ا" ت‬2 ‫ ء و‬[email protected]‫ ا‬%J
( 2 ‫ق ا آ ة‬C) P 342 ‫دة‬
‫ هـ‬1424/1423 ‫ول‬0‫ ا‬M ` 3? U‫ا@ ر ا‬
‫ ت‬3 ! G‫ا‬
: ‫ ا‬/K'‫ = ! ا‬U/2 -=‫أ‬
:‫ا ‚ال اول‬
(w:; 3 ‫ )إ ر‬:, ‫ ا‬COMMANDS ‫وا‬0‫ ا‬M ‫أ( أح‬
1- Seats
STORAGE
10
2- TimeInSys TABLE
M1,5,10,20
3- Delay
VARIABLE
[email protected]+50
4- InterAT
FUNCTION
RN1,D7
0,0/.05,1/.18,3/.34,4/.56,6/.85,7/1.0,8
(w:; 3 ‫ )إ ر‬:, ‫ ا‬BLOCKS S‫ا‬2:‫ ا‬M ‫ب( أح‬
1-
GENERATE
Exponential(1,0,3))
2-
ADVANCE
P1
3-
TABULATE
TimeInSys
4-
TEST GE
X$Seats,P$Delay
5-
SAVEVALUE
Seats-,P$Delay
:‫ا ‚ال ا‬
(w:; 3 ‫ )إ ر‬:, ‫ ا‬S‫ا‬2: , / ‫ ا‬S‫ا‬2:‫أ( أذآ ا‬
1- GENERATE
2- QUEUE
3- RELEASE
4- LEAVE
5- ADVANCE
6- TRANSFER
.aV2‫ ا‬R TRANSFER S :‫ ا‬MODES ‫ار‬2C‫! ! أ‬9‫ر‬2C ‫ب( أذآ‬
404
: ‫ ا ‚ا ا‬# )‫ وا‬U/2 -=‫أ‬
: ‫ا ‚ال ا‬
:3 ‫ ا‬R9‫ز‬2‫ ا‬U ‫ل‬2'‫! و‬
, ‫ز‬e _Y‫ ا‬,7: ‫ إ‬M I ,"
R7J
Time Between Arrivals Probability
0
0.23
1
0.37
2
0.28
3
0.12
. 0.1 ‫ وإ اف " ري‬0.5 w2 3"C R9‫ز‬2I U , ‫ق أز‬YI _Y‫ ت ا‬
.? J ‫ س‬:I ‫ ت‬J‫و‬0‫ ا‬R ‫ر‬J‫ و‬.,"7J 100 _YI ! ‫ ء‬[email protected]‫ ا‬6 ‫ م‬N ‫ى آ ة‬-‫ أ‬EXCEL ‫أ( ام‬
."; ‫ت‬N‫ أ‬3‫ ا‬R7:‫ و‬R7:‫ ا‬R H _Y‫ر ا‬2 C 3; ‫ ر‬[email protected]‫ ا‬, ‫ أز‬w2 -1
.‫_ اى‬YI ,7: ‫ ج إ‬M‫_ وه‬Y‫ ا‬, , "; -2
.‫ر‬2 7 ‫ل‬2C J‫ أ‬-3
. 3 ‫ و‬2 ‫ و‬1 3; ‫ب آ‬27 ‫ ا‬-‫ وأو‬,: ‫ة ا‬:`‫ ا‬3; ‫ى ا آ ة آ‬-‫ أ‬GPSS ‫ب( ام‬
:! ‫ا ‚ال اا‬
.g. w7 37"9 ‫ ا‬M/O‫ ا‬.‫ رات‬7:‫ ا‬,7
‫ ا‬%H ! % `‫ ا‬M: ‫م‬I ‫ ت‬6 6 9
Station
Travelig
text
Loading
text
Scale
Weighing
Queue
Loader
Queue
text
text
،‫زن‬2I 3/ ‫ إ ر'_ وزن‬,6 O‫ ك ا‬I M ‫ ر'`! و " ا‬6‫ ! ا‬6‫ ! ر'_ وا‬M I ,6 M‫آ‬
‫ رات‬7:‫ ا‬,7 ‫ ا‬,6 O‫ ك ا‬I ‫زن‬2‫ " ا‬،,:J‫ د‬2 ± 1 ‫ق‬YI ‫ان‬G ! O‫ ا‬,`'‫ ! ار‬,6‫ز ! ا‬
‫ه ب‬.‫زن وز ! ا‬2‫ ت ا‬J‫ ! واو‬O‫ ت ا‬J‫" ت او‬9‫ز‬2I ., X ‫ ! ة‬O‫ ا‬,`'‫د ا ار‬2"I‫ و‬U ‫`غ‬I‫و‬
:, ‫اول ا‬H‫ ا‬3; ‫ ة‬7" ‫ رات‬7:‫ ا‬,7 ‫دة ! وا‬2"‫وا‬
.M ‫ ا‬, ‫ول از‬- -1
Loading Time
5
Probability
0.3
405
10
15
0.5
0.2
.‫زن‬2‫ ا‬, ‫ول از‬- -2
Weighing Time
12
16
Probability
0.7
0.3
.‫ رات‬7:‫ ا‬,7
Travel Time
40
60
80
100
‫دة إ‬2"‫ه ب وا‬.‫ ا‬, ‫ول از‬- -3
Probability
0.4
0.3
0.2
0.1
.? J ‫ س‬:I ‫ ت‬J‫و‬0‫ ا‬R ‫ر‬J‫ و‬.,6 M/ ,6‫ ر‬100 ‫ @آ ل‬GPSS ‫ م ] ا آ ة‬N‫ج ا‬. .‫زن‬2‫ ! ور'_ ا‬O‫ ا‬,`'‫ ! ار‬M‫ آ‬, "; -1
