Robust Wardrop’s user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach

Various models of traffic assignment under stochastic environment have been proposed recently, mainly by assuming different travelers’ behavior against uncertainties. This paper focuses on the expected residual minimization (ERM) model to provide a robust traffic assignment with an emphasis on the planner’s perspective. The model is further extended to obtain a stochastic prediction of the traffic volumes by the technique of path choice approach. We show theoretically the existence and the robustness of the ERM solution. In addition, we employ an improved solution algorithm for solving the ERM model. Numerical experiments are carried out to illustrate the characteristics of the proposed model, by comparing with other existing models.

Research highlights
► The paper proposes an equilibrium traffic assignment formulation for providing a robust prediction of future traffic volume against uncertain future demand and supply. The model is formulated as an expected residue minimization (ERM) problem.
► The paper shows that under a mild condition the ERM model will provide a robust prediction of traffic volume as well as robust project evaluation (assuming that the project evaluation function a globally Lipschitz continuous function).
► The test results show that the proposed smoothing projected gradient (SPG) algorithm for solving the ERM model is applicable to a medium sized network.