Theoretical predictions for vehicular headways and their clusters

TL;DR

This paper derives analytical predictions for steady-state vehicle headway distributions in traffic clusters using a socio-physical model, validating them with empirical data and discussing implications for three-phase traffic theory.

Contribution

It provides a novel analytical framework for predicting vehicle headway distributions in traffic clusters based on a socio-physical model, validated by empirical data.

Findings

Analytical formulas for time-clearance distributions derived.

Theoretical predictions match empirical traffic data.

Discussion of results within three-phase traffic theory.

Abstract

This article presents a derivation of analytical predictions for steady-state distributions of netto time gaps among clusters of vehicles moving inside a traffic stream. Using the thermodynamic socio-physical traffic model with short-ranged repulsion between particles (originally introduced in [Physica A \textbf{333} (2004) 370]) we firstly derive the time-clearance distribution in the model. Consecutively, the statistical distributions for the so-called time multi-clearances are calculated by means of theory of functional convolutions. Moreover, all the theoretical surmises used during the above-mentioned calculations are proven by the statistical analysis of traffic data. The mathematical predictions acquired in this paper are thoroughly compared with relevant empirical quantities and discussed in the context of three-phase traffic theory.