Modeling travel time uncertainty in traffic networks

Abstract

Uncertainty in travel time is one of the key factors that could allow us to understand and manage congestion in transportation networks. Models that incorporate uncertainty in travel time need to specify two mechanisms: the mechanism through which travel time uncertainty is generated and the mechanism through which travel time uncertainty influences users' behavior. Existing traffic equilibrium models are not sufficient in capturing these two mechanisms in an integrated way. This thesis proposes a new stochastic traffic equilibrium model that incorporates travel time uncertainty in an integrated manner. We focus on how uncertainty in travel time induces uncertainty in the traffic flow and vice versa. Travelers independently make probabilistic path choice decisions, inducing stochastic traffic flows in the network, which in turn result in uncertain travel times. Our model, based on the distribution of the travel time, uses the mean-variance approach in order to evaluate travelers' travel times and subsequently induce a stochastic traffic equilibrium flow pattern. In this thesis, we also examine when the new model we present has a solution as well as when the solution is unique. We discuss algorithms for solving this new model, and compare the model with existing traffic equilibrium models in the literature. We find that existing models tend to overestimate traffic flows on links with high travel time variance-to-mean ratios. To benchmark the various traffic network equilibrium models in the literature relative to the model we introduce, we investigate the total system cost, namely the total travel time in the network, for all these models. We prove three bounds that allow us to compare the system cost for the new model relative to existing models. We discuss the tightness of these bounds but also test them through numerical experimentation on test networks.