Regenerative Simulation for Estimating Extreme Values

Donald L. Iglehart and Mark L. Stone
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Donald L. Iglehart: Stanford University, Stanford, California
Mark L. Stone: Stanford University, Stanford, California

Operations Research, 1983, vol. 31, issue 6, 1145-1166

Abstract: Let X ( t ) denote the regenerative process being simulated and assume that it converges in distribution to a steady state random variable. This paper considers estimating the extreme values of the regenerative process. Suppose we are interested in the largest value attained in the interval [0, t ], call it X *( t ). The paper develops a method for estimating the distribution of X *( t ). When the regenerative process is either the GI / G /1 queue or a birth-death process, theoretical results are available for the distribution of X *( t ). Our development simulated the waiting time, queue length, and virtual waiting time for an M / M /1 queue, employed the method for estimating the distribution of X *( t ), and compared the simulation results with the theoretical results.

Keywords: 767 simulation output analysis; 799 extreme value estimation (search for similar items in EconPapers)
Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:31:y:1983:i:6:p:1145-1166

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