Time Petri Nets with Dynamic Firing Dates: Semantics and Applications

TL;DR

This paper introduces an extension to time Petri nets allowing dynamic updates of transition firing dates based on system state and concurrency, enhancing modeling flexibility for scheduling and hybrid systems.

Contribution

It proposes new mechanisms for dynamically updating firing dates in time Petri nets and extends the state class abstraction to this new model, with exactness for certain classes.

Findings

The extended Petri nets can model preemptive scheduling and hybrid systems effectively.

The state class abstraction remains exact for a specific class of these nets.

Applications demonstrate improved modeling capabilities for complex timing behaviors.

Abstract

We define an extension of time Petri nets such that the time at which a transition can fire, also called its firing date, may be dynamically updated. Our extension provides two mechanisms for updating the timing constraints of a net. First, we propose to change the static time interval of a transition each time it is newly enabled; in this case the new time interval is given as a function of the current marking. Next, we allow to update the firing date of a transition when it is persistent, that is when a concurrent transition fires. We show how to carry the widely used state class abstraction to this new kind of time Petri nets and define a class of nets for which the abstraction is exact. We show the usefulness of our approach with two applications: first for scheduling preemptive task, as a poor man's substitute for stopwatch, then to model hybrid systems with non trivial continuous behavior.