## Simulation & Modelling - May 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 the properties of random numbers(5 marks)
**1 (b)** Define the following terms -

(i) Activity (ii) System (iii) Simulation (iv) Delay (v) Model(5 marks)
**1 (c) ** If the interarrival time ranges from 2 to six minutes with equal probability and random digits generated are 51, 27, 63, 89, 11 and 45. Generated FEL with primary events.(5 marks)
**1 (d) ** Explain Time series input model.(5 marks)
**2 (a)** Explain the steps in simulation study.(10 marks)
**2 (b)** Distinguish between -

(i) Terminating and non-terminating simulation

(ii) Endogenous and exogenous event

(iii) Random numbers and random variates.(10 marks)
**3 (a)** Describe the characteristics of queuing systems. Name and explain some of the useful statistical models for queuing system.(10 marks)
**3 (b)** Explain inventory system. Discuss the cost involved in inventory systems.(10 marks)
**4 (a)** Describe the procedure to generate samples from :-

(i) Erlang distibution

(ii) Exponential distribution.(10 marks)
**4 (b)** Write down the steps for K-S test. The sequence of numbers 0.54, 0.75, 0.98, 0.12 and 0.68 has been generated. Used K-S test with ?=0.05 to learn whether the hypothesis that the numbers are uniformly distributed on the interval [0,1] can be rejected. (Critical value D?=0.565)(10 marks)
**5 (a)** What do you understand by model verification and validation? Describe Briefly the various method of validating input model.(10 marks)
**5 (b)** Describe initialization bias in steady-state simulation.(10 marks)
**6 (a)** Test the following random numbers for independence by runs up and down test. Take ?=0.05 and 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)(10 marks)
**6 (b)** What are the method used to generate random numbers?(10 marks)

### Write shot notes on (any two) :-

**7 (a)** Cobweb model.(10 marks)
**7 (b)** Selection of a simulation software(10 marks)
**7 (c) ** Manufacturing system simulation(10 marks)