Perturbed utility Markovian traffic equilibrium: theory and computation

2026-07-10

AI Summary

This study addresses the challenge of reconciling behavioral realism with computational scalability in large-scale traffic assignment models. The authors propose the Perturbed Utility Markov Equilibrium (PUME) framework, which defines a Bellman optimality operator via a convex surplus function and expresses the optimal policy as its gradient. This formulation unifies the treatment of boundary and interior path choice probabilities and characterizes equilibrium through a variational inequality. By moving beyond traditional additive random utility models, PUME naturally generates zero-flow paths without requiring a predefined choice set and accommodates nonseparable, asymmetric cost structures. Coupled with a modified policy iteration scheme and a safeguarded accelerated meta-algorithm, the method achieves global convergence and demonstrates high scalability and robustness across diverse demand-supply scenarios on both benchmark and synthetic networks.

Abstract

Large-scale traffic assignment requires equilibrium models that are both behaviorally plausible and computationally tractable. This paper develops a perturbed utility Markovian equilibrium (PUME) framework that preserves the scalability of link-based Markovian traffic equilibrium models and extends their applicability to settings with boundary choice probabilities, undiscounted network loading, and general link interactions. As the behavioral basis of PUME, we first develop the perturbed utility Markovian choice model (PUMCM) in which the Bellman optimality operator is defined through a convex surplus function whose gradient directly yields the optimal policy. The model generalizes existing additive random utility (ARUM) Markovian choice models and admits both interior and boundary choice probabilities. Accordingly, unattractive links can receive zero flow without imposing ex ante choice-set restrictions as in existing ARUM models. We establish conditions under which the corresponding Markov decision problem is well posed and yields a proper demand mapping. We then formulate the equilibrium as a variational inequality (VI) problem on the dual cost space and establish its existence and uniqueness. Particularly, the VI formulation of PUME accommodates non-separable and asymmetric cost structures and thus offers a more flexible modeling framework than existing Markovian traffic equilibrium (MTE) models. For computation, we develop a modified policy iteration method for network loading and a safeguarded accelerated meta-algorithm for computing equilibrium. Both algorithms are proven to be globally convergent and have demonstrated satisfactory numerical performances. Experiments on benchmark and synthetic networks further show that the proposed framework is highly scalable and robust towards a wide variety of demand-supply settings.

Problem

• traffic equilibrium
• Markovian choice model
• perturbed utility
• large-scale assignment
• behavioral plausibility

Innovation

• perturbed utility
• Markovian traffic equilibrium
• variational inequality
• convex surplus function
• non-separable costs