Augmented infinitesimal perturbation analysis: An alternate explanation

Augmented infinitesimalperturbation analysis (APA) was introduced by GaJvoronski [ 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 by generalized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a telrn 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.