Stochastic User Equilibrium Traffic Assignment Problem with Tradable Credit Scheme: Model and Algorithm

Abstract

In this paper, the generalized stochastic user equilibrium (SUE) and credit market equilibrium (ME) conditions are firstly presented, and a novel equivalent linearly-constrained minimization model is established. Due to the specialty of the proposed model, the conventional solution algorithm, such as method of successive average (MSA) can’t be applied. In order to develop an efficient solution algorithm, the Lagrangian dual formulation of the proposed model is analyzed. The authors find that the Lagrangian dual formulation is a continuously differentiable concave maximization problem sharing the same optimal solution with the original model, and that its gradient can be obtained by invoking MSA. According to these two desirable properties, a convergent solution algorithm is developed, of which the outer iteration is implemented by using gradient projection method with a predetermined step size sequence while the inner iteration is implemented by using MSA. Finally, a numerical example is presented to illustrate the proposed model and algorithm.