## Simulation & Modelling - Dec 2014

### Information Technology (Semester 7)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

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

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Explain different steps in Simulation study.(10 marks)
**1 (b)** How will you validate simulation model?(10 marks)
**2 (a)** For the following data find the Queue Statstics. (Time in minutes). IAT denote inter arrival time and ST denotes the service time. Assume first customer arrives at time=0.

IAT |
- | 08 | 06 | 01 | 08 | 03 | 08 | 07 | 02 | 03 |

ST |
04 | 01 | 04 | 03 | 02 | 04 | 05 | 04 | 05 | 03 |

**2 (b)**Explain the following terms: Event scheduling, Process interaction, activity scanning, bootstrapping and terminating event.(10 marks)

**3 (a)**The sequence of numbers 0.54, 0.73, 0.98, 0.11 and 0.68 has been generated. Use the Kolmogorov-Smirnov test with ?=0.05 to determine if the hypothesis that the numbers are uniformly distributed on the interval [0,1] can be rejected given D?=0.565.(10 marks)

**3 (b)**Explain various methods for random numbers generation.(10 marks)

**4 (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, ?=0.05 and X

^{2}

_{.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(10 marks)

**4 (b)**Differentiate random variables and random variates. Generate random variates of exponential distribution.(10 marks)

**5 (a)**Lt X

_{1}represent the average lead time to deliver (in months), and X

_{2}the annual demand, for industrial robots. The following data were available on demand and lead time for last ten years. Estimate the correlation and co-yariance.

Lead Time | 0.9 | 6.5 | 4.3 | 6.9 | 6.0 | 6.9 | 5.8 | 7.3 | 4.5 | 6.3 |

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

**5 (b)**Define correlation and covariance. Explain Time-Series model.(10 marks)

**6 (a)**Derive the steady State parameters of M/G/I queue and M/M/I.(10 marks)

**6 (b)**What are the issues in manufacturing and material handling system.(10 marks)

### Write short notes on any two:

**7 (a)** Cobweb model.(10 marks)
**7 (b)** Probability distributions and the process related to them.(10 marks)
**7 (c)** Need for output Analysis in simulations.(10 marks)