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Game-Theoretic Context and Interpretation of Kerner’s Three-Phase Traffic Theory

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Game Theoretic Analysis of Congestion, Safety and Security

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

We present four classical developments in traffic theory and Kerner’s (Phys A 392:5261–5282, 2013, [36]) critique that these are not consistent with fundamental empirical features of traffic breakdown at a highway bottleneck (transition from free flow (F) to congested traffic at the bottleneck) that is the basic empiric of traffic theory. Kerner argued that traffic breakdown is probabilistic, can be spontaneous (emerging internally at the bottleneck) or induced (emerging from a downstream bottleneck), and is a transition from free flow to synchronized flow (S) (synchronized flow is one of the two traffic phases of congested traffic) called as a F → S transition, after which wide moving jam (J) (J is another from two phases of congested traffic) may arise. Return to free flow occurs through hysteresis and usually at smaller flow rates. Common games in traffic theory are presented and exemplified, i.e. the chicken game, battle of the sexes, prisoner’s dilemma, and coordination game. The four developments and Kerner’s theory are linked to game theory, and especially to the chicken game. For the first F → S transition the density increases at a constant flow rate. Increasing density increases the prevalence of the chicken strategy due to drivers in a congested environment becoming apprehensive, fearful, and wary of accidents. For the second S → J the chicken strategy is equally likely while the flow rate decreases at constant density. For the third J → F transition the density decreases which decreases the prevalence of the chicken strategy. Finally, within free flow F where the flow rate and density again increase, the chicken strategy is played with higher probability.

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Notes

  1. 1.

    See [29] for a new mechanism for metastability.

  2. 2.

    The difference between S and J is that while the downstream front of a wide moving jam propagates through a highway bottleneck upstream with a mean velocity (often about −15 km/h), the downstream front of synchronized flow is usually fixed at the bottleneck (Figs. 1, 2 and 3).

  3. 3.

    A platoon is a group of vehicles following each other with low distance between each vehicle, accomplished by electronic, and sometimes mechanical, coupling. Traffic throughput increases because of the synchronization where e.g. reaction times are decreased or eliminated.

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Acknowledgments

Hubert Rehborn thanks for the funding in the project “UR:BAN—Urbaner Raum: Benutzergerechte Assistenzsysteme und Netzmanagement,” funded by the German Federal Ministry of Economic Affairs and Energy. We thank Boris S. Kerner, Micha Koller, Peter Hemmerle, and anonymous referees for their helpful suggestions.

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Authors and Affiliations

  1. Faculty of Social Sciences, University of Stavanger, 4036, Stavanger, Norway

    Kjell Hausken

  2. Group Research and Advanced Engineering, Daimler AG, HPC: 059-X832, 71063, Sindelfingen, Germany

    Hubert Rehborn

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  1. Kjell Hausken
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Correspondence to Kjell Hausken .

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  1. Faculty of Sciences, University of Stavanger, Stavanger, Norway

    Kjell Hausken

  2. Dept of Industrial & Systems Engineering, University at Buffalo State University of New York, Buffalo, New York, USA

    Jun Zhuang

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Hausken, K., Rehborn, H. (2015). Game-Theoretic Context and Interpretation of Kerner’s Three-Phase Traffic Theory. In: Hausken, K., Zhuang, J. (eds) Game Theoretic Analysis of Congestion, Safety and Security. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-11674-7_5

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