.‫ر‬2 C M‫ آ‬3; ‫ ر‬[email protected]‫ ز ! ا‬w2 -2
406
‫‪4‬ر‪:‬‬
‫‪ 9 I 9 (1‬ا@ا‪ ,HI‬ا [ ‪HI ,29G`I ,: 3; a 3/‬ى ا ‪ 2‬ا ‪:3‬‬
‫‪"9‬ض ا ‪ ,XX‬ا ‪2‬اب `‪2- U‬ا?‪ G‬أ‪ 6‬ه‪ 5.‬ا‪2H‬ا?‪ , J G‬وا‪،, J U ˆ !9T‬‬
‫‪ ! S79‬ا إ ر أ‪ 6‬ه‪ 5.‬ا‪2 0‬اب و " إ رة و‪ MJ‬أن ‪ a`9‬ا ب ";‪ ,‬ا‪G? H‬ة‬
‫‪2:9‬م ‪:‬م ا ‪ a` ,:‬أ‪ 6‬أ‪2 0‬اب ا‪T‬ى ‪G? - U` UN9 3/‬ة ^ ذات ‪e9 ،, J‬ل ‪:‬م‬
‫إذا آ ن ‪ YI 99‬رأ‪ &9‬وإال إ ر‪ 5‬أ‪0‬ول وذ‪ g‬ر ا ب‬
‫ا ] ا ;‬
‫ا‪ h‬ا‪.‬ي ‪.:I‬‬
‫ا‪A‬ال ه‪ :2‬ه‪ SH9 M‬ا ‪ YI‬رأ‪ &9‬وإ ر ا ب ا‪h‬؟‬
‫ ا‬
‫آ ة أ‪ S-‬ا‪A‬ال ا ‬
‫آ ة ا ر‪29‬ه ت ا ‪:,‬‬
‫أ( `ض أن ‪ & a :‬ا"‪ 500 S‬ة‪ ،‬و`ض أ& دا? ‪ 9‬ر ا ب ر‪ 1 %J‬وأ&‬
‫‪ Y9T‬إ ر‪ a; " 5‬أ‪ 6‬ا‪2 T‬اب ا ‪; .,:‬ذا ‪ W‬أن ا‪G? H‬ة ا‪2/I J , :‬ن _ أي ب‬
‫! ا‪2 0‬اب `ˆ ا@‪ 6‬ل ا‪ ,9‬ا"‪ ! %/; ،,‬ا ات ‪ a 9‬ا ا‪G? H‬ة ا‪, :‬؟‬
‫ب( `ض أن ه‪.‬ا ا ‪ 500 S" & a‬ة اى‪ 3; ،‬ه‪ 5.‬ا ة ‪ 9‬ر دا? ا ب‬
‫ر‪ 3; 1 %J‬اا‪ Y9 %X ,9‬إ ا ب ا‪ O " h‬ه‪ 5‬ا ب ا `‪2‬ح ا‪.‬ي ‪2 9‬ي ‪G? -‬ة ^‬
‫‪; ., J‬ذا ‪ W‬أن ا‪G? H‬ة ا‪2/I J , :‬ن _ أي ب ! ا‪2 0‬اب `ˆ ا@‪ 6‬ل ا‪,9‬‬
‫ا"‪ ! %/; ،,‬ا ات ‪ a 9‬ا ا‪G? H‬ة ا‪, :‬؟‬
‫ج( إذا آ‪: W‬‬
‫ذا آ‪ M"` W‬إذا ‪ YI g SC‬إ رك ا‪0‬ول؟‬
‫‪ (2‬ا‪ S7‬ا‪UO‬ي ( ‪2‬د‪ ! M9‬ا ت ‪O‬آ‪ R9 W -3 3 ,‬ا‪2‬ز‪ R9‬ا‪3"7‬‬
‫‪ 350 w2‬وإ اف " ري ‪OI .75‬ي ‪ W -3 3‬ه‪ 5.‬ا ت‬
‫و‪U"I‬‬
‫” ‪ 4500‬ر‪ 9‬ل‬
‫” ‪ 8625‬ر‪ 9‬ل‪ _/I .‬ا‪O‬آ‪ 375 ” ,‬ر‪ 9‬ل ‪ ,C RV2‬و ‪ 4‬ر‪ 9‬ل آ‪M‬‬
‫‪ 3; MN9 S 6‬ا‪ ,9 U !9G‬آ‪ RfI 6 .U M‬ا‪O‬آ‪" ,C ,‬د ‪ S 6 1000‬‬
‫‪ ‹:9‬ا ‪G‬ون ;‪ ,9 U 3‬ا‪ .S 6 100 ! MJ0 UO‬إ;اض ان ا‪ 7‬ت ا‪: IT 3‬‬
‫;‪ 3‬أي ‪ :`I U‬‬
‫‪ a‬آ ت ;‪ ,‬آ أن ا‪ 7‬ت ا ‪ ,9 U 3; ,2V2‬أ‪ 6‬ا‪M I U0‬‬
‫;‪ 3‬ا‪ ,9‬ا‪ UO‬ا ‪.3‬‬
‫أ( ام ا‬
‫آ ة ‪J‬ر أر ح ا‪O‬آ‪ ! ,‬ا‪ :‬د !‪.‬‬
‫ب( أ;ض أن ا‪O‬آ‪ ,7: 9 I 9I ,‬ا‪ Reorder point S7‬و آ ‪ ,‬ا‪Order quantity S7‬‬
‫ا [ ‪9 I‬ا ‪ 100 M/‬و‪6‬ة ز‪ 9‬دة ;‪ ,7: 3‬ا‪2 S7‬ف ‪ : 2 2:9‬ص آ ‪ ,‬ا‪: S7‬ار‬
‫‪407‬‬
‫‪ .100‬أي ‪I‬آ‪ ,7: ! ,‬ا‪ S7‬وآ ‪ ,‬ا‪2 S7‬ف ‪ 37"I‬أ ‪ w2‬أر ح !‬
‫ا‪ :‬د !؟‬
‫‪ ,A 9 (3‬ا ‪2q 3‬اق ا آ‪ 9 ,9G‬ول ا‪: ! A‬ار ا‪ M‬ا‪.‬ي ] ! آ‪M‬‬
‫‪ ! %J‬أ‪ J‬م ا ‪ H‬ل ا‪ J : .2004 ,‬م ا ‪T" 9: 9‬ت ا ‪ 2‬ا ‪Y‬ى وا"‪ N‬‬
‫ا ‪ .%J M/ M ,/‬آ‬
‫أ& ‪e :"9‬ن "‪T‬ت ا ‪ 2‬ا‪ ! R:I 3‬ا‪ ! :‬ا ‪Y‬ى‬
