Asymptotic continuous Petri nets: an efficient approximation of discrete event systems

Two continuous Petri net (CPN) models involving time are defined. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The first model considers constant firing speeds (constant-speed CPN, CCPN). It is very easy to simulate. The second model considers firing speeds depending on the marking (variable speed CPN, VCPN). It provides a better approximation, but its simulation is longer because the markings and speeds are given by differential equations. The authors introduce a third model, which has the advantages of the two preceding ones. This model represents the asymptotic behavior of the VCPN. Their precision is similar. It is as easy to simulate as the CCPN