Macroscopic traffic modeling of heterogeneous road networks using coloured Petri nets

Coloured Petri net (CPN) is adopted for representing the traffic state and dynamics of each subregion, which is derived by partitioning heterogeneous road network for taking the advantage of well-defined MFD. Firstly, tokens in place of Petri net stand for the number of vehicles in each subregion, and different colours of tokens are used to represent OD matrix between subregions. Secondly, directed transitions between places (i.e. the corresponding subregions) are defined as the possible routes between each OD pair, and time delay of a transition can be derived from travel time of a specific route between adjacent places. Equivalently, the weight of transition can be associated with the completed traffic outflow, which is determined by the existing MFD, considering the number of vehicles in subregion. Thirdly, the firing rule of transitions in Petri net is designed considering asynchronous concurrency of traffic dynamics between any two adjacent subregions. Finally, network performances can be evaluated by average number of vehicles and mean sojourn time in a subregion, etc. The simulation verifies the effectiveness of our CPN model.