SIMULATION AND MODELING (SM) DECEMBER 2011 INFORMATION TECHNOLOGY SEMESTER 7
Con. 6503-11 (REVISED COURSE) MP-5755(3 Hours) [Total Marks: 100]
N.B.: (1) Question No.1 is compulsory. Attempt any four out of the remaining questions.
(2) Assume suitable data wherever necessary.
(3) Figures to the right indicate full marks.
Q.1 (a) Define: -System, event, simulation, delay and model. [5 Marks]
(b) Perform the simulation of the following inventory system, given daily demand is presented
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
(c) Explain the properties of a poisson process. [5 Marks]
(d) Explain covariance and correlation. [5 Marks]
Q.2 (a) Explain the verification process. [10 Marks]
(b) Distinguish between(Two points of difference each) :- [6 Marks]
i) Terminating and non-terminating simulations.
ii) Activity and delay
iii) Random numbers and random variates.
(c) Explain the steps in the development of a model of input data. [4 Marks]
Q.3 (a) Describe briefly queueing, inventory and reliability systems. [10 Marks]
(b) Test the following random numbers for independence by poker test: [10 Marks] {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}
Q.4 (a) Draw the figures for service outcomes after service completion and potential unit actions
upon arrival and the flow diagrams for unit entering system and service-just-completed flow
for a queueing system. [5 Marks]
(b) Compare the event scheduling, process interaction and activity scanning
approach. [5 Marks]
(c) Given the following data for utilization and time spent in system for the Able-Baker
Car-hope problem, calculate the overall point estimators, standard error and 95%
confidence intervals for the same, given to t0.025.3 = 3.18
Run r: 1 2 3 4
Able's utilization Pr : 0.808 0.875 0.708 0.842
Average system time Wr(mins): 3.74 4.53 3.84 3.98
Q.5 (a) Give the steady state equations for M/G/1 queue and derive M/M/1 from
M/G/1. [10 Marks]
(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 determine the expected length of the exam. [5 Marks]
(c) In stock brokerage, the following twenty time gaps were recorded between customer
buy and sell orders (in secs) : 1.95,1.75,1.58,1.42,1.28,1.15,1.04,0.93,0.84,0.75,0.68,0.61,11.98,10.79,9.97,
14.02,12.62,11.36,10.22,9.20. Assuming exponential distribution is a good model for
the individual gaps, calculate the lag-1 autocorrelation. [5 Marks]
Q.6 (a) Describe initialization bias in steady-state simulation. [10 Marks]
(b) Explain the AR(1) time series model along with the algorithm. [10 Marks]
(c) Why is it necessary to have program and process documentation in simulation
study? [5 Marks]
Q.7 Write short notes on any four: - [20 Marks]
(i) CobWeb Model
(ii) Costs in queueing problems
(iii) Gap test
(iv) Charateristics desirable in a simulation software
(v) Kolmogorov-Smirnov test
(vi) Network of queues.
Also see Simulation and modeling question papers for May 2012
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