Estimating steady state mean from short transient simulations

  • Authors:
  • Pieter A. Voss;Jorge Haddock;Thomas R. Willemain

  • Affiliations:
  • Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, New York;Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, New York;Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, New York

  • Venue:
  • WSC '96 Proceedings of the 28th conference on Winter simulation
  • Year:
  • 1996

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Abstract

This paper presents a new approach to estimating and constructing confidence intervals for the steady state mean of a stochastic process from short simulations which may exhibit significant transient response. Specifically, we examine the conditional least squares estimator for the mean of an autoregressive process. If the process is autoregressive with normal innovations, this estimator is the conditional maximum likelihood estimate (MLE) of the mean. We show that the MLE is asymptotically normal, and derive a finite-sample approximation to its distribution. This provides the basis for two asymptotically valid single-replication confidence intervals which do not require choosing a batch size. As a point estimator, the MLE is a generalization of the estimator due to Snell and Schruben (1984) and is related to the weighted batch mean (Bischak, Kelton, and Pollock, 1993). Empirical results for a queuing network show that the autoregressive process is a reasonable model of transient response. For short series with reasonable initializations (e.g., empty and idle), the MLE yields confidence inter vals which are comparable or superior to those of existing procedures, in both single and parallel replication simulations.