Stationary solutions of discrete and continuous Petri nets with priorities

TL;DR

This paper analyzes stationary solutions in Petri nets with priority routing, demonstrating their equivalence in discrete and continuous models and showing continuous models eliminate certain oscillations observed in discrete ones.

Contribution

It introduces a continuous dynamics framework for Petri nets with priorities and characterizes stationary solutions, linking discrete and continuous models.

Findings

Stationary solutions are identical in discrete and continuous Petri nets.

Continuous models eliminate oscillations seen in discrete models.

Numerical experiments confirm theoretical results on an emergency call center case study.

Abstract

We study a continuous dynamics for a class of Petri nets which allows the routing at non-free choice places to be determined by priorities rules. We show that this dynamics can be written in terms of policies which identify the bottleneck places. We characterize the stationary solutions, and show that they coincide with the stationary solutions of the discrete dynamics of this class of Petri nets. We provide numerical experiments on a case study of an emergency call center, indicating that pathologies of discrete models (oscillations around a limit different from the stationary limit) vanish by passing to continuous Petri nets.