Comparing comparisons between vehicular traffic states in microscopic and macroscopic first-order models

TL;DR

This paper analyzes how traffic state distances, modeled at microscopic and macroscopic scales, compare and are preserved across scales, revealing Wasserstein distance's effectiveness on single roads but limitations on networks.

Contribution

It demonstrates the scale-invariance of Wasserstein distance for traffic states on single roads and explores its limitations in network contexts through theoretical and numerical methods.

Findings

Wasserstein distance captures human perception of traffic state differences on single roads.

On networks, Wasserstein distance partially loses its scale-preserving properties.

The study combines theoretical analysis with numerical experiments.

Abstract

In this paper we deal with the analysis of the solutions of traffic flow models at multiple scales, both in the case of a single road and of road networks. We are especially interested in measuring the distance between traffic states (as they result from the mathematical modeling) and investigating whether these distances are somehow preserved passing from the microscopic to the macroscopic scale. By means of both theoretical and numerical investigations, we show that, on a single road, the notion of Wasserstein distance fully catches the human perception of distance independently of the scale, while in the case of networks it partially loses its nice properties.