Modelling highway-traffic headway distributions using superstatistics

TL;DR

This paper applies superstatistics to model highway traffic headway distributions, capturing the transition from free flow to congestion and fitting real-world data from Dutch and German freeways.

Contribution

It introduces an analytic model interpolating between Poisson and random matrix theory statistics for traffic headways, validated with empirical data.

Findings

The model accurately fits traffic gap data at various densities.

It captures the transition from free flow to congested traffic.

The approach links traffic flow phases with statistical distributions.

Abstract

We study traffic clearance distributions (i.e., the instantaneous gap between successive vehicles) and time headway distributions by applying Beck and Cohen's superstatistics. We model the transition from free phase to congested phase with the increase of vehicle density as a transition from the Poisson statistics to that of the random matrix theory. We derive an analytic expression for the spacing distributions that interpolates from the Poisson distribution and Wigner's surmise and apply it to the distributions of the nett distance and time gaps among the succeeding cars at different densities of traffic flow. The obtained distribution fits the experimental results for single-vehicle data of the Dutch freeway A9 and the German freeway A5.