‫وا"‪ ˆ` U N‬ا@‪ 6‬ل ;‪ 3‬ا وث‪9:I .‬ات ا ‪ 3; , 9‬ا‪H‬ول ا ‪:3‬‬
‫"ل ا ‪2‬‬
‫د‪ 9 2003 M‬ل‬
‫ا‪Y'0‬‬
‫ا‪%N0‬‬
‫ا‪%:‬‬
‫ا‪0‬دوات ا‪,? U/‬‬
‫‪6342213‬‬
‫‪2%‬‬
‫‪10%‬‬
‫‪ G‬ت ا ا?‬
‫‪1203231‬‬
‫‪- 4%‬‬
‫‪5%‬‬
‫‪4367342‬‬
‫‪- 2%‬‬
‫‪6%‬‬
‫‪3543532‬‬
‫‪- 1%‬‬
‫‪8%‬‬
‫‪4342132‬‬
‫‪4%‬‬
‫‪15%‬‬
‫أ‪,9.6‬‬
‫‪ G‬ت ا‪,V 9‬‬
‫ا" ب‬
‫ام ا‬
‫آ ة ‪ 9: %J‬ا‪ M‬ا‪ 3/‬ا‪.‬ي ‪ " ]9 J‬م ا‪ :‬دم ‪ .2004‬آر ا‬
‫آ ة ‪500‬‬
‫ة وأو‪ -‬ا ‪:3‬‬
‫أ( آ‪2‬ن ;ة ‪2 w2 95% ,:X‬ى ا‪ M‬ا ‪ " RJ2‬م ‪.2004‬‬
‫ب( ‪2 S6‬ذ‪ g-‬ه‪ 3‬ا`ص ;‪ 3‬أن ‪2/9‬ن ا‪ M‬ا‪ 2004 , 3; 3/‬أآ[ ! ‪ 5%‬ز‪ 9‬دة‬
‫‪ ! ,‬ا" م ا ؟‬
‫‪; (4‬ق ا‪? " ,; f‬ت ‪ 29 -AI ,;^ 100 &9‬‬
‫ا`ق ‪ 100‬ر‪ 9‬ل ‪ ,;Y‬آ‬
‫” ‪ 400‬ر‪ 9‬ل ‪ _/I .,;Y‬إدارة‬
‫ر‪ ،_NI) ,2 _9‬روا‪ , ' ،SI‬ا‪29 M/ (d‬م ‪&; -eI‬‬
‫ا‪ ! &2J %I GH6 M/ .,;Y‬ا`ق ه ك إ‪ 6‬ل ‪ 5%‬أن ا‪2f‬ف ! ‪ .2 9‬إذا أ‪ .‬ا`ق‬
‫‪2H6‬زات أآ[ ! د ا‪Y‬ف ا‪^ O‬ة ;ن & ‪ 92"I‬ا‪ _f‬ا‪ :‬دم‬
‫‪A GH‬آ وا‪.‬ي‬
‫‪^ ,;^ H9T‬ة ” ‪ 750‬ر‪ 9‬ل‪6 .‬د د ا ‪2H‬زات ا‪ !/ 9 3‬ان ‪ U:9‬ا`ق‬
‫‪ w2 %N"9‬ر & ا‪ .3 2‬أم ‪/I 500‬ار ‬
‫‪408‬‬
‫آ ة ‪2 M/‬ى ‪.5.eI GH6‬‬
‫‪P‬‬
‫‪ I (5‬أ‪ 6‬ا ‪T2‬ت ا زل ‪HI‬ي ‪ ! Y‬ا ل‪ UI ! .‬ا ‪:I ,:‬ر أن !‬
‫‪ _ ! UC 9‬ا ب ‪ ! %U 80% M/O9‬ا ء و ‪ ! 20%‬ا‪ -‬ل‪ .‬آ ا‪:I U‬ر أن‬
‫‪ ! 70%‬ا ء ا•‪ ! ” U? 7 ! :9 UC 9 3I‬ا ل و‪ ! 40% w:; !/‬ا‪ -‬ل‬
‫ا‪2"`9 U2C 9 !9.‬ن ذ‪ .g‬أ‪ UI ! f9‬ا ‪:I ,:‬ر أن ا ” ا‪.‬ي ‪ &7"9‬ا ء ‪R9‬‬
‫‪2I‬ز‪ 20 w2 3"C R9‬ر‪ 9‬ل وإ اف " ري ‪ 3‬ر‪ 9‬ل ذ‪ - g‬ل ‪ R9‬ا‪2I f9‬ز‪R9‬‬
‫‪ 10 w2 3"C‬ر‪ 9‬ل وإ اف " ري ‪ 2‬ر‪ 9‬ل‪) .‬إذا ‪ W‬أن ا ‪ 10 ! 37YI ,2‬إ‬
‫‪ ˆ` 29 TG 15‬ا@‪ 6‬ل( ;‪:‬ر ‪ w2‬د‪) U‬ا‪ 3;) (3 2‬ز‪ 9‬رة "د ‪G 200‬ل‪(.‬‬
‫‪ a ! " ! ," ,: 3; (6‬ا ‪2‬ن " " أن ‪ %9‬إ ر ا ! ‪,2 H‬‬
‫ ‪79 !:‬ح & ة أ‪2/I ,b‬ن آ‪ ! U M‬أر ‪ R‬إ‪ -‬ت‬
‫ ‪ ,‬وا‪6‬ة ‪; , ' U‬ذا‬
‫أ‪ -‬ب ا ا‪A‬ال ا ‪7‬وح ‪A M:9 &; , ' , -‬ال ا ‪ 3‬وه‪./‬ا ‪M 9 6‬‬
‫إ ‪A‬ال ا ‪2‬ن‪; .‬ض أن ا@‪ , -‬ا[ [‪A M/ ,‬ال ه‪ 3‬ا@‪ , -‬ا‬
‫ ‪ ,‬وأن ا ‬
‫‪ 9‬ر أ‪ 6‬ا@‪ -‬ت ا‪0‬ر "‪2O ,:97 ,‬ا?‪ ˆ` ,‬ا@‪ 6‬ل وإذا آ ن ه ك ‪A 16‬ا‪6 T‬‬
‫‪ a 9‬ا ‪2‬ن‬
‫أ( أو‪ , -‬ا ‪ 500 ! ! !:‬ا‪2 9 !9.‬ن ا ‪2‬ن‪.‬‬
‫ب( إذا آ ‪ W‬ا@‪ , -‬ا‬
‫ ‪A ! YI ,‬ال ‪2O ,:97 h‬ا?‪,‬‬
‫‪2/I P‬ن أي !‬
‫ا@‪ -‬ت ا‪0‬ر "‪ ,‬و `ˆ ا@‪ 6‬ل أو‪ , -‬ا ‪ 500 ! ! !:‬ا‪2 9 !9.‬ن‬
‫ا ‪2‬ن‪.‬‬
