PETRI NETS AND TIMED PETRI NETS BASIC CONCEPTS AND PROPERTIES

Zuberek, W. M. (2000) PETRI NETS AND TIMED PETRI NETS BASIC CONCEPTS AND PROPERTIES. Technical Report. Memorial University of Newfoundland, St. John's, Newfoundland and Labrador.

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Abstract

Petri nets are formal models of systems which exhibit concurrent activities. Communication networks, multiprocessor systems, manufacturing systems and distributed databases are simple examples of such systems. As formal models, Petri nets are bipartite directed graphs, in which the two types of vertices represent, in a very general sense, conditions and events. An event can occur only when all conditions associated with it (represented by arcs directed to the event) are satisfied. An occurrence of an event usually satisfies some other conditions, indicated by arcs directed from the event. So, an occurrence of one event causes some other event to occur, and so on. In order to study performance aspects of systems modeled by Petri nets, the durations of modeled activities must also be taken into account. This can be done in different ways, resulting in different types of temporal nets. In timed Petri nets, occurrence times are associated with events, and the events occur in real-time (as opposed to instantaneous occurrences in other models). For timed nets with constant or exponentially distributed occurrence times, the state graph of a net is a Markov chain, in which the stationary probabilities of states can be determined by known methods. These stationary probabilities can be used for the derivation of many performance characteristics of the model. Analysis of net models based on exhaustive generation of all possible states is called reachability analysis; it provides detailed characterization of model's behavior, but often requires analysis of huge state spaces (the number of states can increase exponentially with some model parameters which is known as "state explosion"). Structural analysis determines the properties of net models on the basis of connections among model elements; structural analysis is usually much simpler than reachability analysis, but can be applied only to models satisfying certain properties. If neither reachability nor structural analysis is feasible, discrete event simulation of timed nets can be used to study the properties of net models. This report introduces basic concepts of Petri nets and timed Petri nets, discusses some of their properties, and presents several straightforward applications. It also includes a comprehensive list of references.

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