Asymptotic continuous Petri nets

Abstract

A Petri net is basically a discrete model. However, continuous Petri nets, such that the markings are real numbers have been defined. Two continuous Petri net models involving time have been drawn up. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The former considers constant firing speeds (CCPN) and is very easy to simulate (few events have to be considered, even when it approximates a timed Petri net with many reachable markings). The latter considers firing speeds depending on the marking (VCPN). Although it provides a better approximation, its simulation is longer because the markings and speeds are given by differential equations. This paper introduces a third model (ACPN) which presents the advantages of the two preceding ones. In most cases, this model represents the asymptotic behavior of the VCPN. Then their precisions are similar. Since the firing speeds of the ACPN are constant, it is as easy to simulate as the CCPN.