‫ج( ‪ 6‬آ‪ a ! " ,: 3‬ا ‪2‬ن " آ ‪ OI‬هه ا`‪29G‬ن وأو‪ , -‬ا ‪! !:‬‬
‫! ‪ 500‬ا‪2 9 !9.‬ن ا ‪2‬ن‪.‬‬
‫‪ (7‬إ ر "د ا@ رات ‪2/9‬ن ! ‪ 10‬أ‪ ،,b‬آ‪A M‬ال ‪ 4 ,‬إ‪ -‬ت )‪ (A‬و )‪ (B‬و )‪ (C‬و‬
‫)‪ (D‬وا‪6‬ة ‪ J ., ' w:; U‬م ‪ S2 ^ S C‬دة ‪ , -‬ا‪ ,:97 ,b0‬ا ‪:,‬‬
‫أو‪; ,G , 3 9 (T‬ذا ƒ‪ U‬و‪ H &-‬أ ر ا@‪ (A) ! -‬و )‪ (B‬وإ‪ T‬أ ر )‪ (C‬و )‪.(D‬‬
‫‪ 3 9 ( X‬ا" ‪ ,‬ة اي ‪ 9 3/‬ر وا‪6‬ة ! ا@‪; ! -‬ذا ƒ‪ U‬و‪ H &-‬أ ر ا@‪& -‬‬
‫)‪ (A‬أو )‪ (C‬وإ‪ T‬ا ر )‪ (B‬أو )‪ .(D‬أ‪ N‬ا‪ M/O‬ا ‪:3‬‬
‫‪409‬‬
‫)‪H (A‬‬
‫)‪H (A & B‬‬
‫)‪T (B‬‬
‫)‪H (C‬‬
‫)‪T (C & D‬‬
‫)‪T (D‬‬
‫)أ( ;ض أن آ‪A M‬ال & ‪ ,‬وا‪6‬ة‪ ،‬وأن ا‪ H‬ح ‪2/9‬ن أ س ا@‪ , -‬ا‬
‫ ‪ 10 ! 5‬أ‪J .,b‬ر ام ا‬
‫ أن ا@‪ -‬ت ا‬
‫ا‪A‬ال‬
‫ا@‪ , -‬ا‬
‫ ‪,‬‬
‫ ‪,‬‬
‫آ ة إ‪ 6‬ل ‪ H‬ح ه‪.‬ا ا‪/I 200 S 7‬ارا‪.‬‬
‫ ‪ ,‬ه‪ 3‬آ ;‪ 3‬ا‪H‬ول ا ‪:3‬‬
‫‪1‬‬
‫‪2‬‬
‫‪3‬‬
‫‪4‬‬
‫‪5‬‬
‫‪6‬‬
‫‪7‬‬
‫‪8‬‬
‫‪9‬‬
‫‪10‬‬
‫‪B‬‬
‫‪A‬‬
‫‪A‬‬
‫‪C‬‬
‫‪B‬‬
‫‪D‬‬
‫‪C‬‬
‫‪D‬‬
‫‪B‬‬
‫‪D‬‬
‫)ب( أ ;‪:‬ة )أ( إذا آ ن ا‪ H‬ح أ س ا@‪ , -‬ا‬
‫ ‪ 10 ! 6 ,‬أ‪.,b‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال اا !‪:‬‬
‫‪ M I‬إ أ‪ 6‬ا ‪2‬ا† ‪ ! !2‬ا`! ‪`I 3/‬غ ‪ 3; -29 . U2 6‬ا ء زور‪7J !J‬‬
‫) ‪ S‬ا`! إ دا‪ M‬و رج ا‪0‬ر'`‪ (,‬ا‪2‬ع ا‪0‬ول ! ا`! '‪Y‬ة ا ‪ %H‬و‪ I‬ج إ‬
‫زورق ‪ 7J‬وا‪ U 6‬إ و ! ا'_ وا‪2‬ع ا[ ‪ 3‬آة ا ‪ %H‬و‪ I‬ج إ آ‪! M‬‬
‫ا‪G‬ور‪7: !J‬ه إ و ! ا'_‪ S .‬إف ‪ %H6‬ا`! ;‪`I U‬غ ‪ 3; U2 6‬أر'`‪,‬‬
‫`‪ ,‬و;‪ 3‬أز ‪ S6 ,` ,‬ا‪H‬ول ا ‪:3‬‬
‫‪2‬ع ا`‪,‬‬
‫'‪Y‬ة‬
‫آة‬
‫‪130 ± 30‬‬
‫‪390 ± 60‬‬
‫ز ! ا ‪)_' S‬د‪(,:J‬‬
‫‪30 ± 7‬‬
‫‪45 ± 12‬‬
‫د أر'`‪ ,‬ا`‪ ”9‬ا ‪,6‬‬
‫‪6‬‬
‫‪3‬‬
‫أز ‪,‬‬
‫! ا‪2'2‬ل)د‪(,:J‬‬
‫‪410‬‬
‫ز ! ا`‪(, )”9‬‬
‫‪12 ± 2‬‬
‫‪18 ± 4‬‬
‫ز ! ا ‪ ! S‬ا'_)د‪(,:J‬‬
‫‪20 ± 5‬‬
‫‪35 ± 10‬‬
‫ا`‪ S IT ,‬إ دا‪ M‬ا ء إ‪ T‬إذا آ ن ه ك ر'_ ح ‪ . U H S‬آ أن ا`!‬
‫! ا ‪ %H‬ا‪ S IT /‬إ‪ T‬إذا آ ن آ‪ ! M‬زور‪ 3J‬ا‪. U ,6 7:‬‬
‫‪ 6‬آ‪ N M 3‬م ا ء ة ا‪2‬ع وا‪ 6‬وأو‪ ˆ9 : R - -‬ا‪0‬داء ‪ N‬م‪.‬‬
‫‪411‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال ا‪:"#$‬‬
‫‪2/9 Y' , : M‬ن ! ‪ 3‬رات ! أر;_ ا‪ R? f‬و‬
‫ا ‪e M‬ز ‪,‬‬
‫! و'‪2‬ل ‪2‬ز‪ ,‬ا‬
‫‪ S‬وا‪ M 9 .6‬ا‪ !? G‬إ‬
‫‪ ., X 90 w2‬و'‪2‬ل ا‪2 G‬ن ‪! , .e9‬‬
‫آ‪2/I , 2‬ن ! ‪ , 20‬و;‪ , 6 3‬م و‪2-‬د ‪; ,‬ن ا‪2 G‬ن ‪ Y9‬در ا ‪ M‬أو ‪; N9 J‬اغ‬
‫‪ 6 ,‬ل ‪ ,H9 J %X 0.55‬إ رأو أآ[ ‪2‬ق ‪ S6‬ا‪H‬ول ا ‪:3‬‬
