Technical Note—Optimal Initial Conditions for a Simulation Problem

Albert Madansky
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Albert Madansky: University of Chicago, Chicago, Illinois

Operations Research, 1976, vol. 24, issue 3, 572-577

Abstract: Suppose one simulates the M / M /1 queue for finite amount of time t , replicating the simulation N times, each time with an initial condition of n in the queue. An estimate of the mean of the steady-state distribution is the average (across replications) number in the queue at time t . We show that for large enough t an initial condition of n = 0 (in contrast to the often-conjectured initial condition n = λ/μ, the steady-state mean) minimizes mean-square error of the estimate. An example illustrates that the “large enough” t need not be very large—one-quarter the relaxation time in the example studied. An approximate tradeoff between N and t when n = 0 is also developed.

Date: 1976
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