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Probabilistic Description of Traffic Breakdown

In: Traffic and Granular Flow’05

Author

Listed:
  • Reinhard Mahnke

    (Rostock University, Institute of Physics)

  • Reinhart Kühne

    (German Aerospace Center, Institute of Transportation Research)

Abstract

Summary Traffic breakdowns are described by a balance equation that models the dynamics of jam formation by the following two contributions. There are discharge rate depending on the length of the congestion and an adhesion rate mainly depending on the traffic volume of the considered road section. With this balance equation it is feasible to calculate the dynamics of traffic pattern formation especially the first passage time for a transition from free flow condition to congested traffic including the influence of the parameters affecting the discharge and adhesion rates. As a simple approximation we consider constant attachment rate as well as constant detachment rate. Starting with the probability density and furtheron with the cumulative probability for breakdowns the change in the incident duration distribution is calculated and qualitatively given. The paper concludes with recommendations for a comprehensive operation improvement and provides necessary steps for a long lasting stabilization of traffic for a given vehicular flow time series pattern.

Suggested Citation

  • Reinhard Mahnke & Reinhart Kühne, 2007. "Probabilistic Description of Traffic Breakdown," Springer Books, in: Andreas Schadschneider & Thorsten Pöschel & Reinhart Kühne & Michael Schreckenberg & Dietrich E. Wol (ed.), Traffic and Granular Flow’05, pages 527-536, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-47641-2_50
    DOI: 10.1007/978-3-540-47641-2_50
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