Annals of Operations Research 39(1992)1-39 1 STOCHASTIC QUASIGRADIENT METHODS FOR OPTIMIZATION OF DISCRETE EVENT SYSTEMS Yury M. ERMOLIEV and Alexei A. GAIVORONSKI V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine Abstract In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported. Keywords: Stochastic programming, stochastic quasigradient methods, discrete event systems, simulation, concurrent approximation and optimization. 1. Optimization of discrete event systems: Informal discussion The objective of this paper is to address several issues which are important for applications of optimization algorithms to stochastic models of discrete event systems. During the last decades, considerable efforts were devoted to the development of various modeling tools for discrete event systems (DES), in particular Petri nets [1,35], queueing models [21,51], finitely recursive processes [23], and others; for further references, see [52]. At the same time, the development of stochastic programming techniques reached the stage of reasonable theoretical understanding, fairly advanced research software and some sophisticated applications [10]. So far, these two fields have interacted relatively weakly ([17,30,40,46] are among the rare exceptions), although discrete event systems seem to be a natural application for stochastic optimization. We assume that it is possible to identify a set Z of states of DES and the system evolves in time t. The set Z can be finite or infinite, the time can be discrete or continuous. The evolution of the system consists of the sequences of "events" which occur at particular time moments ti, each event is a change of the state of the system from zi_ ~ to zi. Thus, the system evolution can be represented as a finite or infinite sequence of pairs © J.C. Baltzer AG, Scientific Publishing Company