A Lagrangian-Based Approach for Reliable User Equilibrium Considering Link Travel Time Variance

The classical user equilibrium problem is to achieve a state that no traveler can improve his/her travel time by unilaterally changing routes. One of the most important assumptions of the travel behaviors in user equilibrium is that travelers will choose the shortest path. However, in a realistic transport network, the link travel cost is not always a constant, but a mean value with a corresponding standard deviation, resulting in a novel reliable user equilibrium problem. In this problem, the auxiliary variable in the convex combinations method for solving user equilibrium problem should be obtained by finding the reliable shortest path instead of all-or-nothing assignment. The most reliable path algorithm can avoid the neglect to stability of path travel time by including the variance that cannot be avoided by all-or-nothing assignment. The proposed algorithms are evaluated under Sioux-Falls-Network.