Multiclass fuzzy user equilibrium with endogenous membership functions and risk-taking behaviors

Over the last decades, several approaches have been proposed in the literature to incorporate users' perceptions of travel costs, their bounded rationality, and risk-taking behaviors into network equilibrium modeling for traffic assignment problem. While theoretically advanced, these models often suffer from high complexity and computational cost and often involve parameters that are difficult to estimate. This study proposes an alternative approach where users' imprecise perceptions of travel times are endogenously constructed as fuzzy sets based on the probability distributions of random link travel times. Two decision rules are proposed accordingly to account for users' heterogeneous risk-taking behaviors, that is, optimistic and pessimistic rules. The proposed approach, namely, the multiclass fuzzy user equilibrium, can be formulated as a link-based variational inequality model. The model can be solved efficiently, and parameters involved can be either easily estimated or treated as factors for calibration against observed traffic flow data. Numerical examples show that the proposed model can be solved efficiently even for a large-scale network of Mashhad, Iran, with 2538 links and 7157 origin–destination pairs. The example also illustrates the calibration capability of the proposed model, highlighting that the model is able to produce much more accurate flow estimates compared with the Wardropian user equilibrium model.