Decoupling Passenger Flows for Improved Load Prediction

Stefan Haar (1, 2) , Simon Theissing (2, 1)

1 MEXICO - Modeling and Exploitation of Interaction and Concurrency
2 LSV - Laboratoire Spécification et Vérification [Cachan]

We elaborate the approximate computation of a stochastic hybrid automaton (SHA) model, which we have developed for the analysis of perturbations in modern multi-modal transportation networks (TNs); where passengers spread the perturbations between the different modes and lines through transfers. In particular, we focus on one major bottleneck, which may arise in the approximate computation of the SHA model: the high-dimensionality of all stochastic differential equations (SDEs). They define how all considered fluid passenger loads evolve in time in a particular mode of the SHA model, which latter might exhibit jumps between its different modes only at equidistantly-spaced discrete points in time. In this context, we replace all high-dimensional SDEs set up for a particular mode of the SHA model by a set of lower-dimensional SDEs; in that we decouple all passenger flows in a mode. We proof that the resulting approximating dynamics converges to the original model dynamics if the fixed time interval between two jump layers of the SHA model approaches zero.

Mots clés: Stochastic Hybrid Automata; Transportation Networks; Fluid Petri Nets; Stochastic Differential Equations Modelling

Domaines: Modélisation et simulation

Stefan Haar, Simon Theissing. Decoupling Passenger Flows for Improved Load Prediction. 2016. ⟨hal-01294498⟩