Unified closed-form expression of logit and weibit and its extension to a transportation network equilibrium assignment

•A unified closed-form expression of logit and weibit with the GEV distributed utility.•Heteroscedastic variance and flexible utility function are allowed in the model.•Traffic assignment with the generalized (or unified) logit model is formulated.•The above formulation includes the generalized entropy (Tsallis entropy) term.•The utilities, route choice, and assignment are generalized in Tsallis statistics.

This study proposes a generalized multinomial logit model that allows heteroscedastic variance and flexible utility function shape. The novelty of our approach is that the model is theoretically derived by applying a generalized extreme-value distribution to the random component of utility, while retaining its closed-form expression. In addition, the weibit model, in which the random utility is assumed to follow the Weibull distribution, is a special case of the proposed model. This is achieved by utilizing the q-generalization method developed in Tsallis statistics. Then, our generalized logit model is incorporated into a transportation network equilibrium model. The network equilibrium model with a generalized logit route choice is formulated as an optimization problem for uncongested networks. The objective function includes Tsallis entropy, a type of generalized entropy. The generalization of the Gumbel and Weibull distributions, logit and weibit models, and network equilibrium model are formulated within a unified framework with q-generalization or Tsallis statistics.