‫ا ر‬
‫إ‪ 6‬ل د‪2‬ل ا ر‬
‫ز ! ا‪2‬ق ;‪ 3‬ا ر‬
‫د ا‪62‬ات ا ‪2e‬ذة ;‪ 3‬ا ر‬
‫‪1‬‬
‫‪0.75‬‬
‫‪, X 120 ± 60‬‬
‫‪3 ±1‬‬
‫‪2‬‬
‫‪0.55‬‬
‫‪, X 150 ± 30‬‬
‫‪4 ±1‬‬
‫‪3‬‬
‫‪0.82‬‬
‫‪, X 120 ± 45‬‬
‫‪5 ±1‬‬
‫ ا@‪ U‬ء ! ا‪2‬ق ‪ &H9‬ا‪2 G‬ن ‪ ,7:‬ا‬
‫ ‪ ,7:‬ا‬
‫‪ S‬و‪2 C 3; N9‬ر ‪ S6‬أو‪ ,92‬ا‪2'2‬ل‪.‬‬
‫‪ -29 S‬رف & " ا‪ R? f‬ا `‪ ,f‬وا‪ 9 J 3‬ر ‪ U‬ا‪2 G‬ن د‬
‫‪ ! 2 ± 1‬ا‪62‬ات ‪ 6‬ل ‪ . 0.25‬ز ! ا‬
‫‪ M/ ,‬ز ‪2‬ن ‪ "9‬د ا‪62‬ات ا‪99 3‬‬
‫ا?‪ U‬وه‪2X 3 2‬ان ‪ M/‬و‪6‬ة‪ " .‬إ‪ U‬ء د;‪ R‬ا ب ‪9‬ك ا‪2 G‬ن ا‪ ,‬و‪ Y9‬در‪.‬‬
‫‪ 6‬آ‪ 3‬ه‪.‬ا ا‪ N‬م ة ا‪2‬ع وا‪29 P6 6‬م ا" ‪ 8 M‬ت وأو‪ w2 -‬د ا‪ !? G‬ا‪!9.‬‬
‫^ درو ا ‪ M‬ون ‪2I‬ق "م ‪ ;2I‬ل‪- .‬ول ز ! ا ‪2/‬ث ‪ N‬م ‪ !? G‬ا ‪،!J2‬‬
‫ه‪ , "; 3‬ال وا‬
‫‪ S‬ه‪ 2‬د ال ا‪ M[ 0‬ا‪.‬ي ‪ SH9‬ان ‪ S6 ' 5;29‬ا ‪M‬‬
‫‪ :`9T 6‬أي ز ‪2‬ن؟‬
‫‪412‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال ا دس‪:‬‬
‫;‪3‬‬
‫‪ R M‬ا `ق ا‪ S7‬ا‪ R9 !" 3 2‬ا‪2‬ز‪ N (10, 4 ) R9‬و‪6‬ة‪ .‬آ ‪‹:‬‬
‫ا ‪G‬ون ! ه‪.‬ا ا ! ‪2‬ى ‪ 30‬و‪6‬ة ;ن ' ‪ S6‬ا ‪ R ,C Rf9 M‬ا ‪2‬رد "د‬
‫‪ 100‬و‪6‬ة وا‪ M I 3‬إ ا ‪; 3; M‬ة ز ‪ 6 ! ,‬و ‪ 10‬أ‪ 9‬م ‪2‬ز‪ ,‬و‪ .,9‬أي ‪,C‬‬
‫‪G HIT‬ون آ ;‪.:`I U 3‬‬
‫أو‪2I -‬ز‪ R9‬ا ‪Y‬ات ا"‪2O‬ا?‪ :,‬ا " ت ا‪ , 2‬ا `‪2:‬دة و د ا‪62‬ات ;‪ 3‬ا ‪G‬ون‬
‫ا‪.3 2‬‬
‫‪413‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال ا !‪:‬‬
‫‪ , %"7‬ا‪ & M "9 ,"9‬د ! و& ‪2 C‬ر وا‪ Nz 6‬ر‪ ،‬ز !‬
‫! ا‪2'2‬ل ‪!? G‬‬
‫& ‪2I‬ز‪ . 2.5 ± 1.5 R9‬أ‪ 6‬ا د ! ‪ 9‬أ‪" 6‬وف ! ‪ MJ‬ا‪ !? G‬وه‪ 2‬أآ[ ة و‪,‬‬
‫;‪ 3‬ا ‪ ! ,‬ز & ا ‪ ،/ H‬ا‪2 G‬ن ا‪.‬ي ‪ M 9‬و‪ H9‬آ‪ ! M‬أ‪ 6‬و ‪ ; /‬ر^! ‪ 9‬ر‬
‫أ‪ ., 6‬ز ! ‪ ,‬ا‪2 G‬ن ‪2I & 60‬ز‪ 3.5 ± 1.5 R9‬و‪. 4.5 ± 1.5 /‬‬
‫‪ 6‬آ‪ 3‬ا‪ N‬م ‪ 6‬إ‪ U‬ء ‪ 1000 ,‬ز ‪2‬ن وأو‪ , "; -‬آ‪ ! M‬أ‪ 6‬و ‪ /‬ود ا‪ !? G‬ا‪!9.‬‬
‫‪2 %U W I‬ا‪ ,7‬آ‪ ! M‬أ‪ 6‬و ‪ /‬وأو‪2I -‬ز‪2C R9‬ل ا‪2 7‬ر‪.‬‬
‫أ=‪ U/2 -‬ا ‚ال ا _'‪)$‬ام ‪: GPSS‬‬
‫ا ‚ال اول‪:‬‬
‫‪2/9‬ن‬
‫ف ! ‪' 5‬ا;!‪ a`9 ،‬ا‬
‫ف أ ‪2‬ا & ا ‪ 6 ' 9:00 ,‬و‪ Y9‬ا ‪5:00 ,‬‬
‫ ا‪ ،‬و‪ ( , 3U9 6 M " 9 !/‬ز ‪2‬ن و'‪ MJ M‬أو ‪ 5:00‬ا‪ .‬أز ‪,‬‬
‫! ا‪2'2‬ل ‪2I U !? G‬ز‪ R9‬ا‪ 1 w2 3‬د‪ ,:J‬وأز ‪ ,‬ا ‪2I U !? G ,‬ز‪ R9‬ا‪3‬‬
‫‪ 4.5 w2‬د‪.,:J‬‬
‫آ‪' M‬اف & ‪2 C‬ر ص &‪ 9 .‬ول أي ز ‪2‬ن و'‪2I M‬ا ا@ ق ‪2 C Je‬ر و;‪ 6 3‬ل‬
