Entropy maximization in multi-class traffic assignment

Qianni Wang, Liyang Feng, Jiayang Li, Jun Xie and Nie, Yu (Marco)

Transportation Research Part B: Methodological, 2025, vol. 192, issue C

Abstract: Entropy maximization is a standard approach to consistently selecting a unique class-specific solution for multi-class traffic assignment. Here, we show the conventional maximum entropy formulation fails to strictly observe the multi-class bi-criteria user equilibrium condition, because a class-specific solution matching the total equilibrium link flow may violate the equilibrium condition. We propose to fix the problem by requiring the class-specific solution, in addition to matching the total equilibrium link flow, also match the objective function value at the equilibrium. This leads to a new formulation that is solved using an exact algorithm based on dualizing the hard, equilibrium-related constraints. Our numerical experiments highlight the superior stability of the maximum entropy solution, in that it is affected by a perturbation in inputs much less than an untreated benchmark multi-class assignment solution. In addition to instability, the benchmark solution also exhibits varying degrees of arbitrariness, potentially rendering it unsuitable for assessing distributional effects across different groups, a capability crucial in applications concerning vertical equity and environmental justice. The proposed formulation and algorithm offer a practical remedy for these shortcomings.

Keywords: Multi-class traffic assignment; Entropy maximization; Stability; Equity (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.trb.2024.103136

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