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Cisy 403:Simulation And Modelling Question Paper

Cisy 403:Simulation And Modelling

Course:Computer Science

Institution: Kenya Methodist University question papers

Exam Year:2012

KENYA METHODIST UNIVERSITY

END OF 3''RD ''TRIMESTER 2012 (EVENING) EXAMINATIONS
FACULTY : COMPUTING AND INFORMATICS
DEPARTMENT : COMPUTER SCIENCE AND BUSINESS
INFORMATION
UNIT CODE : BBIT 417/CISY 403
UNIT TITLE : STIMULATION AND MODELLING
TIME : 2 hours

Instructions:

SECTION A

Question One

A drive in banking service is modeled as an M/M/I quivering system with customers arrival rate of 2 per minute. It is desired to have fewer than five customers line up 99% of the time. How fast should the service rate be?

(5 marks)

A supermarket has a single cashier, during the rush hours; customers arrive at the rate of 10 per hour. The average number of customers that can be processed by the cashier is 12 per hour. On the basis of this information, find:

Probability that the cashier is idle.

(2 marks)

Average time a customer spends in the system.

(2 marks)

Average time a customer spends in the queuing system.

(2 marks)

Average number of customer in the queue and average time a customer spends in queue.

(4 marks)

Using a multiplicative congruential generator defined by Zo = 27, a =8, c=47 and M=100. Generate a sequence of 5 random numbers.

(5 marks)

Question Two

The following data are arrival time (in minutes counting from 0) and service times (in minutes) for the first six customers arriving a dental clinic with one dentist on duty, upon arrival a customer enters service in the dentist is free or joints the waiting line. When the dentist has finished work on a customer, the next one in line enters service.

Arrival Time 12 31 63 95 99 154
Service Time 40 32 55 48 18 50

Assuming a single server develop a simulation table.

(5 marks)

Calculate average waiting time for each customer.

(3 marks)

Determine the idle time the dentist has.

(2 marks)

Explain the main steps involved in a simulation study.

(6 marks)

Describe the Kendall’s notation of queuing networks.

(4 marks)

Question Three

Use linear congruential method to generate five random numbers between 0 and 31 given a=13, c=15 and xo=11.

(5 marks)

State some of the important distributions of arrival interval and service time.

(3 marks)

Explain how random numbers can be generated using the inverse transform method from the functions.

f(x) = 4x3

(2 marks)

f(x) =x -½

(2 marks)

Validation and verification are important in simulation. Distinguish between these two processes.

(4 marks)

State the properties of a good estimator.

(3 marks)

Question Four

State the key factors considered when selecting a simulation language.

(4 marks)

Differentiate between:

Continuous and discrete systems.

(2 marks)

Physical and mathematical system

(2 marks)

Static and dynamic models.

(2 marks)

Using the flow balance equation, show that the proportion of time spent by a system at any state depends on the proportion of time the system spends at state zero and hence stability.

(10 marks)

Cisy 403:Simulation And Modelling Question Paper

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