Comparing alternative methods for derivative estimation when IPA does not apply directly

Alternative methods such as likelihood ratios (LRs), finite perturbation analysis (FPA), smoothed perturbation analysis (SPA), and rare perturbation analysis (RPA) have been proposed and could be used when infinitesimal perturbation analysis (IPA) does not apply directly. The authors discuss some links that exist between these methods and explain them by showing how each of them can be applied to a specific example, namely to estimate the derivative of the expected number of customers per regenerative cycle in a GI/G/1 queue, with respect to parameters of the interarrival and/or service-time distributions. Two efficient SPA estimators for estimating the derivative of the expected number of customers per regenerative cycle in a GI/G/1 queue are introduced. For the examples examined, these estimators outperformed those that had been proposed previously for the same problem