The goal of this research is to continue the development of a mathematical theory for the analysis and control of discrete event systems (DESs). DESs arise in a variety of areas of practical application, including, for example, multi-robot systems, manufacturing systems, data bases, distributed computing, distributed and hierarchical optimization, queuing systems, mixed variable control systems, and the higher level intelligent control of complex processes. A number of proposals have been made for modeling and studying the various aspects of DESs of interest. The recent work on the control of logical DESs has contributed to our understanding of some of the fundamental issues involved in the analysis of DESs. Other approaches, particularly perturbation methods and likelihood ratio methods have had considerable impact on the analysis, simulation and optimization of stochastic DES models. The main thrust of the proposed research is to extend these two approaches by addressing issues such as real-time constraints, algorithmic complexity, aggregated models, mixed variable systems, and stochastic optimization using perturbation analysis and likelihood ratio derivative estimates. The relationship between current models will also be investigated with the aim of unifying the tools available for the study of discrete- event systems.
