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Wave Selection Problems in the Presence of a Bottleneck

  • Conference paper
Traffic and Granular Flow’05

Summary

The Optimal-Velocity (OV) model is posed on an inhomogeneous ring- road and the consequent spatial traffic patterns are described and analysed. Parameters are chosen throughout for which all uniform flows are linearly stable, and a simple model for a bottleneck is used in which the OV function is scaled down on a subsection of the road. The large-time behaviour of this system is stationary and it is shown that there are three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp fronts. These patterns solve simple flow and density balances, which in some cases have non-unique solutions. It is shown how the theory of characteristics for the classical Lighthill-Whitham PDE model may be used to explain qualitatively which solutions the OV model selects. However, fine details of the OV model solution structure may only be explained by higher order PDE modelling.

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Author information

Authors and Affiliations

  1. Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR

    Jonathan Ward & R. Eddie Wilson

  2. Faculty of Science, UOIT, Oshawa, ON, L1H 7K4, Canada

    Peter Berg

Authors
  1. Jonathan Ward
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  2. R. Eddie Wilson
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  3. Peter Berg
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937, Köln, Germany

    Andreas Schadschneider

  2. Campus Virchow Klinikum Centrum für Unfall- und Wiederherstellungschirurgie, Charité, Augustenburger Platz 1, 13353, Berlin, Germany

    Thorsten Pöschel

  3. Institut für Verkehrsforschung, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Rutherfordstr. 2, 12489, Berlin, Germany

    Reinhart Kühne

  4. Physik von Transport und Verkehr, Universität Duisburg-Essen, Lotharstr. 1, 47048, Duisburg, Germany

    Michael Schreckenberg

  5. Theoretische Physik, Universität Duisburg-Essen, Lotharstr. 1, 47048, Duisburg, Germany

    Dietrich E. Wolf

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© 2007 Springer-Verlag Berlin Heidelberg

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Ward, J., Wilson, R.E., Berg, P. (2007). Wave Selection Problems in the Presence of a Bottleneck. In: Schadschneider, A., Pöschel, T., Kühne, R., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow’05. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47641-2_55

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