Simulation of processes with multiple regeneration sequences

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Abstract

The classical regenerative method of simulation output analysis exploits the regenerative structure of a stochastic process to break up a path into independent and identically distributed cycles based on a single sequence of regeneration times. If a process is regenerative with respect to more than one sequence of regeneration times, the classical regenerative method does not exploit the additional structure, and the variance of the resulting estimator for certain performance measures (e.g., the time-average variance constant) can vary greatly, depending on the particular regeneration sequence chosen. In a previous article, we introduced an efficiency-improvement technique for regenerative simulation of processes having two sequences of regeneration times based on permuting regenerative cycles associated with the second sequence of regeneration points. In this article, we show how to exploit more than two regeneration sequences. In particular, for birth-death Markov chains, the regenerations associated with hitting times to each state can all be exploited. We present empirical results that show significant variance reductions in some cases, and the results seem to indicate that the permuted estimator for the time-average variance constant can have a variance that is independent of the primary regeneration sequence used to run the simulation.

Original languageEnglish (US)
Pages (from-to)179-201
Number of pages23
JournalProbability in the Engineering and Informational Sciences
Volume14
Issue number2
DOIs
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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