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Discrete event systems (DES) are characterized by a collection of events, such as the completion of a job in a manufacturing process or the arrival of a message in a communication network. The system state changes only at time instants corresponding to the occurrence of one of the defined events. At the logical level of abstraction, the behavior of a DES is described by the sequences of events that it performs. However, if time constraints are of explicit concern in the system dynamics and its performance specification, its behavior can be characterized by sequences of occurrence times for each event. The objective of this paper is to demonstrate how underlying algebraic similarities between certain logical and timed DES can be exploited to study the control of timed DES.
Logical DES are often modelled by automata known as finite state machines (FSM). A FSM consists of a set of states Q, a collection of events Σ, and a state transition function δ. The occurrence of an event causes the system to move from one state to another as defined by the transition function.
Timed DES which are subject to synchronization constraints can be modelled by automata known as timed event graphs (TEG). A TEG is a timed place Petri net in which forks and joins are permitted only at transitions. A delay or processing time is associated with each place connecting pairs of transitions. Each transition in the graph corresponds to an event in the system. When an event occurs it initiates the processes connecting it to successor events.
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