Simulation Run Length Control in the Presence of an Initial Transient

TLDR

The study develops an automatic method to estimate the steady‑state mean of a discrete‑event simulation output and construct a confidence interval of prescribed width despite an initial transient. The authors propose a run‑length control procedure that uses Schruben’s Brownian‑bridge test for non‑stationarity and a spectral variance estimator, and evaluate its bias, coverage, interval width, run length, and data deletion empirically across various outputs. When a strong transient is present, incorporating the stationarity test yields lower bias, narrower confidence intervals, and shorter run lengths; without a transient the test only slightly degrades performance, but if the run length is too short relative to the transient the test may fail, producing unreliable estimates.

Abstract

This paper studies the estimation of the steady state mean of an output sequence from a discrete event simulation. It considers the problem of the automatic generation of a confidence interval of prespecified width when there is an initial transient present. It explores a procedure based on Schruben's Brownian bridge model for the detection of nonstationarity and a spectral method for estimating the variance of the sample mean. The procedure is evaluated empirically for a variety of output sequences. The performance measures considered are bias, confidence interval coverage, mean confidence interval width, mean run length, and mean amount of deleted data. If the output sequence contains a strong transient, then inclusion of a test for stationarity in the run length control procedure results in point estimates with lower bias, narrower confidence intervals, and shorter run lengths than when no check for stationarity is performed. If the output sequence contains no initial transient, then the performance measures of the procedure with a stationarity test are only slightly degraded from those of the procedure without such a test. If the run length is short relative to the extent of the initial transient, the stationarity tests may not be powerful enough to detect the transient, resulting in a procedure with unreliable point and interval estimates.