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On the Statistical Distribution Function Theory of Traffic Flow

Author

Listed:
  • Robert L. Anderson

    (Research Laboratories, General Motors Corporation, Warren, Michigan)

  • Robert Herman

    (Research Laboratories, General Motors Corporation, Warren, Michigan)

  • I. Prigogine

    (Universite Libre of Brussels, Brussels, Belgium)

Abstract

The homogeneous time-independent solution for a one-car speed distribution function is derived for a Boltzmann-like approach to the statistical theory of traffic flow. Numerical results are discussed for a number of different desired speed-distribution functions. Among these distribution functions, chosen for mathematical simplicity are, for example, the exponential, linear, and parabolic. Flow versus concentration curves and distribution function versus speed curves are given for several of the models.

Suggested Citation

  • Robert L. Anderson & Robert Herman & I. Prigogine, 1962. "On the Statistical Distribution Function Theory of Traffic Flow," Operations Research, INFORMS, vol. 10(2), pages 180-196, April.
    • Handle: RePEc:inm:oropre:v:10:y:1962:i:2:p:180-196
    DOI: 10.1287/opre.10.2.180
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    Cited by:

    1. Fiems, Dieter & Prabhu, Balakrishna & De Turck, Koen, 2019. "Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 412-421.
    2. André de Palma, 2003. "In Memoriam: Ilya Prigogine (1917–2003)," Transportation Science, INFORMS, vol. 37(3), pages 255-256, August.
    3. Marques, W. & Méndez, A.R. & Velasco, R.M., 2021. "The vehicle length effect on the traffic flow fundamental diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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