Simulation Techniques	Sept/Oct 1998

Part - A
1    a) For the following systems, develop a High level system diagram
     (Flow Chart), List the entities, attributes and activities. Indicate
     the system parameters and experimental parameters. Describe the system
     environment and classify the system as either open or closed.
          i)   A super market with both regular and express check outs. The
          purpose of simulation is to determine optimum number of check outs.
          ii) A computer system that accepts both Batch and Interactive jobs.
          The purpose of the simulation is to determine possible processing
          bottlenecks.                14.
     b) State and explain atleast three guiding principles used in
          Modelling.               6.

2    a) What is 'System Analysis' ? Demonstrate a system analysis study
        for a portion of corporate model.                                               6.
     b) Explain how Monte-Carlo method can be used to determine the value
        of p.          6.
     c) Use a Cobweb model to investigate a market in which the supply and
        demand functions are
		D = (18/P) - 4.7) ;	S = 0.56(P-1 -1)				
		Assume the market is always cleared.						8.

3    a) Explain each of the following as applied to CSMP:                                       9.
		i)	Functional blocks.
		ii) Data statements.
		iii)Control Statements.
     b)      Explain what do you understand by                                               6.
		i)	Interactive systems.
		ii)	Real-time simulation.									
     c)   Write a note on 'system dynamics diagrams'.           5.

4    a) Develop a multiplicate congruential random number generation
     subroutine for a computer with 8 bits to a word, including a sign bit.
     Using '31' as a seed number, generate 5 random numbers using the logic
     expressed in your subroutine. (The subroutine shall be either in PASCAL
     or 'C').                                           10.
     b) For the equations given velow compute the constant 'A' that makes
     f(x) a pdf and generate three random numbers corresponding to the
     uniform random numbers 0.3754, 0.1280 and 0.6607.										10.
		i)	f(x) = A sin x		0 = x = p/2
		ii)	f(x) = 1/(x+A)		0 = x = 1
			        = 	0 else where

5   a) Calculate the portability of three being n - arrivvals(n=0, 1, 2,
          ......10) ion an interval of 10 seconds when the arrivals have a
          Poisson distribution with parameter 0.4.          6.
    b) For a single server queue with Poisson arrival pattern and
       exponential service time derive expressions for                                           8.
          i)      Average length of non empty queues.
         ii)     Average waiting time of a customer before he is served.                  
    c) Develop diagrams (Flow-Charts) for arrival and separate operations
       for queues in the following system. Indicate the queuing discipline
       for the queue.
         "Treatment of patients in a hospital emergency room served by
          multiple doctors. Patients are selected for treatment by the
          severity of illness and then by waiting time"

Part - B

6   a)      A handsome boy and a beautiful girl, who are in love, decide to
          meet in a park at 6.00 pm. The girl is always late. To keep himself
          amusing, the boy adopts the following game: He tosses a coin. If it
          falls head he would walk to the North by 10 meters and if it shows
          tails he walks to the South by 10 meters. Thus he executes what is
          called a 'Random walk'. Assume the probability of head showing =
          0.52. Simulate the game for various distances, D, (say 100, 200,
          300, 400, 500 meters) the boy has walked in total and determine
          how far he is from the starting point at the end of each run.
                                  10.
    b)      Classify the discrete system simulation languages into three main
          categories and explain any one of them.        5.
    c)   What are the advantages of a simulation language over conventional
          languages like FORTRAN, PASCAL or C

7   a)      Write the GPSS block-diagram symbols for the following:                         10
		i)   ADVANCE		iv) GATE
		ii) UNLINK		v)  SEIZE		iii)LEAVE
    b)   "A machine tool in a manufacturing shop is turning out parts at
          the rate of one every 5 minutes. As they are finished the parts
          go to an inspector who takes 4 + 3 minutes to examine each one and
          rejects about 10% of the parts. The rejected parts are sent back
          for further work. Re-working takes 15 +  3 minutes and does not
          involve the machine that originally made parts. After correction,
          the parts are resubmitted for inspection. Simulate for 1000 parts."
		For the above problem give a GPSS, with appropriate examples:
          			10.

8   a) Explain the following with reference to GPSS, with appropriate
       examples.      12.
		i)  SNA's
		ii) Set operations.
    b)   Given the following output sequence of 9 numbers, compute the
         sample mean and variance
            0.008, 0.003, 0.0129, 0.009, 0.009, 0.008, 0.004, 0.011, 0.008                  4.
    c)  Define 'Auto-co-variance'. When do you say a stochastic process is
        'co-variance stationary'? Given a set of observations at T uniform
        intervals of time, write the equations for estimating the sample
        mean and auto-covariance.                            4.
