Continuous and timed Petri nets for the macroscopic and microscopic traffic flow modelling

Traffic flow can be considered as a hybrid system which is characterized by two major behaviours: continuous ones in motorways and discrete ones in road junctions. We propose a modelling approach based on Petri nets. For this purpose, places of Petri nets stand for the road sections and transitions describe the flow between two consecutive sections at intersections. Thanks an adaptive spatial discretization the proposed models are suitable to represent the traffic flow either from a macroscopic point of view where only global variables are observed or from a microscopic one where the individual trajectories of vehicles are discussed. The proposed models suggest a mathematical framework for the analysis and control design in urban and interurban networks.