‫‪ I‬وي أ‪2C‬ال ا‪27‬ا ‪ 9‬ا‪2 G‬ن ‪2 7‬ر ;‪ 3‬أ‪ J‬ا ر‪ .‬أي ز ‪2‬ن ;‪ ,9 U 3‬أي ‪2 C‬ر‬
‫‪9‬ك ‪2 C‬ر‪ 5‬و‪2 7 9‬ر ا‪ 6 3; J0‬ل آ‪2‬ن ه ك ‪2 C‬ر أ‪2 C ! J‬ر‪ 5‬و‬
‫‪2/9‬ن ه ك ‪2 C‬ر‪ !9‬و‪ !9‬أ‪2 C ! J‬ر‪ 9 5‬ا‪2 G‬ن ‪2 7‬ر ا‪ 3; J0‬أ‪ J‬‬
‫ا ر‪ ،‬وإذا آ ن ه‪.‬ا ا‪2 7‬ر ‪9‬أ ا‪2 G‬ن ‪2; ,‬را‪.‬‬
‫‪ I‬ص إدارة ا‬
‫ف إر‪ V‬ء ا‪ !? G‬و‪ 3; /`I‬ز‪ 9‬دة 'اف أو أآ[ و‪ 9I !/‬ا‪ :‬م‬
‫را‪ U %I ,‬ه‪.‬ا ا‪:‬ار‪%J .‬‬
‫آ ة ‪ N‬م ا‬
‫إ‪ 3; V‬ة ‪ ، 29 30‬ه‪gI '2I 3‬؟‬
‫‪414‬‬
‫ف ‪ 6‬و;‪ , 6 3‬إ‪ 1 ,; V‬أو ‪' 2‬اف‬
‫أ=‪ U/2 -‬ا ‚ال ا _'‪)$‬ام ‪: GPSS‬‬
‫ا ‚ال ا‪:‬‬
‫‪ 2 H 5 & R‬ت ! ا‪Th‬ت‪ ،‬ا ‪ ,2 H‬ا‪0‬و ‪T( 3 U‬ت وا ‪ ,2 H‬ا[ ‪,( 2 U ,‬‬
‫وا[ [‪T( 4 U ,‬ت واا "‪T( 3 U ,‬ت وا ‪ ,( 1 U ,‬وا‪6‬ة و‪ R -‬ا‪Th‬ت ه‪3; U` 3‬‬
‫ا ‪ ,2 H‬ا‪2‬ا‪6‬ة‪ M I .‬ا‪ _? ƒ2‬ا اد ‪ U" I‬إ ا‬
‫ا‪3‬‬
‫‪e R‬ز ‪,‬‬
‫! و'‪2‬ل ‪2I U‬ز‪R9‬‬
‫‪ ., 0.25 w2‬ا‪ _? ƒ2‬ا‪2‬ا'‪2/I ,‬ن ! ‪ 3‬أ‪2‬اع‪ ،‬ا‪ ! _? ƒ2‬ا‪2‬ع ا‪0‬ول‬
‫‪2/I‬ن ‪ ! 30%‬ا‪ _? ƒ2‬و ! ا‪2‬ع ا[ ‪2/I 3‬ن ‪ ! 50%‬ا‪ _? ƒ2‬و ! ا‪2‬ع ا[ ‪2/I P‬ن‬
‫‪ ! 20%‬ا‪ ._? ƒ2‬ا‪ ! _? ƒ2‬ا‪2‬ع ا‪0‬ول ‪ I‬ج إ ‪ U 4‬م @‪ H‬زه و ! ا‪2‬ع ا[ ‪ 3‬إ‬
‫‪ U 3‬م @‪ H‬زه و ! ا‪2‬ع ا[ ‪ P‬إ ‪ U 5‬م @‪ H‬زه وآ‪ SH9 , U M‬أن ‪,2 H %I‬‬
‫"‪ ! ,‬ا‪Th‬ت و ‪ !" SI‬آ ;‪ 3‬ا‪H‬ول ا ‪:3‬‬
‫‪2‬ع ا‪,`ƒ2‬‬
‫‪ ,2 H‬ا ‪ ! ) SI !? /‬ا ر(‬
‫‪1‬‬
‫‪3, 1, 2, 5‬‬
‫‪2‬‬
‫‪4, 1, 3‬‬
‫‪3‬‬
‫‪2, 5, 1, 4, 3‬‬
‫أز ‪ ,‬ا ‪ ,2 H S6 , U M/ ,‬ا‪Th‬ت ‪2I U‬ز‪ "9‬ت و‪ S6 ,9‬ا‪H‬ول ا ‪:3‬‬
‫‪2‬ع ا‪,`ƒ2‬‬
‫أز ‪ ,‬ا ‪ U ,‬م ‪ ! ) ,‬ا ر(‬
‫‪1‬‬
‫) ‪( 0.50 ± 0.10 ) , ( 0.60 ± 0.05 ) , ( 0.85 ± 0.15 ) , ( 0.50 ± 0.20‬‬
‫‪2‬‬
‫)‪(1.10 ± 0.20 ) , ( 0.80 ± 0.15) , ( 0.75 ± 0.25‬‬
‫‪3‬‬
‫) ‪(1.20 ± 0.15 ) , ( 0.25 ± 0.05 ) , ( 0.70 ± 0.15 ) , ( 0.90 ± 0.20 ) , (1.00 ± 0.10‬‬
‫ا‪ _? ƒ2‬ا‪2‬ا'‪ NI ,2 H M/ ,‬دوره ;‪ , 6 3‬إ‪ YO‬ل ا‪ ,h‬ا‪2: 3‬م " ‪U M‬‬
‫وا‪ ,`ƒ2 ,f;0‬ا‪ M I 3‬أو‪.T‬‬
‫‪ 6‬آ‪ 29 365 3‬‬
‫‪ R‬إ ر أن ا‪2‬م ‪2/9‬ن ! ‪ 8‬ت و‪J‬ر ‪ w2‬أز ‪ ,‬ا‪e‬‬
‫;‪ 3‬ا‪27‬ا و‪J‬ر ‪2C w2‬ل و;" ‪ ,‬آ‪2 C M‬ر ;‪ 3‬آ‪.,2 H M‬‬
‫‪415‬‬
‫أ=‪ U/2 -‬ا ‚ال ا _'‪)$‬ام ‪: GPSS‬‬
‫ا ‚ال ا ‪:‬‬
‫‪ M I‬ا`! إ ء ‪e‬ز ‪,‬‬
‫! و'‪2‬ل ‪2I U‬ز‪ R9‬ا‪ . 29 1.25 w2 3‬ا ء ‪2/9‬ن‬
‫! ر'`! ‪) ”9`I ,( U M/‬و›( وا‪6‬ة‪ .‬ا`! ا‪ M I 3‬و‪ HI‬ا‪0‬ر'`‪NI ,2YO ,‬‬
