In this study, a new SUE model using the Weibull random error terms is proposed as an alternative to overcome the drawbacks of the multinomial logit (MNL) SUE model. A path-size weibit (PSW) model is developed to relax both independently and identically distributed assumptions, while retaining an analytical closed-form solution. Specifically, this route choice model handles route overlapping through the path-size factor and captures the route-specific perception variance through the Weibull distributed random error terms. Both constrained entropy-type and unconstrained equivalent MP formulations for the PSW-SUE are provided. In addition, model extensions to consider the demand elasticity and combined travel choice of the PSW-SUE model are also provided. Unlike the logit-based model, these model extensions incorporate the logarithmic expected perceived travel cost as the network level of service to determine the demand elasticity and travel choice. Qualitative properties of these minimization programs are given to establish equivalency and uniqueness conditions. Both path-based and link-based algorithms are developed for solving the proposed MP formulations. Numerical examples show that the proposed models can produce a compatible traffic flow pattern compared to the multinomial probit (MNP) SUE model, and these models can be implemented in a real-world transportation network.

Stochastic User Equilibrium (SUE) models allow the representation of the perceptual and preferential differences that exist when drivers compare alternative routes through a transportation network. However, as an effect of the used choice models, conventional applications of SUE are based on the assumption that all available routes have a positive probability of being chosen, however unattractive. In this paper, a novel choice model, the Bounded Choice Model (BCM), is presented along with network conditions for a corresponding Bounded SUE. The model integrates an exogenously-defined bound on the random utility of the set of paths that are used at equilibrium, within a Random Utility Theory (RUT) framework. The model predicts which routes are used and unused (the choice sets are equilibrated), while still ensuring that the distribution of flows on used routes accords to a Discrete Choice Model. Importantly, conditions to guarantee existence and uniqueness of the Bounded SUE are shown. Also, a corresponding solution algorithm is proposed and numerical results are reported by applying this to the Sioux Falls network.

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