MDTA: Markovian dynamic traffic assignment, a new approach for stochastic DTA

Abstract

This doctoral thesis focuses on a new modeling approach for dynamic traffic assignment. Considering the advances at present in aspects that in earlier stages of the study of traffic assignment were more restrictive, such as technology or data availability, the problem can be faced from a more realistic point of view by approaching the process of assignment from a dynamic perspective. In fact, a major feature of the Dynamic Traffic Assignment (DTA) concept is to recognize explicitly the evolution of the transport network status over a time period unlike the typical static models where such information is aggregated. On a different dimension, before getting interested in the dynamic version of the problem, researchers have devoted time and effort in representing another important aspect of the behavior of motorists traveling over a transport network, which is the uncertainty of their decisions when choosing how to proceed to their destinations. Thus, many works on traffic assignment and equilibrium have integrated the stochasticity as part of their formulations. The way to model that behavior has been at a route-choice level, considering that the route-choice criterion is based on the perceived costs by motorists of the routes from the origin to the destination. In this doctoral thesis, a novel approach that tackles the stochasticity in the context of DTA problems is proposed. The core contribution of this work is the Markovian Dynamic Traffic Assignment (MDTA) model, developed first for the multiple origins and a single destination general case, which is later extended to general transport networks. The basis of the presented results is the integration of the concept of the Markovian Traffic Equilibrium proposed by Baillon and Cominetti, for the case of an assignment performed by a logit model for the static case, and the developments on DTA modelling proposed by Addison and Heydecker. The proposed approach is arc-based unlike the typical route-based formulations generally found in the specialized literature. The nested structure of the costs in the resulting formulation is a relevant feature of this approach, in which motorists make their route choice decisions dynamically, according to the perceived costs of the remaining portion of the trip, namely, from their current node to their final destination. The MDTA model has as a key feature that, given its arc-based choice model, it allows working with overlapping routes with no assumptions of independence of their costs and, thus, it does not require the enumeration of the many transport network routes.