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.