Question Paper: Computer Simulation And Modelling Question Paper - May 17 - Information Technology (Semester 8) - Mumbai University (MU)

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## Computer Simulation And Modelling - May 17

### Information Technology (Semester 8)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**1.a.**Explain steps in simulation study along with the flowchart.

**1.b**Explain the properties of a Poisson Process

**1.c**Perform the simulation of the following inventory system, given daily demand is represented by the random numbers 4,1,8,5,2 and the demand probability is given by

Demand | Probability |
---|---|

0 | 0.2 |

1 | 0.5 |

2 | 0.3 |

If the initial inventory is 4 units, determine on which day the shortage condition occurs.

**2.a**State the queueing notation, queue discipline and queue behavior.

**2.b**Given the input parameters, simulation variable, output statistics for the queueing system. Calculate the output statistics for the queueing system whose inter-arrival and service times for ten arrivals are given below:

Inter-arrival time | - | 8 | 6 | 1 | 8 | 3 | 8 | 7 | 2 | 3 |
---|---|---|---|---|---|---|---|---|---|---|

Service time | 4 | 1 | 4 | 3 | 2 | 4 | 5 | 4 | 5 | 3 |

**3.a**Consider the following sequence of random numbers. How would you test it for independence based on runs above and runs below the mean for the significance level $\alpha$= 0.05 and the critical value Z$_{0.025}$=1.96

0.12 | 0.01 | 0.23 | 0.28 | 0.89 | 0.31 | 0.64 | 0.28 | 0.33 | 0.93 |
---|---|---|---|---|---|---|---|---|---|

0.39 | 0.15 | 0.33 | 0.35 | 0.91 | 0.41 | 0.60 | 0.25 | 0.55 | 0.88 |

**3.b**Explain Inverse transform technique for random variate generation. Support your answer with suitable example.

**4.a**What is the purpose of model verification? What are the different ways available to verify a model?

**4.b**Draw the flowchart for arrival and departure event in single server system. Compare event-scheduling, process interaction and activity scanning algorithms.

**5.a**The following is set of single digit numbers from a random number generator. Using appropriate test check whether the numbers are uniformly distributed. N=50, $\alpha$= 0.05, $\chi _{0.05,9}$= 16.9. {6,7,0,6,9,9,0,6,4,6,4,0,8,2,6,6,1,2,6,8,5,6,0,4,7,1,3,5,0,7,1,4,9,8,6,0,9,6,6,7,1,0,4,7,9,2,0,1,4,8}

**5.b**The following data were available for the past 10 years on demand and lead time.

Lead Time | 6.5 | 4.3 | 6.9 | 6.0 | 6.9 | 6.9 | 5.8 | 7.3 | 4.5 | 6.3 |
---|---|---|---|---|---|---|---|---|---|---|

Demand | 103 | 83 | 116 | 97 | 112 | 104 | 106 | 109 | 92 | 96 |

Estimate correlation and co variance.

**6.a**Explain the batch means for interval estimation in steady state simulation.

**6.b**What are the objectives of simulation in a manufacturing system? Give the block diagram and explain the sequence of operations in a manufacturing system. Suggest a suitable simulation language for the same.