Self-sustained nonlinear waves in traffic flow

Abstract

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Terms of UseArticle 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. 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 ͑2008͔͒, 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. Self-sustained nonlinear waves in traffic flow

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