On Evaluating SFM-Based Infinitesimal Perturbation Analysis Estimates From Discrete Event System Data

Abstract

This paper investigates the evaluation of infinitesimal perturbation analysis (IPA) estimates that have been derived based on a stochastic fluid model (SFM) using data observed from the sample path of a discrete event system (DES). First, we show that a straightforward implementation of the SFM-based IPA estimates may yield biased estimates when the data are obtained from the actual DES. Then, in order to better approximate the sample path of the DES, we propose a special case of SFM where the arrival and service processes are modeled by piecewise constant on/off sources. The proposed SFM violates some of the assumptions made in [1]-[4] , and, as a result, the sample derivatives no longer exist. However, using the proposed SFM, we obtain the left and right sided sample derivative estimates. As shown in this paper, the sided sample derivatives are much better in approximating the required derivatives compared to the straightforward implementation of the SFM-based IPA estimates.