Inner structure of vehicular ensembles and random matrix theory

TL;DR

This paper demonstrates that traffic flow systems exhibit spectral statistics similar to those of certain random matrix ensembles, suggesting a universal behavior that extends to vehicular ensembles.

Contribution

It introduces a new class of random matrices (DUE) that model the microscopical statistics of vehicular flows, linking traffic data to random matrix theory.

Findings

Spectral statistics of DUE matrices match traffic flow data.

Traffic systems show universality with classical random matrix ensembles.

Traffic data exhibits level spacing distributions similar to RMT predictions.

Abstract

We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.