Self-sustained nonlinear waves in traffic flow
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Flynn-2009-Self-sustained nonli.pdf
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Author(s)
Flynn, Morris R.
Kasimov, Aslan R.
Nave, Jean-Christophe
Rosales, Rodolfo R.
Seibold, Benjamin
Date Issued
May 2009
Journal
Physical Review E
Publisher
American Physical Society
Citation
Flynn, M. R. et al. “Self-sustained nonlinear waves in traffic flow.” Physical Review E 79.5 (2009): 056113. © 2009 The American Physical Society.
Version
Final published version
Abstract
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 et al., 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevE.79.056113
