A Unified Closed-form Expression of Logit and Weibit and its Application to a Transportation Network Equilibrium Assignment

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