Timed Continuous Petri Nets

The basic model is an autonomous continuous PN, as defined in Chapter 4, plus a maximal speed associated with every transition. Firing of a transition is continuous, like a flow limited by the maximal speed. For the models considered in this chapter, the maximal speeds do not depend on the marking.

For the basic model, the maximal speeds are constant. In Section 5.1, the behavior of such a PN is presented as a limit case of timed discrete PN behavior. Various basic behaviors are then analyzed, in order to understand clearly the semantics of the model.

After a presentation of the conflicts in a timed continuous PN and their resolutions in Section 5.2, an algorithm used to calculate the behavior for such a PN is proposed in Section 5.3. Some applications and properties are presented in Section 5.4.

The basic model is then generalized in Section 5.5. The maximal speeds may depend on time but remain independent from the marking (models in which the speeds may depend on the marking are presented in Chapter 7).

In this chapter, the expression “continuous PN” means “timed continuous PN” (with constant maximal speeds up to the end of Section 5.4). Whenever an autonomous PN is concerned, this is specified.