Simulation Techniques, March/April 1999

Part - A

1    a)   Define and explain the following:                        8.
     i)   System-Entities-Attributes-Activities
     ii)  System Environment-Endogenous system.
     Exogenous system-open and closed system.
     b)   List at least two entities-Attributes and activities, each for
     the following systems,	6.
			i) Restaurant
               ii) High School
               iii) Movie Theatre
     c)   Explain, what do you understand by the terms:             6.
			i) Iconic Model
               ii) Analog Model
               iii) Mathematical Model.

2    a) For a manufacturing industry, list and explain the three major
     segments of a corporate model. Also sketch the full corporate Model. 10.
     b) The equation below relates a company's average unit cost, C to the
     number of units produced 'x'.									10.
		C (x) = 50 - 0.04 x - 0.002 x2	
     i)  Using differential calculus techniques find the value of x that
     minimizes C (x). As part of system analysis, is this solution approach
     an example of an analytic or a numeric mode of analysis?
     ii)  Suppose you do not know any calculus but that your professional
     career depends on finding the solution. How might you solve the problem
     using a computer? Describe the mode of analysis employee.

3    a) Discuss some of the conditions when simulation should and should
     not be used.   8.
     b) Describe the Monte-Carlo method. Compare it with Stochastic
     simulation.		6.
     c) With the help of a Flow-chart, briefly describe the basic steps
     involved in the progress of a simulation study.                                           6.

4    a) Describe the three general types of statements from which a CSMP
     program is constructed.6
     b) Find the value of A that makes 'y' a probability density function.
     Derive a formula for generating random numbers having this distribution.
     Compare these random numbers corresponding to the uniform random
     numbers (10097, 27542, 08422, 99019, 12807)
		         =  __1__		0  x  1   
		  y =      x + A									10.
		         =  0		else where
     c) With an example, explain the structure of a system dynamics model.
     4.


5    a) Explain the important parameters of a queuing system  6.
     b) Define the terms 'Balking', 'Reneging' and 'Polling' with respect
     to queuing.	6.
     c) For a single server queue with Poisson arrival pattern and
     negative exponential service time, using first come first serve
     discipline derive an expression for the probability of more than 'n'
     customers being in the queue in terms of its utilization factor of the
     service facility.

Part - B

6    a) With examples, explain the differences between time to time
     simulation and event to event simulation methodologies used in the
     study of discrete systems.       8.
     b) Explain the three main tasks involved in the preparing a computer
     program for a simulation.                                         6.
     c) Write a note on discrete simulation languages.               8.

7    a) Discuss the main features of GPSS.                           8.
     b) With appropriate GPSS Block diagram and GPSS program, discuss
     the simulation of a simple telephone system.                      12.

8    a) Write short notes on the following:
     i)   Recording distributions and Transit time in Discrete system
          simulation.
     ii)  Set operations in GPSS.
     iii) Problems faced while analysing a simulation output. 
     iv)  Time series analysis.
