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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:2013
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QUESTION ONE (30 MARKS)
a) Highlight the steps involved in simulation. (3 Marks) b) 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. Find; i. Average number of customers in the system. (2 Marks) ii. Average time a customer spends in the shop. (2 Marks) iii. Average time a customer spends waiting for service. (2 Marks)
Suppose the arrival rate of the customers increase by 10 percent. Find the corresponding changes in the above measures, (i), (ii) and (iii). (3 Marks)
c) Simulate an M/D/2 system over the first 35 minutes of operation taking mean inter-arrival time as 3 minutes and service times of server I and server II as 5 and 6 minutes each. The inter arrival times for the first 12 arrival in min:sec have been generated as 4:13, 2:00, 6:09, 1:37, 3:54, 6:09, 0.05, 2:49, 1.26, 0.52, 3:39, 8:54. Determine the percentage idle time of each server. (5 Marks) d) Dr. Strong is a dentist who 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
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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 min Probability Filling 45 0.25 Crowning 60 0.15 Cleaning 15 0.25 Extracting 45 0.10 Check up 15 0.25 imulate the dentist’s 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 8.00 am. Use the following random numbers for simulating the process 40, 82, 11, 34, 52, 66, 17, 70. (9 Marks) e) Given the random numbers 07, 96, 14, 10, 90, 21, 15, 84, 28, 35 generate random variates from the following distribution.
i. = 1
,90 120 (4 Marks) ii. = 1 , > 0 (3 Marks)
QUESTION TWO (20 MARKS)
a) The following sequence of random numbers have been generated 0.50, 0.64, 0.65, 0.41, 0.86, 0.23, 0.61, 0.11, 0.89, 0.24 Use the Kolmogorov Smirnov test at = 0.05 to determine if these numbers are uniformly distributed. (4 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. (5 Marks) c) Generate 5 random numbers between 0 and 31 using the congruential method given = 13, = 15,0 = 11. (4 Marks) d) Test for serial autocorrelation in the following set of random numbers. (7 Marks) 49 95 82 19 41 31 12 53 62 40 87 83 26 01 91 55 38 75 90 35 71 57 27 85 52 08 35 57 88 38 77 86 29 18 09 96 58 22 08 93 85 45 79 68 20 11 78 93 21 13 06 32 63 79 54 67 35 18 81 40 62 13 76 74 76 45 20 36 80 78 95 25 52
QUESTION THREE (20 MARKS)
a) Highlight the advantages and disadvantages of simulation. (4 Marks)
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b) Discuss the congruential method of generating random numbers. (4 Marks) c) A piece of equipment contains four identical tubes and can function only if all the four are in working order. The lives of tubes has approximately uniform distribution from 1000hrs to 2000hrs. The current maintenance practice is to replace a tube when it fails. Equipment has to be shut down for 1 hour for replacing a tube, the cost of one tube is sh 100 while the shut down time costs sh. 200 per hour. Simulate the system for about 6000hrs of runs and find the maintenance cost given the following random numbers 8, 2, 6, 3, 1, 0, 8, 9, 2, 8, 3, 7, 4, 8, 5, 6, 0, 4, 9. (8 Marks)
QUESTION FOUR (20 MARKS)
a) In an inventory system the demand as well as the lead times are random variables defined by discrete distribution as given below Demand 3 4 5 6 Probability 0.15 0.30 0.35 0.20
Lead time 2 3 4 Probability 0.2 0.6 0.2
Two recorders each of quantity (Q) of 15 units can be outstanding at a time. There are two reorder points RP1 and RP2 at levels of 10 and 5 units respectively. The shortage are lost forever. The reorder cost is insignificant as compared to the carrying cost, and the objective is to determine the service level and the average stock held for the given reorder points and the reorder quantity. Taking the initial stock of 10 units, simulate the inventory system for the first 20 days using the following random numbers 64, 33, 18, 87, 74, 41, 53, 09, 67, 93, 56, 35, 48, 70, 32, 41, 87, 12, 23, 08 b) Draw a flow chart that can implement the problem above on a computer. (8 Marks)
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