Estimating the steady-state mean from short transient simulations

Steady-state mean performance is a common basis for evaluating discrete event simulation models. However, analysis is complicated by autocorrelation and initial transients. We present confidence interval procedures for estimating the steady-state mean of a stochastic process from observed time series which may be short, autocorrelated, and transient. We extend the generalized least squares estimator of Snell and Schruben [IIE Trans. 17 (1985) 354] and develop confidence interval procedures for single and multiple-replication experiments. The procedures are asymptotically valid and, for short series with reasonable initializations (e.g., empty and idle), are comparable or superior to existing procedures. Further, we demonstrate and explain the robustness of the weighted batch means procedure of Bischak et al. [Manage. Sci. 39 (1993) 1002] to initialization bias. The proposed confidence interval procedure requires neither truncation of initial observations nor choice of batch size, and permits the existence of steady-state mean to be inferred from the data.