Question Paper: Simulation & Modelling : Question Paper Dec 2014 - Information Technology (Semester 7) | Mumbai University (MU)
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## 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
(10 marks) 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 X2.05,9= 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 X1 represent the average lead time to deliver (in months), and X2 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 6.9 5.8 7.3 4.5 6.3 Demand 103 83 116 97 112 104 106 109 92 96
(10 marks)
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)