‫;‪2 C 3‬ر وا‪ S6 6‬أو‪ ,92‬و'‪ . U2‬ز ! ‪2I & ,` ”9`I‬ز‪ R9‬وي ! ‪ 0.5‬و ‪1.5‬‬
‫‪ , 6 3; . 29‬و‪2-‬د `‪ ,‬وا‪6‬ة ;‪ 3‬ا ء ;ن (‪T‬ت ا`‪ ”9‬آ‪ "9 U‬ن ‪U‬‬
‫‪ 9‬‬
‫ز ! ‪ UY9`I‬إ ا _‪ .‬و‪2-‬د `! ;‪ 3‬ا ء ;ن (‪T‬ت ا`‪ M "I ”9‬آ‪ M‬وا‪6‬ة ‬
‫`‪ 6 3; .,‬ل ‪ M‬ا‪ ,` !h‬وو'‪2‬ل `‪; , X ,‬ن أ‪ 6‬ا‪Th‬ت ‪2; U R7:I‬را‬
‫و‪I‬أ ا" ‪ M‬ا`‪ ,‬ا‪ 3‬و'‪ W‬وا‪ ! G‬ا ‪ ”9` 3:‬ا`‪ ,‬ا‪0‬و ‪._ f9‬‬
‫أ‪-‬ي‬
‫آ ة ‪ N‬م ا ء ة ‪ 29 90‬و‪J‬ر أ‪ MJ‬و أ ‪ w2‬ز ! ‪2/‬ث ا`! ;‪ 3‬ا‪ N‬م‬
‫وآ‪J g.‬ر ;" ‪ ,‬ا‪0‬ر'`‪ ,‬و(‪T‬ت ا`‪.”9‬‬
‫‪416‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال اا !‪:‬‬
‫‪ M I‬إ أ‪ 6‬ا ‪2‬ا† ‪ ! !2‬ا`! ‪`I 3/‬غ ‪ 3; -29 . U2 6‬ا ء زور‪7J !J‬‬
‫) ‪ S‬ا`! إ دا‪ M‬و رج ا‪0‬ر'`‪ (,‬ا‪2‬ع ا‪0‬ول ! ا`! '‪Y‬ة ا ‪ %H‬و‪ I‬ج إ‬
‫زورق ‪ 7J‬وا‪ U 6‬إ و ! ا'_ وا‪2‬ع ا[ ‪ 3‬آة ا ‪ %H‬و‪ I‬ج إ آ‪! M‬‬
‫ا‪G‬ور‪7: !J‬ه إ و ! ا'_‪ S .‬إف ‪ %H6‬ا`! ;‪`I U‬غ ‪ 3; U2 6‬أر'`‪,‬‬
‫`‪ ,‬و;‪ 3‬أز ‪ S6 ,` ,‬ا‪H‬ول ا ‪:3‬‬
‫‪2‬ع ا`‪,‬‬
‫'‪Y‬ة‬
‫آة‬
‫‪130 ± 30‬‬
‫‪390 ± 60‬‬
‫ز ! ا ‪)_' S‬د‪(,:J‬‬
‫‪30 ± 7‬‬
‫‪45 ± 12‬‬
‫د أر'`‪ ,‬ا`‪ ”9‬ا ‪,6‬‬
‫‪6‬‬
‫‪3‬‬
‫ز ! ا`‪(, )”9‬‬
‫‪12 ± 2‬‬
‫‪18 ± 4‬‬
‫ز ! ا ‪ ! S‬ا'_)د‪(,:J‬‬
‫‪20 ± 5‬‬
‫‪35 ± 10‬‬
‫أز ‪,‬‬
‫! ا‪2'2‬ل)د‪(,:J‬‬
‫ا`‪ S IT ,‬إ دا‪ M‬ا ء إ‪ T‬إذا آ ن ه ك ر'_ ح ‪ . U H S‬آ أن ا`!‬
‫! ا ‪ %H‬ا‪ S IT /‬إ‪ T‬إذا آ ن آ‪ ! M‬زور‪ 3J‬ا‪. U ,6 7:‬‬
‫‪ 6‬آ‪ N M 3‬م ا ء ة ا‪2‬ع وا‪ 6‬وأو‪ ˆ9 : R - -‬ا‪0‬داء ‪ N‬م‪.‬‬
‫‪417‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال ا‪:"#$‬‬
‫‪2/9 Y' , : M‬ن ! ‪ 3‬رات ! أر;_ ا‪ R? f‬و‬
‫ا ‪e M‬ز ‪,‬‬
‫! و'‪2‬ل ‪2‬ز‪ ,‬ا‬
‫‪ S‬وا‪ M 9 .6‬ا‪ !? G‬إ‬
‫‪ ., X 90 w2‬و'‪2‬ل ا‪2 G‬ن ‪! , .e9‬‬
‫آ‪2/I , 2‬ن ! ‪ , 20‬و;‪ , 6 3‬م و‪2-‬د ‪; ,‬ن ا‪2 G‬ن ‪ Y9‬در ا ‪ M‬أو ‪; N9 J‬اغ‬
‫‪ 6 ,‬ل ‪ ,H9 J %X 0.55‬إ رأو أآ[ ‪2‬ق ‪ S6‬ا‪H‬ول ا ‪:3‬‬
‫ا ر‬
‫إ‪ 6‬ل د‪2‬ل ا ر‬
‫ز ! ا‪2‬ق ;‪ 3‬ا ر‬
‫د ا‪62‬ات ا ‪2e‬ذة ;‪ 3‬ا ر‬
‫‪1‬‬
‫‪0.75‬‬
‫‪, X 120 ± 60‬‬
‫‪3 ±1‬‬
‫‪2‬‬
‫‪0.55‬‬
‫‪, X 150 ± 30‬‬
‫‪4 ±1‬‬
‫‪3‬‬
‫‪0.82‬‬
‫‪, X 120 ± 45‬‬
‫‪5 ±1‬‬
‫ ا@‪ U‬ء ! ا‪2‬ق ‪ &H9‬ا‪2 G‬ن ‪ ,7:‬ا‬
‫ ‪ ,7:‬ا‬
‫‪ S‬و‪2 C 3; N9‬ر ‪ S6‬أو‪ ,92‬ا‪2'2‬ل‪.‬‬
‫‪ -29 S‬رف & " ا‪ R? f‬ا `‪ ,f‬وا‪ 9 J 3‬ر ‪ U‬ا‪2 G‬ن د‬
‫‪ ! 2 ± 1‬ا‪62‬ات ‪ 6‬ل ‪ . 0.25‬ز ! ا‬
‫‪ M/ ,‬ز ‪2‬ن ‪ "9‬د ا‪62‬ات ا‪99 3‬‬
