Spectral rigidity of vehicular streams (Random Matrix Theory approach)

TL;DR

This paper applies Random Matrix Theory to analyze the spectral rigidity of vehicular streams, deriving an exact formula for number variance and comparing it with real traffic data to understand driver mental strain.

Contribution

It introduces a novel application of Random Matrix Theory to traffic flow analysis, deriving an exact formula for particle ensemble rigidity and linking it to driver mental strain.

Findings

Derived an exact formula for number variance in vehicular streams

Identified a correlation between inverse temperature and traffic conditions

Compared theoretical predictions with real traffic data from Dutch freeway A9

Abstract

Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is consequently compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of an inverse temperature, which can be identified as a coefficient of a mental strain of car drivers, is then discussed in detail with the respect to the traffic density and flow.