## Simulation & Modelling - May 2016

### MU Information Technology (Semester 7)

Total marks: --

Total time: --
INSTRUCTIONS

(1) Assume appropriate data and state your reasons

(2) Marks are given to the right of every question

(3) Draw neat diagrams wherever necessary
**1(a)** State when simulation appropriate.
5 marks

**1(b)** What are the characteristics of queuing system?
5 marks

**1(c)** Define system state, event notice, activity, delay and clock.
5 marks

**2(a)** Explain Inverse transform to generate random variate.
5 marks

**2(b)** What is world view? Discuss different types of world views.
5 marks

**3(a)** The sequence of numbers {0.12,0.01,0.23,0.28,0.89,0.31,0.64,0.28,03,0.93} has been generated Test the random numbers for independence by runs and down test. Take α = 0.05 and critical value z_{0.025} = 1.96
5 marks

**3(b)** Explain Poisson Process along with its properties.
5 marks

**4(a)** State the properties of random numbers. What are the methods used to generate random numbers?
5 marks

**4(b)** What is Time Series input model. Explain AR(1) and EAR(1) model.
5 marks

**5(a)** What do you understand by 'Goodness of Fit Test'? Write the procedure for the same.
5 marks

**5(b)** Derive steady state parameters for M/G/1 and M/M/1 queue.
5 marks

**6(a)** A Medical examination is given in three stages by physician. Each stage is exponentially distributed with a mean service time of 20 minutes. Find the probability that exam will take 50 minutes or less. Also determine the expected length of the exam.
5 marks

**6(b)** What is the purpose of model verification? What are the different ways available to verify a model.
5 marks

### Write short notes on any Two of the following

**7(a)**Acceptance-rejection Technique 5 marks

**7(b)** Cobweb Model
5 marks

**7(c)** issues in Manufacturing System and Material handling system.
5 marks