Simulation Techniques Aug 1996

Part - A
1	a)With suitable examples, explain the different types of models
	  used in system studies.
       b) Explain the concept of subsystem and use it to develop a corporate
	  model.

2	a) With suitable examples, illustrate the use of system postulation.
	b) Compare simulation methods with analytical methods and discuss the
	  implications of the experimental nature of simulation.
	c) Describe distributed lag models. Draw a cobweb model for a market
	  in which the supply and demand functions are:
		S = 1.0 + 0.9 P-1
		D = 12.4 - 1.2 P
	   Assume that the initial price is 1.0 and market is always cleared.

3	a) Develop a CSMP III program for the following problem.
	   A torsional pendulum consists of a bar suspended from a spring
	  that winds and unwinds as the bar oscillates up and down. If y
	  is the vertical displacement q is the angle the spring turns,
	  the following equations describe the motion:
		a  + by -c q = F(t)
		e q + f q - gy = G(t)
	  Assume that the system starts from the rest with y and q equal to
	  zero, F(t) is zero and G(t) is 1.Simulate the system for 2.5 units
	  of time, with integration inberval of 0.005, for the following
	  values of constants:
		a = e = 1; b = f = 40; c = g = 4.

4	a) Using a suitable multisegment model, explain the concept of a
	  system dynamics diagram, and the synbols used in such a diagram.
	b) Explain the inverse transformation and rejection methods for
	  generating non-uniform continuously distributed random numbers.

5	a)Descrive the Poisson  arrival pattern and discuss its importance.
	  Using the uniform random generator output given in question 6 (a)
	  compute arrival times of the first 5 arrivals of a Poisson arrival
	  pattern, with a mean interval arrival time of 100 seconds.
	b) Explain the concept of the grade of service and describe how
	  waiting time probabilities can be used to design a system to
	  provide a specified grade of service.

Part - B

6	a) Consider a single server system in which customers arrive at an
	  interval of 5 + 2 minutes and are serviced in 4 + 1 minutes. The
	  customer wait in a queue if the server is busy. Simulate the sysem
	  manually for the first 5 arrivals. Assume a following output from
	  a uniform random number generator.
	   i)	0.1009, 0.3754, 0.0842, 0.9901, 0.1280
	  ii)  0.6606, 0.3106, 0.8526, 0.6357, 0.7379                           12.
	b) Describe the different statistic generally required from a
	  simulation study.        8.





7	a) Draw the GPS block diagram and write the program for the following
	  problem.
	   "Customers arrive at a single server counter. Assume that the
	  distribution of arrivals is Poisson with a mean inter-arrival time
	  of 4 minutes. They purchase *_________  4 items with the following
	  probabilities.			(* The word was not legible.)
			No of Items		Probability
		    1                 0.5
		    2                 0.2
		    3                 0.2
		    4                 0.1
	   It takes one minute to purchase each item. Tabulate the
	  distribution of time for servicing the first hundred customers.								12.
	b) Describe any 4 standard numerical attributes available in GPSS and
	  clearly illustrate their use.    8.

8	a) Describe the LINK and UNLINK blocks of GPSS and illustrate their
	  uses.
	b) Describe the methods of replicaions of runs and batch means to
	  estimate the ****nce of the sample mean.
