System representations and performance sensitivity estimates of discrete event systems

A recently developed technique, called Infinitesimal Perturbation Analysis (IPA), provides an effective method of estimating the sensitivity of performance of a discrete event system based on one simulation of the system. IPA stimulates the study of the sensitivity estimation. One important property of the IPA sensitivity estimate, which differs from that of the ordinary performance estimate, is that the convergence property of the IPA sensitivity estimate depends on the representation of a system. We propose a formulation of IPA estimates which explicitly indicates this dependency on the system representations. We discuss different aspects of the related issues. In particular, we show that the necessary condition developed by Cao (1987) and Heidelberger et al. (1988) for multiple IPA estimates to simultaneously converge is not necessary for any IPA estimate to converge.