Markovian traffic equilibrium

Jean-Bernard Baillon (1) , Roberto Cominetti (2)

1 Marin Mersenne - Pour les Mathématiques, l'Informatique et l'Interdisciplinarité
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

We analyse an equilibrium model for traffic networks based on stochastic dynamic programming. In this model passengers move towards their destinatios by a sequential process of arc selection based on a discrete choice model at every intermediaete node in their trip. Route selection is the outcome of this sequential process while network flows correspond to the invariant measures of the underlying Markov chains. The approach may handle different discrete choice models at every node, including the possibility of mixing deterministic and stochastic distribution rules. It can also be used over a multimodal network in order to model the simultaneous selection of mode and route, as well as to treat the case of elastic demands. We establish the existence of a unique equilibrium. We report some numerical experiences comparing different methods.

Mots clés: Traffic Equilibrium; stochastic assignment; variational formulation; numerical computation

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Jean-Bernard Baillon, Roberto Cominetti. Markovian traffic equilibrium. Mathematical Programming, 2008, 111 (1-2), pp.33-56. ⟨hal-00446468⟩