A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem

Jiayang Li (), Qianni Wang (), Liyang Feng (), Jun Xie () and Yu (Marco) Nie ()
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Jiayang Li: Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208
Qianni Wang: Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208
Liyang Feng: School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756, China
Jun Xie: School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756, China
Yu (Marco) Nie: Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208;

Transportation Science, 2024, vol. 58, issue 6, 1193-1213

Abstract: The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution, is often used to address the challenge. Built on a recently proposed day-to-day discrete-time dynamical model called cumulative logit (CumLog), this study provides a new behavioral underpinning for the maximum-entropy user equilibrium (MEUE) route flow. It has been proven that CumLog can reach a UE state without presuming that travelers are perfectly rational. Here, we further establish that CumLog always converges to the MEUE route flow if (i) travelers have no prior information about routes and thus, are forced to give all routes an equal initial choice probability or if (ii) all travelers gather information from the same source such that the general proportionality condition is satisfied. Thus, CumLog may be used as a practical solution algorithm for the MEUE problem. To put this idea into practice, we propose to eliminate the route enumeration requirement of the original CumLog model through an iterative route discovery scheme. We also examine the discrete-time versions of four popular continuous-time dynamical models and compare them with CumLog. The analysis shows that the replicator dynamic is the only one that has the potential to reach the MEUE solution with some regularity. The analytical results are confirmed through numerical experiments.

Keywords: maximum entropy; traffic assignment; cumulative logit; day-to-day dynamical model; proportionality condition (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:58:y:2024:i:6:p:1193-1213

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