Non-expected Route Choice Model under Risk on Stochastic Traffic Networks

Abstract In this paper, we propose a novel non-expected route travel time (NERTT) model, which belong to the rank-dependent expected utility model. The NERTT consists of two parts, which are the route travel time distribution and the distortion function. With the strictly increasing and strictly concave distortion function, we can prove that the route travel time in the proposed model is risk-averse, which is the main focus of this paper. We show two different reduction methods from the NERTT model to the travel time budget model and mean-excess travel time model. One method is based on the properly selected distortion functions and the other one is based on a general distortion function. Besides, the behavioral inconsistency of the expected utility model in the route choice can be overcome with the proposed model. The NERTT model can also be generalized to the non-expected disutility (NED) model, and some relationship between the NED model and the route choice model based on the cumulative prospect theory can be shown. This indicates that the proposed model has some generality. Finally, we develop a non-expected risk-averse user equilibrium model and formulate it as a variational inequality (VI) problem. A heuristic gradient projection algorithm with column generation is used to solve the VI. The proposed model and algorithm are tested on some hypothetical traffic networks and on some large-scale traffic networks.