already consumed by the priority transition $q_+$ is available to $q_-$.

The first two properties of homogeneity in Proposition \[thm:prop2\] are still satisfied by the dynamics extended by the routing rules –.

\[rk:comparison\] We already mentioned in the introduction that our model differs from the standard continuous Petri net model in which transitions are equipped with firing rates, in the sense that in the latter model, the flows of the output transitions of a given place are pairwise independent. To overcome this limitation, *immediate transitions* have been introduced [@recalde2006improving]. These transitions come with the specification of routing rules, for instance, in the case of conflict pattern. In this way, our model could be reduced to a classical continuous model enriched with immediate transitions. In this reduction, we require timed transitions to have exactly one upstream place and one downstream place, so that all the routing is determined by immediate transitions, which inherit the equations defined in our place-timed dynamics.

Simply put, our model is the continuous analogue of discrete Petri nets equipped with “holding durations”, in which tokens are frozen during processing, whereas the usual continuous Petri net model can be seen as the continuous analogues of Petri nets with 