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

if the initial inventory is 4 units, determine on which day the storage condition occurs.

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

(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, Χ

{ 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, Χ

^{2}_{0.05,2}=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 t

_{0.025,3}=3.18Run r : | 1 | 2 | 3 | 4 |

Able's utilization ρ_{r} : | 0.808 | 0.875 | 0.708 | 0.842 |

Average system time w_{r} (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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