Equilibrium distributions in thermodynamical traffic gas

TL;DR

This paper derives the exact equilibrium spacing distribution for a one-dimensional particle gas with a specific repulsive potential and compares it with real highway traffic data, supporting the application of statistical physics to traffic modeling.

Contribution

It provides an exact formula for the equilibrium spacing distribution in a thermodynamical traffic gas and validates it against empirical traffic data.

Findings

Derived the exact distribution formula for a specific potential

Compared theoretical distribution with highway traffic data

Supported the use of statistical physics in traffic modeling

Abstract

We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution (for a=1) is successfully compared with the highway-traffic clearance distributions, which provides a detailed view of changes in microscopical structure of traffic sample depending on traffic density. In addition to that, the observed correspondence is a strong support of studies applying the equilibrium statistical physics to traffic modelling.