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Exploiting regenerative structure to estimate finite time averages via simulation

Exploiting regenerative structure to estimate finite time averages via simulation Exploiting Regenerative Structure to Estimate Finite Time Averages via Simulation WANMO KANG, PERWEZ SHAHABUDDIN, and WARD WHITT Columbia University We propose nonstandard simulation estimators of expected time averages over nite intervals [0, t], seeking to enhance estimation ef ciency. We make three key assumptions: (i) the underlying stochastic process has regenerative structure, (ii) the time average approaches a known limit as time t increases and (iii) time 0 is a regeneration time. To exploit those properties, we propose a residual-cycle estimator, based on data from the regenerative cycle in progress at time t, using only the data after time t. We prove that the residual-cycle estimator is unbiased and more ef cient than the standard estimator for all suf ciently large t. Since the relative ef ciency increases in t, the method is ideally suited to use when applying simulation to study the rate of convergence to the known limit. We also consider two other simulation techniques to be used with the residual-cycle estimator. The rst involves overlapping cycles, paralleling the technique of overlapping batch means in steady-state estimation; multiple observations are taken from each replication, starting a new observation each time the initial regenerative state is revisited. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

Exploiting regenerative structure to estimate finite time averages via simulation

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2007 by ACM Inc.
ISSN
1049-3301
DOI
10.1145/1225275.1225279
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Abstract

Exploiting Regenerative Structure to Estimate Finite Time Averages via Simulation WANMO KANG, PERWEZ SHAHABUDDIN, and WARD WHITT Columbia University We propose nonstandard simulation estimators of expected time averages over nite intervals [0, t], seeking to enhance estimation ef ciency. We make three key assumptions: (i) the underlying stochastic process has regenerative structure, (ii) the time average approaches a known limit as time t increases and (iii) time 0 is a regeneration time. To exploit those properties, we propose a residual-cycle estimator, based on data from the regenerative cycle in progress at time t, using only the data after time t. We prove that the residual-cycle estimator is unbiased and more ef cient than the standard estimator for all suf ciently large t. Since the relative ef ciency increases in t, the method is ideally suited to use when applying simulation to study the rate of convergence to the known limit. We also consider two other simulation techniques to be used with the residual-cycle estimator. The rst involves overlapping cycles, paralleling the technique of overlapping batch means in steady-state estimation; multiple observations are taken from each replication, starting a new observation each time the initial regenerative state is revisited.

Journal

ACM Transactions on Modeling and Computer Simulation (TOMACS) – Association for Computing Machinery

Published: Apr 1, 2007

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