A stochastic jump process applied to traffic flow modelling

摘要

The paper presents the main aspects of a stochastic conservative model of the evolution of the number of vehicles per road section. The model, defined in continuous time on a discrete space, follows a misanthrope Markovian process. It is a mesoscopic traffic model in the following sense: the vehicles are individually considered, but their dynamics are aggregated per section. The model parameters are supply and demand functions in equilibrium (i.e. a fundamental diagram). In order to model flows on a traffic network, different schemes of junction dynamics are proposed. The model properties in transient and stationary states are investigated analytically in simple cases and by simulation. The results show that the process presents classical properties of deterministic macroscopic model such as the propagation of shock or rarefaction wave for Riemann initial condition. On the other hand, one observes phenomena usually related to high order models, such as a wide scattering of the flow performances or the propagation (backward or forward according to the density level) of local perturbations, due to the stochasticity.