On Route Choice Models with Closed-Form Probability Expressions

In this paper, the authors analyze route choice models with closed-form probability expressions. Route utility is correlated and heteroscedastic by nature, which can be captured using Multivariate Extreme Value (MEV) distributions and Generalized Extreme Value (GEV) distributions. The authors show that all existing models fit in the MEV or GEV class; especially, they show that Path-Size Logit-like models are equivalent to MEV models. The MEV models can be based on either additive or multiplicative utility formulations. Three new MEV models based on the multiplicative formulation are described. Furthermore, a formulation is proposed in which the overlap between routes is explicitly removed; this leads to another four new MEV models. These models perform well if the differences as well as the ratios between routes in different route sets change; this is achieved without adding parameters and retaining closed-form probability expressions. The authors compare all models using a small hypothetical network with strongly different route sets, and show that the newly proposed models outperform existing ones.