Bias properties of infinitesimal perturbation analysis for systems with parallel servers

Infinitesimal perturbation analysis (IPA) is a technique for estimating derivatives of performance measures from a single simulation of a stochastic discrete-event system, which might, for example, be modeling a computer/communication network or a manufacturing system. Such derivative estimates are useful in sensitivity analysis of the system and in optimizing-or at least improving-the performance of the system through gradient algorithms. However, it is well-known that IPA gives biased estimates for systems with multiple servers (channels or machines) in parallel when the server characteristics are not identical. In this paper, the authors investigate the seriousness of the bias both theoretically and experimentally. From the present study, they believe the IPA estimator is relatively insensitive to small differences in the service time distributions of the servers. Specifically, the authors conjecture that for nearly-identical servers, the bias is proportional to the square of the difference between the means of the service time distributions. To support this conjecture, they present a tractable analytical example and investigate, via simulation experiments, more general systems.