In analyzing a stochastic system, such as a network of queues, one is often interested in how system performance depends on system parameters. Gradients provide useful information on this dependence. If the system in question is simulated (or perhaps just observed) one may therefore be interested in estimating gradients from sample paths.
This monograph brings together a circle of ideas on the validation and implementation of a class of gradient estimates, those based on infinitesimal perturbation analysis (IPA). IPA is easy to use, but it does not always yield correct results. Our purpose here is to bring together fairly simple, structural conditions under which IPA works, and to stretch its scope to make it work on as many problems as possible.