Dynamic Tolling in Arc-based Traffic Assignment Models

TL;DR

This paper develops an arc-based traffic assignment model incorporating dynamic tolling, demonstrating convergence of adaptive toll updates to socially optimal congestion levels through theoretical proofs and empirical validation.

Contribution

It introduces an arc-based TAM with adaptive tolling, proving convergence to social optimality, addressing limitations of route-based models.

Findings

Marginal pricing achieves social optimality in arc-based TAMs.

Adaptive toll updates converge to near-optimal congestion levels.

Empirical results confirm theoretical convergence.

Abstract

Tolling in traffic networks offers a popular measure to minimize overall congestion. Existing toll designs primarily focus on congestion in route-based traffic assignment models (TAMs), in which travelers make a single route selection from their source to destination. However, these models do not reflect real-world traveler decisions because they preclude deviations from a chosen route, and because the enumeration of all routes is computationally expensive. To address these limitations, our work focuses on arc-based TAMs, in which travelers sequentially select individual arcs (or edges) on the network to reach their destination. We first demonstrate that marginal pricing, a tolling scheme commonly used in route-based TAMs, also achieves socially optimal congestion levels in our arc-based formulation. Then, we use perturbed best response dynamics to model the evolution of travelers' arc selection preferences over time, and a marginal pricing scheme to the social planner's adaptive toll updates in response. We prove that our adaptive learning and marginal pricing dynamics converge to a neighborhood of the socially optimal loads and tolls. We then present empirical results that verify our theoretical claims.