On choosing the characterization for smoothed perturbation analysis

Using second derivative estimators of the GI/G/1 queue as an illustrative example, the authors demonstrate that smoothed perturbation analysis estimators are not necessarily as distribution-free as infinitesimal perturbation analysis estimators, in the sense that the appropriate choice of conditioning quantities-the so-called characterization-may depend on the underlying distribution. Through a different choice of characterization, the authors derive an estimator that works for distributions for which a previously derived estimator fails. The importance of finding the appropriate characterization, or set of conditioning quantities, when applying the technique of smoothed perturbation analysis is illustrated by the contrast between two estimators of the same quantity (second derivative of mean steady-state system time) based on different characterizations of the simple path