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A superstatistical model of vehicular traffic flow

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  • Kosun, Caglar
  • Ozdemir, Serhan

Abstract

In the analysis of vehicular traffic flow, a myriad of techniques have been implemented. In this study, superstatistics is used in modeling the traffic flow on a highway segment. Traffic variables such as vehicular speeds, volume, and headway were collected for three days. For the superstatistical approach, at least two distinct time scales must exist, so that a superposition of nonequilibrium systems assumption could hold. When the slow dynamics of the vehicle speeds exhibit a Gaussian distribution in between the fluctuations of the system at large, one speaks of a relaxation to a local equilibrium. These Gaussian distributions are found with corresponding standard deviations 1/β. This translates into a series of fluctuating beta values, hence the statistics of statistics, superstatistics. The traffic flow model has generated an inverse temperature parameter (beta) distribution as well as the speed distribution. This beta distribution has shown that the fluctuations in beta are distributed with respect to a chi-square distribution. It must be mentioned that two distinct Tsallis q values are specified: one is time-dependent and the other is independent. A ramification of these q values is that the highway segment and the traffic flow generate separate characteristics. This highway segment in question is not only nonadditive in nature, but a nonequilibrium driven system, with frequent relaxations to a Gaussian.

Suggested Citation

  • Kosun, Caglar & Ozdemir, Serhan, 2016. "A superstatistical model of vehicular traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 466-475.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:466-475
    DOI: 10.1016/j.physa.2015.10.042
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    References listed on IDEAS

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    Cited by:

    1. Ewin Sánchez & Manuel González-Navarrete & Christian Caamaño-Carrillo, 2021. "Bivariate superstatistics: an application to statistical plasma physics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(2), pages 1-7, February.
    2. Umpierrez, Haridas & Davis, Sergio, 2021. "Fluctuation theorems in q-canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    3. Kosun, Caglar & Ozdemir, Serhan, 2017. "Determining the complexity of multi-component conformal systems: A platoon-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 688-695.
    4. Mondal, Satyajit & Gupta, Ankit, 2021. "Speed distribution for interrupted flow facility under mixed traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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