An Evaluation of Contemporary Heuristics for the Startup Problem

The startup problem occurs when the initial conditions of a non-terminating, discrete-event simulation do not represent the central tendency of the steady-state distribution. The net effect of the startup problem, when it is not controlled, is a biased estimate of the sample mean.

Researchers and practitioners have devised numerous techniques for mitigating the effects of the startup problem, including tests for initialization bias, selection of appropriate initial conditions, dilution, and truncation. Of these, the most practical and widely used technique is truncation, although there is no generally accepted truncation methodology that has been shown to be effective and robust on data from a wide range of systems.

The focus of this research was an evaluation of the effectiveness of five contemporary truncation heuristics in mitigating the effects of the startup problem. Two of these rules are variations of a simple heuristic first presented in McClarnon (1990). The remaining three rules were developed from well-known tests for initialization bias. The rules were applied to data generated by several autoregressive processes combined with a multitude of bias functions. The resulting mean estimates from each rule were then compared to the mean estimates of the unbiased process. The result of the evaluation is the recommendation of a modification of the McClarnon rule as an effective and robust, general-purpose, truncation heuristic.