CONTINUOUS AND HYBRID PETRI NETS

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Abstract
Petri nets are widely used to model discrete event dynamic systems (computer systems, manufacturing systems, communication systems…). When a PN contains a large number of tokens, the number of reachable states explodes. This is a practical limitation to the use of Petri nets. Continuous models may provide very good approximations for discrete event systems: this is the basic idea leading to the definition of continuous Petri nets. A continuous PN is a model in which the marking of each place is a real number. In a timed continuous PN, a firing speed is associated with each transition (this basic model is unique although the firing speed may be defined in several ways). Various timed continuous PN models have been defined and they correspond to a specific calculation of the firing speeds. They provide good approximations for performance evaluation when a PN contains a large number of tokens. Modeling a number of parts in a buffer by a real number may generally be an acceptable approximation. However, the state of a machine, up or down, cannot be modeled by a real number. This naturally leads to the idea of hybrid PNs, containing a discrete part and a continuous part. Autonomous and timed hybrid PNs are presented. A large of the presentation is informal and intuitive. Three examples illustrate the application of the different models.

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