A Fuzzy Network Assignment Model Based on User Equilibrium Condition

In this paper, a new traffic 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 membership function based on link congestion levels using probabilistic models. Then, a new index is presented based on percentage of users’ risk-acceptance for comparison of fuzzy numbers. Using this index, two approaches, fuzzy Dijkestra shortest path algorithm and defuzzification method, are established for solving shortest path problem. Fuzzy equilibrium condition is defined based on the two proposed fuzzy shortest path methods and a traffic 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 traffic assignment problem. The assignment model is applied to a small and medium-sized network. Sensitivity analysis for link flows is performed under different levels of users’ risk-acceptance to understand the route choice of different 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 traffic assignment model provides more accurate estimation of volume compared to conventional traffic assignment.