The effect of initial transient on the steady-state simulation harmonic analysis gradient estimators

Steady-state simulation runs typically contain an initial transient phase that biases output performance measure estimators, unless the simulation observations at the beginning of the simulation runs are discarded. It is useful to understand the effect of this initial transient on output performance estimators, since determining an accurate truncation point is a difficult problem. In this paper, the initial transient effect is measured for harmonic analysis gradient estimators. A comparison with finite differences gradient estimators is provided as a base case. Four additive forms are used to model the initial transient. The effect of these initial transients is evaluated with respect to how they bias the harmonic analysis gradient estimators and the finite differences gradient estimators. In particular, guidelines are given that indicate when each estimator is better designed to mitigate the effect of the initial transient bias. Computations on an M/M/1 queueing system simulation model illustrate these results.