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MU Information Technology (Semester 8)
Computer Simulation & Modelling
December 2011
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) Define :- System, Event, Simulation, Delay and Model.
5 M
1 (b) Perform the simulation of the following inventory system, given daily demand is represented by the random numbers 4,3,8,2,5 and the demand probability is given by
 Demand 0 1 2 Probability 0.2 0.5 0.3

if the initial inventory is 4 units, determine on which day the storage condition occurs.
5 M
1 (c) Explain the properties of a Poisson Process.
5 M
1 (d) Explain covariance and correlation.
5 M

2 (a) Explain the verification process
10 M
2 (b) Distinguish between (two points of difference each):-
(i) Terminating and non-terminating simulations
(ii) Activity and delay
(iii) Random numbers and random variates
6 M
2 (c) Explain the steps in the development of a model of input data
4 M

3 (a) Describe briefly Queing, Inventory and Reliability systems.
10 M
3 (b) Test the following random numbers for independence by poker test:
{ 0.594, 0.928, 0.515, 0.055, 0.507, 0.351, 0.262, 0.797, 0.788, 0.442, 0.097, 0.798, 0.227, 0.127, 0.474, 0.825, 0.007, 0.182, 0.929, 0.852}; α=0.05, Χ20.05,2=5.99
10 M

4 (a) Draw the figure for service outcomes after service completion and potential uint actions upon arrival and the flow diagrams for unit- entering-system and service -just-completed flow for a queueing system.
5 M
4 (b) Compare the event scheduling, process interaction and activity scanning approach
5 M
4 (c) Given the following data for utilization and time spent for the Able-Baker car-hop problem, calculate the overall points estimators, standard error and 95% confidence interval for the same, given t0.025,3=3.18
 Run r : 1 2 3 4 Able's utilization ρr : 0.808 0.875 0.708 0.842 Average system time wr (min) : 3.74 4.53 3.84 3.98

10 M

5 (a) Give the steady-state equations for M/G/1 queue and derive M/M/1 from M/G/1
10 M
5 (b) A medical examination is given in three stages by a physician, each stage is exponentially distributed with a mean service time of 20 minutes. Find the probability that the exam will take 50 minutes or less. Also detemine the expected length of the exam
5 M
5 (c) In stoke brokerage, the following twenty time maps were recorded between customer buy and sell order (in sec) : 1.95, 1.75. 1.58, 1.42, 1.28, 1.15, 1.04, 0.93, 0.84, 0.75, 0.68, 0.61, 11.98, 10.79, 9.71, 14.02, 12.62, 11.36, 10.22, 9.20. Assume exponential distribution is a good model for the individual gaps, calculate the lag-1 autocorrelation
5 M

6 (a) Describe initialization bias in steady-state simulation
10 M
6 (b) Explain the AR(1) time series model along with the algorithm
5 M
6 (c) Why is it necessary to have program and process documentation in simulation study?
5 M

Write short notes on any four :-
7 (a) Cobweb model.
5 M
7 (b) Costs in queueing problems
5 M
7 (c) Gap test
5 M
7 (d) Characteristics desirable in a simulation software
5 M
7 (e) kolmogorov-Smirnov test
5 M
7 (f) Network of queues.
5 M

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