Self-sustained nonlinear waves in traffic flow
Author(s)Flynn, Morris R.; Kasimov, Aslan R.; Nave, Jean-Christophe; Rosales, Rodolfo R.; Seibold, Benjamin
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Physical Review E
American Physical Society
Flynn, M. R. et al. “Self-sustained nonlinear waves in traffic flow.” Physical Review E 79.5 (2009): 056113. © 2009 The American Physical Society.
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