Multi-user multi-mode stochastic user equilibrium model based on paired combinatorial Logit models

In a multi-user multi-mode transportation network,a stochastic user equilibrium is established based on a paired combinatorial Logit model,which overcomes the shortcoming of independent and identically distributed of Logit model,under the hypothesis that its paths selection satisfy Wardrop principle and its mode selection satisfy Logit models.Construct an equivalent mathematical programming problem to show the mixed equilibrium status,under the hypothesis that many categories of users exist in the network whose value of time are different and different modes have symmetry effects on each other.Then prove the equivalence of the mathematical programming problem and the equilibrium conditions and also the existence and uniqueness of the optimum solution.A simple illustration is last used to prove the correctness and feasibility of the model.