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Recursive Equations and Basic Properties of Timed Petri Nets.

Baccelli, F.; Cohen, G.; Gaujal, B.

In: Rapports de recherche 1432, INRIA, Rocquencourt. 1992.

Abstract: Timed Petri Nets provide a general formalism for describing the dynamics of Discrete Event Systems. The aim of this paper is to provide the basic equations that govern their evolution, when structural consumption conflicts are resolved by a predefined `switching' mechanism. These equations can be seen as a non-linear extension of the recursive equations for conflict free timed Petri nets, which are known to be linear in the (max,+) semi-field. These equations are shown to be `constructive' whenever the Petri net is live, and a computational scheme is given that allows one to determine the firing times of the transitions recursively. In the case of strochastic timed Petri nets, various structural properties are derived from these equations, including new stochastic monotony properties for certain queueing networks.

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