Hybrid Petri nets for the performance analysis of transportation systems

Transportation systems are usually complex, large-scale systems which require dedicated modelling and control methodologies. In this paper, 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, on which acts as a regulator. 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, making the continuous-time part adapt according to the variation occurred in the system behaviour. As a result, the model reacts to any change in the current system behaviour by adapting the traffic parameters to the new state.