The α-reliable mean-excess traffic equilibrium model with stochastic travel times

In this paper, we propose a new model called the α-reliable mean-excess traffic equilibrium (METE) model that explicitly considers both reliability and unreliability aspects of travel time variability in the route choice decision process. In contrast to the travel time budget (TTB) models that consider only the reliability aspect defined by TTB, this new model hypothesizes that travelers are willing to minimize their mean-excess travel times (METT) defined as the conditional expectation of travel times beyond the TTB. As a route choice criterion, METT can be regarded as a combination of the buffer time measure that ensures the reliability aspect of on-time arrival at a confidence level αα, and the tardy time measure that represents the unreliability aspect of encountering worst travel times beyond the acceptable travel time allowed by TTB in the distribution tail of 1 − αα. It addresses both questions of “how much time do I need to allow?” and “how bad should I expect from the worse cases?” Therefore, travelers’ route choice behavior can be considered in a more accurate and complete manner in a network equilibrium framework to reflect their risk preferences under an uncertain environment. The METE model is formulated as a variational inequality problem and solved by a route-based traffic assignment algorithm via the self-adaptive alternating direction method. Some qualitative properties of the model are rigorously proved. Illustrative examples are also presented to demonstrate the characteristics of the model as well as its differences compared to the recently proposed travel time budget models.