Stochastic User Equilibrium Formulation for Generalized Nested Logit Model

Abstract

The route choice problem is complicated in typical transportation networks because of the size of the choice set and because of the overlapping problem since many routes share links. Well-known models like the probit and the logit were further developed in an attempt to overcome these problems. The logit model has the appeal of being relatively close to the probit model while keeping a convenient analytical closed form. However, the simple multinomial logit model cannot correctly represent route choice, especially with respect to the overlapping problem. Other hierarchical logit models can potentially overcome the overlapping problem. The recently developed generalized nested logit (GNL) model is found to be very suitable for route choice, as is the cross-nested logit (CNL) model. The inclusion of the congestion effect in the route choice problem is accounted for in stochastic user equilibrium (SUE) problems. The development of a SUE formulation for the GNL model is presented. In addition, how to adapt the GNL model to route choice in a way similar to that of the CNL model is shown. An equivalent SUE formulation for the GNL model is developed. In this way, a unified framework is presented to relate GNL-type models, which are derived from discrete choice theory, with aggregate entropy formulations. A preliminary algorithm is developed to illustrate the potential application of the GNL formulation for real networks.