A fresh look at symmetric traffic assignment and algorithm convergence

TL;DR

This paper re-examines static traffic assignment with symmetric link interactions, showing that equilibrium exists uniquely, algorithms converge efficiently, and symmetric models can approximate asymmetric ones, encouraging further research.

Contribution

It demonstrates that symmetric, monotone link interactions ensure existence, uniqueness, and convergence of equilibrium, and shows how efficient algorithms can be adapted for these models.

Findings

Equilibrium exists and is unique under symmetric, monotone link interactions.

Algorithms for separable traffic assignment can be applied with symmetric interactions.

Convergence to equilibrium is faster with symmetric, monotone link interactions.

Abstract

Extensions of the static traffic assignment problem with link interactions were studied extensively in the past. Much of the network modeling community has since shifted to dynamic traffic assignment incorporating these interactions. We believe there are several reasons to re-examine static assignment with link interactions. First, if link interactions can be captured in a symmetric, monotone manner, equilibrium always exists and is unique, and provably-correct algorithms exist. We show that several of the most efficient algorithms for the separable traffic assignment problem can be readily applied with symmetric interactions. We discuss how the (asymmetric) Daganzo merge model can be approximated by symmetric linear cost functions. Second, we present computational evidence suggesting that convergence to equilibrium is faster when symmetric, monotone link interactions are present. This is true even when interactions are asymmetric, despite the lack of a provable convergence result. Lastly, we present convergence behavior analysis for commonly used network and link metrics. For these reasons, we think static assignment with link interactions deserves additional attention in research and practice.