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

In this paper, we deal with the analysis of the solutions of traffic flow models at multiple scales in both cases of a single road and 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.