A Hybrid-Dynamical Model for Passenger-flow in Transportation Systems*

In a network with different transportation modes, or multimodal public transportation system (MPTS), modes are linked among one another not by resources or infrastructure elements - which are not shared, e.g., between different metro lines -, but by the flow of passengers between them. Now, the movements of passengers are steered by the destinations that individual passengers have, and by which they can be grouped into trip profiles. To use the strength of fluid dynamics, we therefore introduce a multiphase hybrid Petri net model, in which the vehicle dynamics is rendered by individual tokens moving in an infrastructure net, while passenger quantities are given as vectors - whose components correspond to trip profiles - and evolve at stations according to fluid dynamics. This model is intended as a building block for obtaining supervisory control, via transport operator actions, to mitigate congestion.