Augmented infinitesimal perturbation analysis: An alternate explanation

Augmented infinitesimal perturbation analysis (APA) was introduced by Gaivoronski [1991] to increase the purview of the theory of Infinitesimal Perturbation Analysis (IPA). In reference [Gaivoronski 1991] it is shown that an unbiased estimate for the gradient of a class of performance measures of DEDS represented bygeneralized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a term that takes into account the event order changes. In this paper we present an alternate approach to establishing the result of Gaivoronski, and from this we derive a necessary and sufficient condition for the validity of the IPA algorithm for this class of performance measures. Finally we validate our results by simulation examples.This research was supported by the National Science Foundation under grant number ECS-85-15449, Office of Naval Research Grants Nos. N00014-90-K-1093 and N00014-89-J-1023 and by Army Grant No. DAAL-03-86-K-0171.