DOEACC Society 2006 DOEACC B Level BE4 Principle of Modelling & Simulation ( ) - Question Paper

BE4-R3: PRINCIPLES OF MODELING AND SIMULATION
NOTE:
Time: three Hours Total Marks: 100
1.
a) The cdf of a discrete random variables is provided by x k
k k
F X x x , 1,2,...,
( 1)
( ) ( 1) =
+
= +
Using inverse transform technique, develop a procedure for generating random variable
X.
b) Name entities, attributes, activities, events and state variables for
i) Communication system
ii) Banking system
c) Every simulation must have a stopping time, which describes how long the simulation will
run. explain ways to stop a simulation.
d) 1 of the important steps in the development of a useful model of input data is to
identify a probability distribution to represent the input process. explain methods for
selecting input distributions when data are available.
e) Let X and Y be independent exponential random variables with mean 1. discuss how
can you use Monte Carlo technique to estimate E[eXY].
f) Consider the M/M/¥ queuing system with infinite number of servers. In this queuing
system every arriving customer is assigned to its own server of rate µ. Therefore if there
are n customers, the aggregate output rate is nµ. find equilibrium state probability
and the mean queue size.
g) As an aid in the validation process, a three-step approach is widely followed
i) Build a model that has high face validity.
ii) Validate model assumptions.
iii) Compare the model input-output transformations to that for real systems.
discuss the above-mentioned steps.
(7x4)
2.
a) It is often necessary in practice to develop a simulation model (perhaps for
demonstration purposes or a preliminary study) before any process data are available.
i) explain ways to find info about a process even if data are not
available.
ii) Which statistical distributions are generally used as input models when data are
not available?
b) Verification and validation of simulation models is of great importance. What is the
purpose of model verification? Compare and contrast the problems involved in validation
and verification.
(9+9)
BE4-R3 Page one of three January, 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.
3. Tankers carrying crude oil arrive at a singe unloading dock, supplying a storage tank that
in turn feeds a refinery through a pipeline. An unloading tanker delivers oil to the
storage tank at a specified constant rate. The storage tank supplies oil to the refinery at
a specified rate. Unloading the tanker is considered complete when the level of oil in the
tanker is less than 5% of its capacity, but unloading must be temporarily stopped if level

Earning:   Approval pending.