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Regenerative Simulation for Estimating Extreme Values

Author

Listed:
  • Donald L. Iglehart

    (Stanford University, Stanford, California)

  • Mark L. Stone

    (Stanford University, Stanford, California)

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.

Suggested Citation

  • Donald L. Iglehart & Mark L. Stone, 1983. "Regenerative Simulation for Estimating Extreme Values," Operations Research, INFORMS, vol. 31(6), pages 1145-1166, December.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:6:p:1145-1166
    DOI: 10.1287/opre.31.6.1145
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    Cited by:

    1. V. Abramov & M. K. Khan & R. A. Khan, 2008. "A probabilistic analysis of the trading the line strategy," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 499-512.

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