Evolution equations of timed Petri nets

Timed Petri nets provide a general formalism for describing the dynamics of discrete event systems. The authors attempt 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 nonlinear 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 makes it possible to determine the firing times of the transitions recursively. In the case of stochastic timed Petri nets, various structural properties are derived from these equations, including stochastic monotony properties for certain queuing networks