Modelling and Controlling Traffic Behaviour with Continuous Petri Nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to such heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a very compositional and efficient formalism to model traffic behaviour in between intersections. This paper introduces some new features of continuous Petri nets that are useful in order to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing traffic light controllers that minimize the total delay of the vehicles in the system.