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Existence and Classification of Travelling Wave Solutions to Second Order Highway Traffic Models

In: Traffic and Granular Flow’01

Author

Listed:
  • R. E. Wilson

    (University of Bristol, Department of Engineering Mathematics)

  • P. Berg

    (Simon Fraser University, Pacific Institute for the Mathematical Sciences)

Abstract

The Bando optimal velocity model has a rich structure of wave solutions of travelling, composite and expansion types, even in the stable regime. We analyse these waves via a continuum limit which resembles the Kerner-Konhäuser PDE model, to which our analysis also applies. Geometrical properties of the fundamental diagram, in combination with global bifurcation theory of the travelling wave phase plane, lead to a complete classification of wave types which applies to several second order highway traffic models.

Suggested Citation

  • R. E. Wilson & P. Berg, 2003. "Existence and Classification of Travelling Wave Solutions to Second Order Highway Traffic Models," Springer Books, in: Minoru Fukui & Yuki Sugiyama & Michael Schreckenberg & Dietrich E. Wolf (ed.), Traffic and Granular Flow’01, pages 85-90, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-10583-2_6
    DOI: 10.1007/978-3-662-10583-2_6
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