DOEACC Society 2006 DOEACC B Level BE4 Principle of Modelling

of the oil in the storage tank reaches its capacity.
i) Justify that the description of the above model would require combined discretecontinuous
simulation.
ii) Identify the discrete events for this model.
iii) State the continuous state variables here. How will you model their dynamics?
iv) Develop a model that defines the situation of arriving tankers forming a queue
when the dock is busy.
v) define the fundamental interaction that can occur ranging from discretely changing
and continuously changing state variables.
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4.
a) You are provided the multiplicative congruential generator x0=1 and xn+1= seven xn (modulo 13)
for n=0,1,2,…
i) compute xn for n=1,2,…,12
ii) How often does every integer ranging from one and 12 appear in the sequence in part i)
above?
iii) Without performing additional calculations, indicate how x13, x14,… will compare
with x1, x2,…, x12
b) Apply the inverse transform method to generate random observations from the uniform
distribution ranging from -10 and 40 by using the random numbers 0.0965, 0.5692, 0.6658.
i) Apply this method graphically.
ii) Apply the method algebraically.
c) elaborate pseudo random numbers? Briefly explain the frequency test for testing
whether they form random sequences.
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5. Consider a single run of a simulation model whose purpose is to estimate a steady state
or long-run characteristic of the system. Suppose that the single run produces
observations Y1,Y2,… Here Yi denotes the total time job i takes in a job shop.
i) How do you find the steady state avg. time a job takes in the shop?
ii) How does the simulation analyst decide when to stop the simulation? explain the
considerations in this regard.
iii) What steps are needed for reducing initialization bias in steady-state simulation?
iv) For making initialization bias negligible, how does 1 decide the extent of data
to be deleted?
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6.
a) Though in terms of specifics, the simulation packages differ, generally they have many
common characteristics. define a few of them.
b) What is embedded simulation?
c) When do you think simulation is inappropriate?
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BE4-R3 Page two of three January, 2006
7.
a) Consider a single finite buffer single server system with arrival and service rates such
that equilibrium probabilities of state are
n 0 one two three ³ 4
------------------------------------------------------------
p(n) 0.415 0.277 0.185 0.123 0.0
Take µ=10. compute mean throughput and mean number of customers in the queuing
system and mean delay.
b) Is the subsequent table realizable for a finite buffer state-independent M/M/1 system? Why
or why not?
n 0 one two three ³ 4
p(n) 0.4 0.3 0.2 0.1 0.0
c) The demand rate of a particular item is 12000 units per year. The set up cost per run is
Rs 350 and the holding cost is Re 0.20 per unit per month. If no shortages are allowed
and the replacement is instantaneous, determine (i) the optimum lot size and (ii) the
optimum scheduling period.
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BE4-R3 Page three of three January, 2006

Earning:   Approval pending.