Self-sustained nonlinear waves in traffic flow.

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic ("inviscid") continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway [Y. Sugiyama, N. J. Phys. 10, 033001 (2008)], our numerical calculations show that nonlinear traveling waves are attracting solutions, with the time evolution of the system converging toward a wave-dominated configuration. Theoretical principles are elucidated by considering examples of traffic flow on open and closed roadways.

• Publication year

  2008

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2008-10-15

• Fields of study

  Physics, Computer Science, Mathematics, Engineering, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.79.056113arXiv 0810.2820PMID 19518527
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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