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Register a new userTheoretical predictions for vehicular headways and their clusters
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Added by
Milan Krbalek Ph.D.
Publication date
2012
fields
Physics
and research's language is
English
Authors
Milan Krbalek
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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.
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This article mediates an mathematical insight to the theory of vehicular headways measured on signalized crossroads. Considering both, mathematical and empirical substances of the socio-physical system studied, we firstly formulate several theoretical and empirically-inspired criteria for acceptability of theoretical headway-distributions. Sequentially, the multifarious families of statistical distributions (commonly used to fit real-road headway statistics) are confronted with these criteria, and with original experimental time-clearances gauged among neighboring vehicles leaving signal-controlled crossroads after a green signal appears. Another goal of this paper is, however, to decide (by means of three completely different numerical schemes) on the origin of statistical distributions recorded by stop-line-detectors. Specifically, we intend to examine whether an arrangement of vehicles is a consequence of traffic rules, drivers estimation-processes, and decision-making procedures or, on contrary, if it is a consequence of general stochastic nature of queueing systems.
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