An Effective Truncation Heuristic for Bias Reduction in Simulation Output

The start-up or warm-up problem arises in steady-state, discrete-event simulation, where the arbitrary selection of initial conditions introduces bias in simulated output sequences. In this paper, we develop and test a new truncation heuristic or resolving the start-up problem. Given a finite sequence, the truncation rule deletes initial observations until the width of the marginal confidence interval about the truncated sample mean is minimized. This rule is easy to implement, has strong intuitive appeal, and is remarkably effective in mitigating initialization bias. We illustrate the performance of the heuristic by comparison with enhanced implementations of alternative truncation rules proposed in the literature. All rules are applied to output sequences generated by ten runs each of four representative queuing simulations. Results confirm the significance of the start-up problem and demonstrate that simple truncation heuristics can solve this problem. All of the rules tested are shown to provide improved accuracy without undue loss of precision. We conclude that all four of the rules tested represent attractive solutions to the start-up problem.