‫ا?‪ U‬وه‪2X 3 2‬ان ‪ M/‬و‪6‬ة‪ " .‬إ‪ U‬ء د;‪ R‬ا ب ‪9‬ك ا‪2 G‬ن ا‪ ,‬و‪ Y9‬در‪.‬‬
‫‪ 6‬آ‪ 3‬ه‪.‬ا ا‪ N‬م ة ا‪2‬ع وا‪29 P6 6‬م ا" ‪ 8 M‬ت وأو‪ w2 -‬د ا‪ !? G‬ا‪!9.‬‬
‫^ درو ا ‪ M‬ون ‪2I‬ق "م ‪ ;2I‬ل‪- .‬ول ز ! ا ‪2/‬ث ‪ N‬م ‪ !? G‬ا ‪،!J2‬‬
‫ه‪ , "; 3‬ال وا‬
‫‪S‬‬
‫ه‪ 2‬د ال ا‪ M[ 0‬ا‪.‬ي ‪ SH9‬ان ‪ S6 ' 5;29‬ا ‪M‬‬
‫‪ :`9T 6‬أي ز ‪2‬ن؟‬
‫‪418‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال ا دس‪:‬‬
‫;‪3‬‬
‫‪ R M‬ا `ق ا‪ S7‬ا‪ R9 !" 3 2‬ا‪2‬ز‪ N (10, 4 ) R9‬و‪6‬ة‪ .‬آ ‪‹:‬‬
‫ا ‪G‬ون ! ه‪.‬ا ا ! ‪2‬ى ‪ 30‬و‪6‬ة ;ن ' ‪ S6‬ا ‪ R ,C Rf9 M‬ا ‪2‬رد "د‬
‫‪ 100‬و‪6‬ة وا‪ M I 3‬إ ا ‪; 3; M‬ة ز ‪ 6 ! ,‬و ‪ 10‬أ‪ 9‬م ‪2‬ز‪ ,‬و‪ .,9‬أي ‪,C‬‬
‫‪G HIT‬ون آ ;‪.:`I U 3‬‬
‫أو‪2I -‬ز‪ R9‬ا ‪Y‬ات ا"‪2O‬ا?‪ :,‬ا " ت ا‪ , 2‬ا `‪2:‬دة و د ا‪62‬ات ;‪ 3‬ا ‪G‬ون‬
‫ا‪.3 2‬‬
‫‪419‬‬
‫ ا ‚ال ا _'‪)$‬ام ‪:GPSS‬‬
‫ا ‚ال ا !‪:‬‬
‫‪ , %"7‬ا‪ & M "9 ,"9‬د ! و& ‪2 C‬ر وا‪ Nz 6‬ر‪ ،‬ز !‬
‫! ا‪2'2‬ل ‪!? G‬‬
‫& ‪2I‬ز‪ . 2.5 ± 1.5 R9‬أ‪ 6‬ا د ! ‪ 9‬أ‪" 6‬وف ! ‪ MJ‬ا‪ !? G‬وه‪ 2‬أآ[ ة و‪,‬‬
‫;‪ 3‬ا ‪ ! ,‬ز & ا ‪ ،/ H‬ا‪2 G‬ن ا‪.‬ي ‪ M 9‬و‪ H9‬آ‪ ! M‬أ‪ 6‬و ‪ ; /‬ر^! ‪ 9‬ر‬
‫أ‪ ., 6‬ز ! ‪ ,‬ا‪2 G‬ن ‪2I & 60‬ز‪ 3.5 ± 1.5 R9‬و‪. 4.5 ± 1.5 /‬‬
‫‪ 6‬آ‪ 3‬ا‪ N‬م ‪ 6‬إ‪ U‬ء ‪ 1000 ,‬ز ‪2‬ن وأو‪ , "; -‬آ‪ ! M‬أ‪ 6‬و ‪ /‬ود ا‪ !? G‬ا‪!9.‬‬
‫‪2 %U W I‬ا‪ ,7‬آ‪ ! M‬أ‪ 6‬و ‪ /‬وأو‪2I -‬ز‪2C R9‬ل ا‪2 7‬ر‪.‬‬
‫‪420‬‬
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http://www.abarry.ws/books/or221book1.pdf RJ2 ‫ ا‬3; [email protected]‫ ا‬: ‫ا‬
4) Discrete-Event System Simulation, Second Ed.
By: Jerry Banks, John S. Carson, II and Barry L. Nelson.
Published by: Prentice Hall, 1996
5) Simulation Modelling and Analysis, Second Ed.
By: Avrill M. Law and W. David Kelton.
Published by: McGraw-Hill, 1991
6) Simulation with Arena.
By: W. David Kelton, Randall P. Sadowski and Deborah A. Sadowski.
Published by: McGraw-Hill,1998
7) Applied Management Science, Modelling, Spreadsheet Analysis,
and Communication for Decision Making, Second Ed.
By: John A. Lawrence, Jr. and Barry A. Pasternack.
Published by: Wiley 2002.
8) GPSS World Reference Manual. Student Version.
Published by: Minuteman Software.
421
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