Simulation Techniques August 1997

Part - A

1    a)   With a flow diagram explain the approach for a system study.   10.
     b)   With suitable illustrations, bring out the differences between the
     following:		10
           i)   Physical and Mathematical models.
          ii)  Static and Dynamic model.

2    a)   Explain how Analog Computers are used to simulate continuous
     systems. Illustrate the role of different analog computer blocks. What
     are the limitations and advantages of analog computer simulation?    10.
     b)   A new extension has potential to build 4 houses. The number of
     houses built is proportional to the number of vacant sites. Set up a
     model to represent this continuous system. Also devise a procedure to
     simulate this system.						10.

3    a) What are the differences between continuous system simulation and
     discrete system simulation? Explain with examples.      8.
     b) Draw the Cobweb model of market economy represented using
     distributed lag model by:
          D = 10 - 0.9 P
          S = - 2.4 + 1.2 P -1
          P0 = 5.0
     Where D = Demand, S = Supply, P = Market price and P0 is initial price.
     From the model solution find out whether the market price is stable or
     not.                  12.

4    a) What are pseudo random numbers? Why are they used in computer
     simulation rather than random numbers? Explain the three different
     methods of generating uniformly distributed pseudo random numbers by
     congruential method.                      10.
     b) An arbitrary continuous probability distribution is given below:
		X	0	2	4	6	8	10
	  F(X)	0	0.04	0.21	0.42	0.73	1.0
	Compute the random numbers from this distribution when the following
     uniform random numbers are generated
	i) 0.28	ii) 0.63

5    a) What are the three main characteristics used to describe a queuing
     system in a simulation study? Explain them.                        8.
     b) For a single server queuing system, the inter arrival an service
     times of eight customers are given below:
     ATi = { 0, 10, 15, 10, 35, 30, 10, 5}
     STi  = {20, 15, 10, 5, 15, 15, 110, 10}
Compute the average waiting time and average queue length.			12.

Part - B

6    a) Explain the differences between fixed-time step simulation and
     Event-to-event simulation technique used in discrete system simulation.
     Give examples and explain.         8.
     b) People arrive at the rate of one every 10 + 5 min to use a single
     telephone. If the telephone is busy, 50% of the people come back 5 min
     later to try again. The rest give up. Assuming that a call takes 6 + 3
     min, count how many people would give up by the time 1000 calls have
     been completed. Use GPSS for writing the program.                   12.

7    a) Write a GPSS program to simulate the behaviour of a computer
     system to evaluate the CPU and memory performance and collect relevant
     queuing statistics for them. The system parameters are as follows:
		Machine: Memory Size = 640 KB
		CPU = Time slice = 500 millisec
		Task initiation overhead = 60 millisec.
		Jobs:
		Arrival rate = 20         , exponentially distributed
		CPU service time = 15 to 35 sec, uniformly distributed

Ques number 8 not available.
