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An N-path UE with recourse for traffic assignment

Traffic assignment plays an essential role in transportation planning because it offers methods to predict the flow allocation on paths and evaluating the performance of traffic network. The conventional user equilibrium(UE) makes sure that no road user will change routing choices unilaterally due to the risk of more loss. In this paper, we consider more complicated but practical scenario which is that not only each road user has a limited choice set N to choose when going through the network, but they can access to information provision when traversing. Under this new condition, we can get a novel equilibrium named N-path user equilibrium with recourse, short for NPUER. A new mathematical formulation is proposed according this new scenario and the equivalence between the result of this formulation and NPUER as well as the existence of the equilibrium are all showed in this paper. In order to solve the formulation, we use techniques of conventional convex programming to deal with this problem and invent an algorithm from Frank-Wolfe algorithm to apply to an example which achieves an interesting but inspiring result that more freedom may bring an unexpected consequence.