Robert Griffiths
HW#7
10/25/99
ProModel Homework:
Create from scratch a model of the system described in Ex9.mod (see Homework 3). The key here is
for you to develop the model on your own from the start. Run your model and compare your results against
the results of Ex9.mod.
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Formatted Listing of Model:
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C:\My Documents\grad_school\sma\hw7.mod
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Time Units:
Minutes
Distance Units:
Feet
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Locations
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Name
Cap
Units Stats
Rules
Cost
------------- -------- ----- ----------- -------------- -----------secretary_loc infinite 1 Time Series Oldest, FIFO,
station_1 1
1 Time Series Oldest, ,
station_2 1
1 Time Series Oldest, ,
station_3 1
1 Time Series Oldest, ,
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Entities
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Name
Speed (fpm) Stats
Cost
---------- ------------ ----------- -----------customer 100
Time Series
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Path Networks
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Name Type
T/S
From To
BI Dist/Time Speed Factor
-------- ----------- ---------------- -------- -------- ---- ---------- -----------Net1 Non-Passing Time
N1
N2
Bi .5
N2
N4
Bi .5
N4
N6
Bi .5
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Interfaces
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Net
Node
Location
---------- ---------- ------------Net1
N1
secretary_loc
N2
station_1
N4
station_2
N6
station_3
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Processing
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Process
Routing
Entity Location
Operation
Blk Output Destination Rule
Move Logic
-------- ------------- ------------------ ---- -------- ----------- ------- -----------customer secretary_loc wait 2
1 customer station_1 FIRST 1 move on net1
customer station_1
customer station_2
customer station_3
wait 5
wait 5
wait 5
1 customer station_2 FIRST 1 move on net1
1 customer station_3 FIRST 1 move on net1
1 customer EXIT
FIRST 1 move for 0
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Arrivals
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Entity Location
Qty each First Time Occurrences Frequency Logic
-------- ------------- ---------- ---------- ----------- ---------- -----------customer secretary_loc 1
0
150
e(5)
The results of my model are very similar to the example given in the text/software:
Total exits
Avg. minutes in system
% busy: Station 1
% busy: Station 2
% busy: Station 3
% occupied: secretary
Avg min @ secretary
Avg # @ secretary
My simulation output
84
49.1
90.52
89.5
88.4
99.1
32
6.1
Ex9.mod output
79
84
83
82.9
63.97
10.7
1.8
Some differences I noted:
1) My capacity of the secretary / receptionist was INFINITE vs a value of 5 for the supplied example
simulation. This explains why the secretary queue grew to the extent it did with a longer wait in my
simulation.
2) Distance and speed travelled by customers differed in the two sims.
DESS 8.22
Generate 100 sets of random numbers, each set containing 100 random numbers. Perform tests to determine
uniformity and independence.
The file hw7.xls contains the spreadsheet, here some results:
Frequency test
Kolmogrov-Smirnov: From Table A.8, for alpha=.05, Dcrit = .136
For the given set of random numbers, I find D = max(D+,D-) = .170
therefore, the null hypothesis that the data are a sample from a uniform distribution is rejected
Run Test
Runs up and runs down: the test statistic Z0 = varies from –10.85..-5.345
Runs above and below the mean: the test statistic Z0 = [-3.1..1,7]
DESS 9.11
Interval (Seconds)
15 – 30
30 – 45
45 – 60
60 – 90
90 – 120
120 – 180
180 – 300
Frequency
10
20
25
35
30
20
10
Relative Frequency
0.067
0.133
0.166
0.233
0.2
0.133
0.067
Cumulative Frequency
0.067
0.2
0.365
0.599
0.799
0.932
1.0
The cumulative probability is plotted against repair times based on the empirical distribution:
180 , .932
120 , .799
90 , .599
60 , .365
45 , .2
30 , .067
15 , 0
300 , 1.0
The Inverse CDF of repair times is also plotted:
1.0 , 300
a7=1764.7
.932 , 180
a6=451.1
.799 , 120
a5=150
.599 , 90
a3=90.9
.365 , 60
.067 , 30
0 , 15
a4=128.2
.2 , 45
a2=112.8
a1=224
Intervals and slopes are given as:
I
Input,
Output,
ri
xi
1
0
15
2
0.067
30
3
.2
45
4
.365
60
5
.599
90
6
.799
120
7
.932
180
8
1.0
300
Slope,
ai
224
112.8
90.9
128.2
150
451.1
1764.7
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Generate five values of service time using four-digit random numbers:
Random
ri
ai
xi
X=xi+ai(R-ri)
Number
.4756
.365
128.2
60
74.2
.6314
.599
150
90
94.9
.6752
.599
150
90
101.43
.1878
.067
112.8
30
43.626
.6711
.599
150
90
100.815