Stochastic User-Equilibrium Formulations for Extended-Logit Assignment Models

Abstract

New stochastic user-equilibrium formulations are presented. In the transportation literature, the “logit assignment” stands for a stochastic user-equilibrium model in which the multinomial logit is the route-choice model. Efficient algorithms using this mathematical formulation were proposed to solve the logit assignment. However, the use of the logit function for route choice has some theoretical drawbacks. In typical transportation networks, many routes have common links, and the structure of the model is not able to account for these common links because the probability for choosing a route is computed based solely on the total route cost. Recently, extended logit-based models were proposed to overcome the overlapping problem and keep the analytical tractability of the logit function. It is demonstrated how extended logit models—such as the Cross-Nested Logit and the Paired Combinatorial Logit—can be derived from more general entropy-type formulations, thus allowing the use of existing (and yet under development) algorithmic solutions for the more general logit-family stochastic assignment model.