Rethinking the initialization bias problem in steady-state discrete event simulation

The state in which a discrete event simulation is started causes the estimators for equilibrium measures obtained from the simulation to be biased, and to reduce this bias, the collection of data is delayed until a so-called warm-up period is completed. In this paper, we determine the optimal warm-up periods for steady-state discrete event simulations. We do this by using deterministic numerical methods, that is, methods not using random numbers. We found that in the systems investigated, transient expectations give no indication regarding the optimal length of the warm-up periods, which is counterintuitive. This requires some re-evaluation of some of commonly held opinions about the factors one should take into account when determining warm-up periods. Such factors will also be discussed.