Formulations of extended logit stochastic user equilibrium assignments

In the transportation literature, the "logit assignment" stands for a stochastic user equilibrium model in which the multinomial legit is the route choice model. Efficient algorithms using this mathematical formulation were proposed to solve the legit assignment. However, the use of the legit function for route choice has some theoretical drawbacks. Recently, extended legit-base models were proposed to overcome the overlapping problem, while keeping the analytical tractability of the legit function. The purpose of this paper is to present new stochastic user equilibrium formulations. The paper shows how two extended legit models - such as the Cross-Nested Legit and the Paired Combinatorial Legit, can be derived from more general entropy-type formulations, and thus allowing the use of existing land yet under development) algorithmic solutions for the more general legit-family stochastic assignment model. The paper also shows how the general stochastic user equilibrium formulation can be adapted for the new route choice models.