Hybrid modelling of transportation systems by means of Petri nets

A novel hybrid model for transportation systems is proposed, in which the functioning is represented via a continuous-time model whenever no changes in the traffic flow occur, whereas the changes in the system behaviour are modelled through a discrete event system coupled with the continuous-time system. Via the discrete-event part of the hybrid model, its continuous-time part is adapted according to the variation occurred in the system behaviour. The hybrid modelling methodology proposed is based on the use of a special class of Petri nets, the hybrid stochastic Petri nets (HSPN). These nets are composed of some discrete parts, and some continuous parts, so that a hybrid Petri net can be viewed as a combination of an usual (discrete) Petri net and a continuous Petri net, the 'fluid' version of usual timed Petri nets. The discrete part of the HSPN 'regulates' the continuous PN, which models the functioning of the transportation system. This results in the model reacting to any change to the current system behaviour by adapting the traffic parameters to the new state.