Introduction

With advances in computer technology came the emergence of a new class of dynamic systems, examples of which include – but are not limited to – automated manufacturing systems, computer networks, communication systems, air traffic control systems, and office information systems. These, often manmade, complex systems are formed by interconnecting several subsystems with well understood dynamics. The interconnected system is then driven according to the asynchronous occurrences of discrete events resulting from the interactions between the subsystems. These systems are now commonly known as discrete event dynamic systems (DEDS) [3].

Over the past decade, a great deal of work has been done on the many aspects of the efficient functioning of these systems. There are now a variety of approaches based on Markov chains [14], queueing networks [15], Petri nets [20], formal language theory [22], sample path methods [13], perturbation analysis [24], object-oriented techniques [10], and (max, +) or dioid algebra [1].

Within the field of study of DEDS, issues related to modeling, control, and performance analysis of a particular class, namely the automated manufacturing systems, have recently attracted a lot of interest from researchers in engineering, computer science, and mathematics. In this paper, the term discrete event manufacturing systems (DEMS) is used to refer to these systems, in order to stress the event-driven nature of their dynamics. Special cases of this broad classification are flexible manufacturing systems (FMS) [11], and computer integrated manufacturing (CIM) systems [23].

Apart from being event-driven, two other characterizing features of DEMS are concurrency (many operations are causally independent [20], and/or occur simultaneously [8]), and asynchronous operations (certain tasks are not always completed in the same amount of time [8]).