An algorithm for the equilibrium assignment problem with random link times

In this article we offer an equivalent minimization formulation for the traffic assignment problem when the link travel times are flow-dependent random variables. The paper shows the equivalency between the first-order conditions of this program and the stochastic equilibrium conditions as well as the uniqueness of the solution. The paper also describes an algorithmic approach to the solution of this program, including a proof of convergence. Finally, we conduct some limited numerical experiments on the rate of convergence of the algorithm and the merits of the stochastic equilibrium model, in general, as compared with deterministic approaches.

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