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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:2013
KENYA METHODIST UNIVERSITY
END OF 1''ST ''TRIMESTER 2013(DAY) EXAMINATION
FACULTY : COMPUTING & INFORMATICS
DEPARTMENT : COMPUTER SCIENCE & BUSINESS INFORMATION
UNIT CODE : BBIT 417/CISY 403
UNIT TITLE : SIMULATION AND MODELLING
TIME : 2 HOURS
INSTRUCTIONS
Answer question one (compulsory) and any other two questions.
Question One (30 marks)
Highlight the steps involved in a Monte-Carlo simulation.
(6 Marks)
Discuss the factors considered when selecting a simulation language.
(4 Marks)
(i) Use the linear congruential method to generate five random numbers given that Xo = 1, a =3, c=7 and m=15.
(5 marks)
(ii) From the generated numbers, identify the seed and the period of the sequence. (2 marks)
(iii) Obtain uniformly distributed random numbers in the interval (0,1) from the generated random numbers in (i) above. (2 marks)
A drive in banking service modeled as M/M/1 queuing 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?
(4 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 cahier 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 queue.
(3 Marks)
Question Two (2 marks)
Why are random numbers used in simulation?
(2 marks)
With the aid of a flow diagram, characterize all the events involved when modeling a real system to obtain results. On the diagram, clearly indicate the importance of the following
(8 Marks)
Conceptual validity
Model validity
Program validity
Discuss how reliability analysis can be done after results have been obtained from a simulation run.
(3 Marks)
Discuss the random numbers generators commonly in use.
(7 Marks)
Question Three (20 Marks)
Dr. Strong is a dentist who schedules all her patients for 30 min appointments some of the patients take more or less than 30 minutes depending upon the type of dental work to be done. The following table shows the various categories of work, their probabilities and the time actually needed to complete the work
Category Time required in Minutes Probability
Filing 45 25
Crowning 60 15
Cleaning 15 25
Extrovetion 45 10
Checkup 15 25
Simulate the dentist’s clinic for about four hours and determine the average time for the patients and the percentage idle time for the dentist. Assume that all patients show up at the clinic at exactly their scheduled arrival time starting at 8.00 A.M.
Use the following random numbers for simulating the process: 40, 82, 11, 34, 52, 66, 17 and 70. (12 marks)
(i) Highlight the methods used to test the suitability of random numbers.
(4 Marks)
(ii) State some important distributions of arrival interval and service time. (2 Marks)
Question Four (20 marks)
Differentiate the following;
Logical and physical models.
(2 Marks)
Static and dynamic models
(2 Marks)
Given the function
f(x) = 4x3, explain how random numbers
can be generated using the reverse transform method. (4 marks)
Highlight the essential characteristics of the queuing process.
(3 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 is at state zero and hence the system is stable.
(9 Marks)
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