A fuzzy network assignment model based on user equilibrium condition

In this paper, a new trac assignment model is proposed based on fuzzy equilibrium condition where perceived travel times of users are assumed to follow fuzzy values. First, a new method is proposed to determine the membership function based on link congestion levels using probabilistic models. Then, a new index is presented based on percentage of usersʹ risk-acceptance for comparison of fuzzy numbers. Using this index, two approaches, fuzzy Dijkestra shortest path algorithm and defuzzication method, are established for solving the shortest path problem. Fuzzy equilibrium condition is dened based on the two proposed fuzzy shortest path methods, and a trac assignment model is developed with consideration of fuzzy equivalency equilibrium condition. Frank-Wolfe algorithm and fuzzy shortest path method are combined to solve the proposed trac assignment problem. The assignment model is applied to a small and medium-sized network. Sensitivity analysis for link ows is performed under dierent levels of usersʹ risk-acceptance to understand the route choice of dierent types of users. To apply the model to a large-scale network, the network of Mashhad, Iran is considered as a case study. The fuzzy trac assignment model provides more accurate estimation of volume compared to conventional trac assignment.