General stochastic user equilibrium traffic assignment problem with link capacity constraints

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.