Abstract

In the context of dynamic traffic assignment (DTA) applications, it seems relevant to consider the uncertainty inherent to motorist route choices as part of the proposed DTA formulations. In particular, the choices made by motorists on realistic transport networks are mostly based on the perceived costs of all routes from their origins to their destinations. In this work, we present an approach to address stochasticity in a DTA context based on nested cost operators, where motorists choose their route taking into account the perceived costs of the remaining part of the trip, namely, from their current node to their final destination, resulting in an arc-based choice model instead of a route-based one. We integrate the concept of Markovian traffic equilibrium proposed by Baillon and Cominetti with the DTA formulation developments proposed by Addison and Heydecker. In this paper, we present what we call the Markovian dynamic traffic assignment (MDTA) model for general transport networks, which is a stochastic DTA model that allows working with overlapping routes with no assumptions of independence of their costs. We also develop an efficient solution method, called the MDTA algorithm, that solves the MDTA problem over discrete time. We show computational results of the model and the application of the algorithm to an illustrative network, showing sensitivity analyses with respect to the relevant parameters of the model.