---
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.'
address:
- 'INRIA and CMAP, École polytechnique, CNRS, Université de Paris-Saclay'
- 'École des Ponts ParisTech INRIA and CMAP, École polytechnique, CNRS, Université de Paris-Saclay Brigade de sapeurs-pompiers de Paris'
author:
- Xavier Allamigeon
- Vianney Bœuf
- Stéphane Gaubert
title: Stationary solutions of discrete and continuous Petri nets with priorities
---

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Introduction
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Context {#context .unnumbered}
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The study of continuous analogues of Petri nets dates back to the works of David and Alla [@david1987continuous] and Silva and Colom [@silva1987structural] in 1987. It has given rise to a large scope of research in the field 