Stochastic initialization in steady state simulations.

Abstract

The goal of steady-state simulation is often to obtain point and interval estimators for a steady-state parameter. The technique of making independent and identically distributed replications is a simple way to obtain these estimates; unfortunately, the initial conditions used to start a simulation frequently bias the estimators thus obtained. A common method to deal with this initialization bias is to delete an initial portion of the output, but this can necessitate the deletion of large amounts of data. In this dissertation, we investigate a method of initialization for steady-state simulations which reduces the initialization bias and , consequently, the amount of deletion required. We call this method stochastic initialization. We use a first-order autoregressive process with high autocorrelation to study the effect of stochastic initialization on various point and interval estimator criteria: bias, variance, mean squared error, coverage and expected half-length. We show that the method can be highly effective in reducing bias in the point estimator and increasing coverage to desired levels. We also demonstrate the effectiveness of stochastic initialization in the simulation of a few queueing systems; this study required the derivation of the transient behavior of the queueing systems, results of value in their own right. We also show that the effectiveness of our stochastic initialization procedure is not very sensitive to the specification of methodological parameters, allowing room for error in implementation by a simulation practitioner.