Mean-Risk Traffic Assignment Under the Continuously Distributed Risk-Aversion Factor

This study generalizes the single-class traffic assignment problem of Nikolova and Stier-Moses [Nikolova and Stier-Moses (2014) A mean-risk model for the traffic assignment problem with stochastic travel times. Oper. Res. 62(2):366–382] by considering the continuously distributed risk-aversion factor, termed the continuous mean-risk traffic assignment (CMRTA) problem. In CMRTA, travelers categorized into infinitely many user classes play a congestion routing game based on their risk attitude toward the mean–standard deviation trade-off. We identify and verify the following finite-dimensional complementarity condition: All used paths must have an equal and minimum “virtual” cost, called the cumulative path cost, which enables the characterization of Wardrop’s equilibrium for CMRTA. Based on this result, we present general formulations to model CMRTA problems with exogenous and endogenous variability sources. A tailored path-based column generation with the gradient projection algorithm is then proposed to solve large-scale problems. The results show that CMRTA is more computationally efficient and less memory intensive than the traditional discrete multiclass method.

Funding: This research was supported by the National Natural Science Foundation of China [Grants 72201220, 72571224, 52232011], the Sichuan Science and Technology Program [Grant 2025HJPJ0011], and the Research Grants Council of the Hong Kong Special Administrative Region [PolyU 15218325].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1027.