Q-Generalized Logit Route Choice an Network Equilibrium Model

Abstract

The multinomial logit model is expressed as a closed-form equation, and plays an important role in the field of tra sportation. The Gumbel-distributed utility in the multinomial logit model is restrictive in certain applications, especially in ro te choice behavior and network equilibrium analysis, although it is mathematically convenient. The range of variation of utility in the logit model is unbounded. The Gumbel distribution is left-skewed and has a very thi tail to the left. In additionFor example, the utility in the multinomial logit has a the homogeneity of homosce astic variance. In this study, the multinomial logit model is extended by generalizing the Gumbel-distributed utility to allow heteroscedastic variance and flexible shape. Then, the generalized logit model with a generalized Gumbel distribution is incorporated into the transportation network equilibrium model. The network equilibrium model with a 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. In this study, the generalization of the Gumbel distribution, logit model, and network equilibrium model has a unified framework with q-analysis or Tsallis statistics.