DOEACC Society 2006 DOEACC B Level BE4 Principle of Modelling & Simulation ( ) - Question Paper
Friday, 14 June 2013 04:15Web
BE4-R3: PRINCIPLES OF MODELLING AND SIMULATION
NOTE:
Time: three Hours Total Marks: 100
1.
a) What do you mean by simulation? define 1 application of simulation in
manufacturing system.
b) Bring out the differences between:
i) Deterministic vs. Stochastic models
ii) Continuous vs. Discrete models
c) Customers arrive to a single server service station, in accordance with the Poisson
distribution, at the rate of 10 per hour. The exponentially distributed service time in every
of the counters is two minutes per customer. obtain the avg. time spent by a customer in
the system and in the queue.
d) A set of random numbers is generated by using linear congruential method. Why will it
be necessary to conduct frequency test?
e) Consider a random variable X with the subsequent probability density function:
f(x) = 5x4 , 0 £ x £ 1
obtain its cumulative distribution function. Suggest a procedure to generate random
numbers from the provided pdf.
f) What is GPSS? Why is it used?
g) describe the terms “factor” and “response” in the situation of a simulation experiment.
Illustrate them in the case of inventory simulation issue.
(7x4)
2.
a) elaborate pseudorandom numbers? Why are they called pseudorandom numbers and
not simply random numbers?
b) explain the Linear Congruential method of generating pseudorandom numbers.
c) elaborate the various tests to check randomness in pseudorandom numbers? Why are
these tests required?
(4+6+8)
3.
a) An algorithm for generating X is as follows:
i) Generate U ~ U(0,1)
ii) Let V=F(a)+[F(b)-F(a)]U
iii) Return X=F-1(V)
BE4-R3 Page one of three July, 2006
1. ans ques. one and any 4 ques. from two to 7.
2. Parts of the identical ques. should be answered together and in the identical
sequence.
Show that X described by this algorithm has the distribution function F*(x) described by
0 if x
F( x ) F( a )
-
-
if a £ x £ b
b) Briefly outline the Box and Muller technique for generating normal variates.
c) explain how will you find random variates from an ERLANG distribution with the help
of convolution.
(8+6+4)
4. A vendor buys cakes at Rs. four every and sells them at Rs. five every. Cakes not sold at the
end of the day are discarded fetching only 50 p. every. There could be any 1 of the
three possible market scenarios every day – good, fair, and poor – with probabilities 0.30,
0.40, and 0.30 respectively. The distribution of the demand of the cakes every day is
provided beneath.
Demand
Demand Probability Distribution
Good Fair Poor
500 0.00 0.20 0.50
600 0.15 0.45 0.25
700 0.25 0.20 0.15
800 0.35 0.10 0.10
900 0.15 0.05 0.00
1000 0.10 0.00 0.00
a) obtain the random digit assignments for the following:
i) Daily Market Scenarios
ii) Daily Cake Demand
b) If the vendor purchases 700 cakes a day, conduct a simulation experiment for 10 days using
the random digit assignments as provided in a) above to obtain out the following:
i) The number of occasions for which the vendor will have excess demand, lower
demand, and demand of exactly 700 cakes.
ii) His total profits for the period of 10 days.
iii) His lost profits during the period due to excess demand.
Use the subsequent random digits:
Random digits for Daily Market Scenario: 14, 72, 41, 92, 23, 38, 67, 02, 85, 56
Random digits for demand: 80, 27, 15, 54, 98, 62, 36, 73, 92, 61
(6+12)
5.
a) Differentiate ranging from continuous and discrete event system simulation. Do we require
pseudorandom numbers in continuous simulation?
b) elaborate distributed lag models? provide an example. Also discuss, how a distributed lag
model can be simulated over time.
c) What is Monte Carlo Simulation? Suggest a procedure to calculate approximate value of
p using uniformly distributed random numbers over [0, 1].
(6+8+4)
BE4-R3 Page two of three July, 2006
6.
a) Why is it necessary to carry out output analysis of data generated in simulation
experiments?
b) Are output data from simulation experiments normally distributed? Justify your ans.
c) explain briefly Variance-reduction techniques in simulation experiments. How is it
carried out?
(4+6+8)
7.
a) Bring out the difference ranging from calibration of a system and validation of a system in
discrete event simulation.
b) Outline how level equations are modelled in system dynamics framework?
c) As full factorial design is often prohibitive from the resource requirement viewpoint,
explain what other option does 1 have.
(6+8+4)
BE4-R3 Page three of three July, 2006
| Earning: Approval pending. |
