The limiting value of derivative estimators based on perturbation analysis

Infinitesimal perturbation analysis is a method of obtaining estimates of performance sensitivity through simulation of a stochastic system. Expressions are derived for the limiting value of a broad class of such estimators associated with queueing networks, in terms of the unique solution to a set of linear equations. The approach used is to augment the underlying queueing process with information about which servers have been ‘perturbed’ and by how much. The augmented process can then be studied as an absorbing Markov chain in which the absorbing set consists of states in which all servers are equally perturbed. An application of these results is a simple proof of the consistency of an estimator previously investigated experimentally.