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Simulation &Amp; Modeling Question Paper

Simulation &Amp; Modeling

Course:Bachelor Of Business Information Technology

Institution: Strathmore University question papers

Exam Year:2008

STRATHMORE UNIVERSITY
FACULTY OF INFORMATION TECHNOLOGY
Bachelor of Business Information Technology
END OF SEMESTER EXAMINATION
STA 4201: SIMULATION & MODELING
DATE: 17TH APRIL 2008 TIME: 2 HOURS
Instructions: Answer Question ONE and any other two questions of your choice

Question ONE
a) What is a model and why is modeling important? 3 Marks
b) With regard to simulation, define the following terminology
i. A system state 1 Mark
ii. A death event 1 Mark
iii. An attribute 1 Mark
c) Justify the stability condition(s) for an M/M/1 queue. 3 Marks
d) How does the arrival rate in a queue affect the proportion of the time that the server is
busy? 3 Marks
e) Intel Corporation manufactures microprocessor chip sets for an array of computer
manufacturers. These devices are expected to have an average current level 5
Amperes and a standard deviation of 0.75 Amps. A standard has been set such that
5% of the chip sets are rejected because they low current levels and another 5% are
rejected because they have current levels higher than expected.
f) Find the cutoff values for acceptable chip sets. 5 Marks
g) Prove that for an M/M/1 queue, Lq = L – 1. Hence or otherwise, calculate Lq and L,
assuming that the traffic intensity, ? = 0.9. 6 Marks
h) Using the inverse transform method, answer the following questions
i) Generate a cdf from the pdf given below; 3 Marks
i. Generate the first 6 random variates from the pdf above, assuming
i 1 2 3 4 5 6
Ri 0.9658 0.3370 0.5820 0.2159 0.0104 0.7803
4 Marks
Total: 30 Marks
x2+x where 0<x<2
x+1
0 otherwise
f(x) =
2

Question TWO
(a) Assuming the mid-square method whose seed is 9326, determine the next four
random numbers 4 Marks
(b) Explain the biase and degeneration of the mid-square method in random number
generation, using appropriate examples. 4 Marks
(c) Given that Xn = (2.5Xn-1+ 4) mod 11 and that X0 = 4 2 Marks
(d) What is the cycle length of the above case 4 Marks
(e) Plot a rough graph of Rn against n upto its first cycle 3 Marks
(f) Discuss the robustness of the algorithm given in (c) at generating random numbers?
3 Marks
Total: 20 Marks

Question THREE
a) At Strathmore University, a survey done on its graduating students shows that the
proportions of job placements in different months after graduation are according to
the table below;
X
(months)
0 1 2 3 6
p(X) 0.12 0.29 0.36 0.0
8
0.1
5
i. Does the above case define a probability distribution? Why? 2 Marks
ii. What is the probability that a graduand gets a job within the first 2 months?
2 Marks
iii. What is the likelihood that graduands will not be placed between the 1st and 6th
month? 2 Marks
b) Suppose that a dry cleaner has it that on average, 130 customers drop their clothes
for laundry in an hour. Calculate the probability of exactly 1 customer arriving in a
given 45-second interval within the hour. 4 Marks
c) In Lang’ata Prison, it has been observed that the terms of imprisonment for petty
offenders are normally distributed with a mean of 3.5 months and a standard
deviation of 0.8 month.
The prison authorities intend to come up with a program of making better public
awareness planning and campaigns in order to sensitize and improve citizenry
welfare. What is the probability that a randomly selected offender has a term
between 3 and 4 months? 4 Marks
d) Professional Competence Score (PCS) is a measure of professional capability for
different professionals across several industries and professions. The PCS is
normally distributed with mean 800 and standard deviation of 83. Alpha is a group
of professionals whose PCS scores exceed 1050.
i. If someone is picked at random, find the probability that he/she will not meet the
Alpha criteria. 4 Marks
ii. In an industry with 150,000 professionals, how many are eligible for Alpha?
2 Marks
Total: 20 Marks
3

Question FOUR
Siwaka Plaza canteen serves Strathmore University students over breaks and lunch times.
On busy days, the canteen receives students at a rate of 140 per hour. Each student's order
takes 25 seconds to put together and to have it served.
(a) For an M/M/1 set up, determine the proportion of time that waiters are busy. 2 Marks.
(b) Derive the following;
i. The average number of students in the system, L. 5 Marks
ii. The average number of students in the queue, Lq. 3 Marks
iii. The average time spent in the system by each student, W. 2 Marks
iv. The average time spent in the queue by each student, Wq. 2 Marks
v. From the above equations, substitute the relevant values. Hence, determine L, Lq,
W and Wq. 6 Marks
Total: 20 Marks
Question FIVE
(a) From a Discrete Event simulation point of view, briefly define the following terms;
i. Event list
ii. Delay 2 Marks
(b) What information is needed for analysis of discrete event simulation sub-systems?
2 Marks
(c) A call centre receives calls with inter-call and service times as follows;
Client Inter-Call times (in min) Service times (in min)
1 2.0 1.2
2 1.1 1.5
3 1.4 0.8
4 0.7 1.1
5 1.0 0.8
6 1.3 1.2
7 2.1 0.7
(d) Assuming a single-server queuing setup, generate a simulation table. 8 Marks
(e) Calculate the following queue statistics
i. Average waiting time for each caller 1 Mark
ii. The Probability that a caller has to wait 1 Mark
iii. Proportion of idle time of the receptionist 1 Mark
iv. Probability of the server being busy 1 Mark
v. The average service time 1 Mark
vi. The average time between arrivals 1 Mark
vii. The average waiting time for those who wait 1 Mark
viii. The average time spent in the system 1 Mark
Total: 20 Marks

Simulation &Amp; Modeling Question Paper

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