Ministry of Higher Education
El-Shorouk Academy
Higher Institute for Computer &
Information Technology
Department
:
Computer Sciences
Instructor
Reviewer
:
Dr. Farouk Shaaban
Dr.Hamdy Reiad
:
No. Questions
: 2010/ 2011
: First
: 3rd
: 4
Date
: 23/1/ 2011
Acad. Year
Term
Year
Time Allowed
: 120 Min
3106 Computer modeling & simulation ( Final Exam )
1- a) Drive the CDF of a distribution whose
p.d.f. is given by
 1

x  20
f x    200

0
5 points
20  x  40
otherwise
Get 4 Random Observations using the above distribution and the following R.N. 0.49, 0.64, 0.36, 0.81.
b) Use the one-digit random number (9, 7, 6, 3, 5, 0, 8, 4) to generate random observations for
5 points
i)
Throwing a fair coin
ii)
Throwing a die
iii)
The color of a traffic found by a randomly arriving car when it is green 40% of the time, yellow 10% of the
time, and red 50% of the time.
c) What methods are used to increment time in a simulation model? And explain the draw backs of each if any. 5 points
d) Jobs arrive at a workstation at fixed intervals of one hour. Processing time is uniform between 50 and 90 minutes.
Using the following random numbers to simulate the processing times for 10 jobs, and determine the amount of
operator idle time, and average waiting time. Assume the first job arrive at time =0.
R.N:0.4, 0.5, 0.3, 0.7, 0.8, 0.9, 0.6, 0.2, 0.1, 0.4.
10 points
2- A service station has one gasoline pump. Because everyone drives big cars, there is room at the station for only three
cars, including the car at the pump. Cars arriving where there are already three cars at the station drive on to another
station. Use the following probability distribution to simulate the arrival of 10 cars to the station.
20 points
Enter
arrival
time(min.)
10
20
30
40
3-
P(x)
Service
time(min.)
P(x)
0.40
0.35
0.20
0.05
5
10
15
33
0.45
0.30
0.20
0.05
Calculate the average time cars spend at the station, the idle
time(assume the station start at time zero), the utilization of the pump,
and the average car's waiting time. Use the following random number
06, 95, 04, 96, 26, 95, 06, 99, 07, 99, 03, 97, 08, 95, 42, 95,
17, 99, 31, 99
Minor breakdowns of machines occur frequently. The breakdowns occur every 5 hours while the service time to fix the
machine is randomly distributed. Management is concerned with minimizing the cost of breakdowns. The cost per hour
for machines to be down is $40. The cost of service repairman is $12 per hour. A preliminary study has produced the
following data on times of services. Assume that the first breakdown is 5 hours.
(20Points)
Betw
Service Times (in hours)
4
5
6
7
8
9
Relative Frequency
0.10
0.40
0.20
0.15
0.10
0.05
Perform a simulation of 10 breakdowns under two conditions with one service repairman and with two service
repairmen and get the total price of both and write down your conclusion.
Use the following random number for service
: 68, 85, 95, 67, 97, 73,
75, 64, 26, 45.
4- a) Give M/M/1 queuing system with arrival rate 25/h and service rate 30/h. Drive the performance measures for that
system (  , Po, Pn, L, Lq, W, and Wq). Calculate  , Po, P8, L, Lq, W, and Wq
5 points
b) Give M/M/1 queuing system with arrival rate 20/h and service rate 25/h. Starting with empty system, simulate the
process using Time-driven Simulation techniques. Stop after 3 completions.
10 points
RN:
092
502
665
407
630
769
843
810
399
8487
291
657
357
510
705
920
828
844
756
684
028
650
290
501
448
837
976
003
349
352
891
851
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23/1/2011