Theoretical predictions for vehicular headways and their clusters

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.

23 pages, 10 figures

References in corpus (8)

• Brownian distance covariance
• Modelling highway-traffic headway distributions using superstatistics
• Approximate Hamiltonian Statistics in One-dimensional Driven Dissipative Many-Particle Systems
• Combined D0 Measurements Constraining the CP-violating Phase and Width Difference in the $B_s^0$ System
• Equilibrium distributions in thermodynamical traffic gas
• Inter-vehicle gap statistics on signal-controlled crossroads
• Inter-particle gap distribution and spectral rigidity of totally asymmetric simple exclusion process with open boundaries
• Statistical mechanics of non-hamiltonian systems: Traffic flow

Cited by in corpus (5)

• Empirical Study of Traffic Velocity Distribution and its Effect on VANETs Connectivity
• Vehicular headways on signalized intersections: theory, models, and reality
• Inner structure of vehicular ensembles and random matrix theory
• Time-headway distribution for periodic totally asymmetric exclusion process with various updates
• 3s-Unification for Vehicular Headway Modeling