1.a. Explain steps in simulation study along with the flowchart.

1.b Explain the properties of a Poisson Process

1.c Perform the simulation of the following inventory system, given daily demand is represented by the random numbers 4,1,8,5,2 and the demand probability is given by

Demand	Probability
0	0.2
1	0.5
2	0.3

If the initial inventory is 4 units, determine on which day the shortage condition occurs.

2.a State the queueing notation, queue discipline and queue behavior.

2.b Given the input parameters, simulation variable, output statistics for the queueing system. Calculate the output statistics for the queueing system whose inter-arrival and service times for ten arrivals are given below:

Inter-arrival time	-	8	6	1	8	3	8	7	2	3
Service time	4	1	4	3	2	4	5	4	5	3

3.a Consider the following sequence of random numbers. How would you test it for independence based on runs above and runs below the mean for the significance level $\alpha$= 0.05 and the 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
0.39	0.15	0.33	0.35	0.91	0.41	0.60	0.25	0.55	0.88

3.b Explain Inverse transform technique for random variate generation. Support your answer with suitable example.

4.a What is the purpose of model verification? What are the different ways available to verify a model?

4.b Draw the flowchart for arrival and departure event in single server system. Compare event-scheduling, process interaction and activity scanning algorithms.

5.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, $\alpha$= 0.05, $\chi _{0.05,9}$= 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}

5.b The following data were available for the past 10 years on demand and lead time.

Lead Time	6.5	4.3	6.9	6.0	6.9	6.9	5.8	7.3	4.5	6.3
Demand	103	83	116	97	112	104	106	109	92	96

Estimate correlation and co variance.

6.a Explain the batch means for interval estimation in steady state simulation.

6.b What are the objectives of simulation in a manufacturing system? Give the block diagram and explain the sequence of operations in a manufacturing system. Suggest a suitable simulation language for the same.