**UNIVERSITY EXAMINATIONS: 2018/2019**

**EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN **

**INFORMATION TECHNOLOGY / BACHELOR OF BUSINESS **

**INFORMATION TECHNOLOGY/ BACHELOR OF SCINCE IN APPLIED **

**COMPUTING**

**BIT2201 BBIT308 BAC2106 SIMULSTION AND MODELING**

**FULL TIME/PART TIME/DISTANCE LEARNING **

**DATE: AUGUST, 2019 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions. [30 MARKS]**

a) The table below shows the number of car hijackings experienced by transport company

in a month.

(i) Using the following random number, simulate the number of car hijacking in a

period of

24

months.

Use the following random numbers:

55,82, 05, 66, 61, 02, 58, 91, 43, 31, 90, 40, 48, 64, 79, 35,17, 62, 04, 98, 63, 42,84, 33

[5 Marks]

(ii) Determine the average monthly rate of car hijacking. [1 Mark]

b) State any three types of simulation. [3 Marks]

c) Using appropriate examples identify four main types of system. [4 Marks]

d) Explain four benefits of simulation to management. [4 Marks]

e) Using the additive Linear Congruential Generator (LCG) with

a 67 , b 17 , m 31

and seed

z0 117

, generate the first five random variates on

0,1 .

[4 Marks]

f) State three shortcomings of taking a simulation approach to solve an operation research

problem. [3 Marks]

g) Describe the Monte-Carlo simulation procedure. [6 Marks]

**QUESTION TWO [20 MARKS]**

a) State four factors to consider when designing simulation experiment. [4 Marks]

b) Not simulation and modeling exercises are a success. Discuss five common pitfalls to

successful simulation. [5 Marks]

c) The automobile company manufactures around

150

scooters. The daily production

ranges from

146

to

154

depending upon the availability of raw materials and other

working conditions. The probability distribution is as given below:

The finished scooters are transported in a specially arranged lorry accommodating

150

scooters. Using the following random numbers:

80, 81, 76, 75, 64, 43, 18, 26, 10, 12, 65, 68, 69, 61, 57

Simulate the process to find out:

(i) What will be average number of scooters waiting in the factory? [6 Marks]

(ii) What will be average number of empty space on the lorry? [5 Marks]

**QUESTION THREE [20 MARKS]**

a) Draw a flow chart to describe the simulation of a simple system. [6 Marks]

b) Define the terms verification and validation in the context of modeling. [4 Marks]

c) The occurrence of rain in a city is dependent upon whether or not it rained on the previous.

If it rained on the previous day, the rain distribution is:

Event No

rain

1 cm rain 2 cm rain 3 cm rain 4 cm rain 5 cm rain

Probability

and determine by simulation the total days without rain

as well as the total rainfall during the period. Assume that for the first day of the simulation

it had rained the day before. Using the following random numbers:

67, 63, 39, 55, 29, 78, 70, 06, 78, 76

[10 Marks]

**QUESTION FOUR [20 MARKS]**

a) Do you think the application of simulation will strongly increase in the next ten years?

Give reasons for your answer. [10 Marks]

b) With the help of a single queueing model having inter-arrival and service time constants

1.5

and

4

minutes respectively and taking

14

minutes as the simulation period . Assume

that initially the system is empty and the first customer arrives at time

t 0.

Determine

the:

i. Average waiting time of a customer. [4 Marks]

ii. Average waiting time per customer for those who must wait.

[4 Marks]

iii. Percentage idle time of the facility. [2 Marks]

**QUESTION FIVE [20 MARKS]**

a) Discuss three cases when it may be necessary to use simulations. [6 Marks]

b) Describe any four statistical methods for testing the random numbers generated by the

uniform generator. [8 Marks]

c) Use the inverse transformation method to generate random variates with probability

density function. [6 Marks]