## Computer Simulation & Modelling - Dec 2013

### Information Technology (Semester 8)

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)** Discuss types of simulation models(5 marks)
**1 (b)** Compare random numbers and random variate(5 marks)
**1 (c) ** How is Pokers test used for testing independence?(5 marks)
**1 (d) ** Event scheduling algorithm.(5 marks)
**2 (a)** Explain the steps in simulation study in detail.(10 marks)
**2 (b)** An industrial chemical that will ratard the spread of fire has been developed. The loacal sales representatives have determined from past experience 48% of sales call will result in an order.

(i) What is the probability that the first order will call on 4^{th} sales call of the day?

(ii) If 8 sales call are made on a day, what is the probability of receiving exactly 6 orders?

(iii) If 4 sales call are made before lunch, what is the probability that one or less result in an order?(10 marks)
**3 (a)** Consider the following sequence of 5 numbers :0,15,0.94,0.05,0.51 and 0.29

Use the Kolmogorov-Smirnov test determine whether the Hypothesis of uniformity can be rejected, given ?=0.05 and the critical value of D=0.565(10 marks)
**3 (b)** Explain Naylor and Finger validation approach(10 marks)
**4 (a)** Explain data collection and analysis for input modeling(10 marks)
**4 (b) ** What are long run measure of performance of Queuing system. Assume : R_{0}=10, d=2 and S_{0}^{2}=25.30. Estimate the long-run mean queue length L_{Q}, within ?=2 customers with 90% cinfidence (a=10%). Form the table the value of Z_{0.05}=1.645. How many additional replications required?(10 marks)
**5 (a)** Explain the cobweb model in detail.(10 marks)
**5 (b)** Explain data collection and analysis for input modeling(10 marks)
**6 (a)** What is time-series input model? Explain AR(1) and EAR(1) model.(10 marks)
**6 (b)** A CNG station has two filling machines. The service time follows the exponential distribution with mean of 5 minutes and taxis arrives for service in Poisson fashion at rate of 15 per hour. Compute the steady state parameter of this M/M/C system.(10 marks)

### Write a short notes

**7 (a)** Cost of Inventory system(5 marks)
**7 (b)** Poisson Process and distribution(5 marks)
**7 (c) ** Terminating and no terminating simulation(5 marks)
**7 (d)** Issue in simulation of Manufacturing System.(5 marks)