Stochastic Traffic Distribution Model Based on Robust Optimization

Travelers always hope to arrive on time, but many uncertainties exist in traffic systems. Based on traffic characteristics, the uncertainties in supply are grouped into three categories: predictable uncertainty, expected uncertainty, and unexpected uncertainty. The stochastic chance-constraint model is used to deal with expected uncertainties, and robust optimization is used to build the model with unexpected uncertainties. The conception of robust chance-constraint travel time is proposed, and the equilibrium conditions are given. Then the multi-class variational inequality (VI) model based on robust optimization under stochastic supply is built. The existence of a solution to this VI problem and its equivalence to the robust chance-constraint traffic equilibrium condition are illustrated using numerical examples. The quasi method of successive average is proposed to solve the VI problem. A medium network is used to test the algorithm performance, and it shows that the algorithm can quickly converge to high accuracy.