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Ics2307:Simulation And Modelling Question Paper
Ics2307:Simulation And Modelling
Course:Bachelor Of Information Technology
Institution: Meru University Of Science And Technology question papers
Exam Year:2011
1
(a) Differentiate between the following: (i) Physical and mathematical model (2 Marks) (ii) Static and Dynamic model (2 Marks) (iii) Reliability and validity (2 Marks) (b) Highlight the steps involved in Monte-Carlo simulation. (5 Marks) (c) A bakery shop keeps stock of a popular brand of cake. Daily demand based on the past experience is given below: Daily demand 0 15 5 35 45 50 frequency 1 15 20 50 12 2
Simulate the demand for the next ten days using the following random numbers 48, 78, 09, 87, 99, 77, 15, 14, 68 and 89. Find out the stock situation if the owner of the bakery decides to make 35 cakes every day. Unmet demand on any day is lost. (6 Marks) (d) Customers arrive at a watch repair shop according to a Poisson process at a rate of one per every 10 minutes and the service time is an exponential random variable with mean 8 minutes.
2
(i) Compute the following measures of performance L, Lq, W, Wq. (5 Marks) (ii) Suppose the arrival rate of the customer increases 10 percent. Find the corresponding changes in L, Lq, W, Wq. (5 Marks) (iii) Is the system stable? Determine the idle time of the server. (3 Marks)
QUESTION TWO (20 MARKS)
(a) Discuss the congruential method as used in generating random numbers. (8 Marks) (b) With the aid of a diagram, highlight the key steps involved in simulation. (5 Marks) (c) Explain how random numbers can be generated from the following functions using the inverse transform method.
(i) b xa ab xF , 1 )( (4 Marks) (ii) 0 1 x exf x (3 Marks)
QUESTION THREE (20 MARKS)
(a) Given the following set of random numbers 0.50,0.64,0.65,0.41,0.86,0.23,0.61,0.89,0.11,0.24. Determine if these numbers are uniformly distributed using Kolmogoror Smirnor test at = 0.05. (6 Marks) (b) A sequence of 10,000 five digit random numbers has been generated and an analysis of numbers indicate that there are 3075 numbers having five different digits, 4935 having a pair, 1135 having two pairs, 695 having three of a kind, 105 having a full house (three of a kind and a pair) 54 having four of a kind and one having all five of a kind. Use Poker test to determine if these random numbers are independent at = 0.01. (6 Marks) (c) A dentist schedules all her patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending upon the type of dental work to be done as summarized below. Category Time required in minute frequency Filling 45 25 Crowning 60 15 Cleaning 15 25 Extracting 45 10 Check up 15 25
Simulate the dentists clinic for about four hours and determine the average waiting time for the patients and the percentage idle time for the dentist. Assume all the patients show up at the clinic at exactly their scheduled arrival time starting at 8.00am. use the following random number 40, 82, 11, 34, 52, 66, 17, 70. (8 Marks)
3
QUESTION FOUR (20 MARKS)
(a) Discuss the techniques used to generate random numbers. (6 Marks) (b) What are the advantages of using simulation other than experimenting with real life systems? (5 Marks) (c) Use the linear congruential method to generate five random numbers given that 0 = 1, = 3, = 7 = 15. (5 Marks) (d) Briefly discuss the areas where simulation is applicable. (4 Marks)
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