The theory of perturbation analysis for discrete event systems (DESs), sometimes also referred to as discrete event dynamic systems, is motivated by the fact that the sample path of a DES observed under a given set of parameter settings contains a surprising large amount of information about the behaviour of the system if it would operate under different parameter settings. This is particularly important when analytical models are not available or simply inadequate for DESs of considerable complexity, specially in a stochastic environment.
This paper extends and unifies several already existing results. The performance measure of the system under consideration is \(J(\theta)= E_\omega\{L(\theta, \omega)\}\), where \(\theta\) represents the system parameters and \(\omega\) the uncertainty; \(E_\omega\) stands for expectation with respect to \(\omega\). The central question is to obtain an estimate of \(dJ(\theta)/d\theta\). The underlying system is described as a generated semi-Markov process (GSMP). As an example one can consider a \(G/G/1/\infty\) queue. An essential part of the description of the GSMP is that the clock and structural mechanisms are “separated”. In case of small clock parameter changes only, the nominal and perturbed path have identical event sequences and the well-known IPA (infinitesimal perturbation analysis) is applicable. The current paper addresses changes in structural parameters (which can lead to different event sequences) as well. The approach taken, called SIPA (structural IPA), calculates the derivate estimate in a fundamentally different way by a two-stage generation of the perturbed sample path. The resulting algorithm seems to be quite general, though the description and derivation is rather mathematical.