PMID: 11308709Apr 20, 2001Paper

Traveling waves in an optimal velocity model of freeway traffic

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
P Berg, A Woods

Abstract

Car-following models provide both a tool to describe traffic flow and algorithms for autonomous cruise control systems. Recently developed optimal velocity models contain a relaxation term that assigns a desirable speed to each headway and a response time over which drivers adjust to optimal velocity conditions. These models predict traffic breakdown phenomena analogous to real traffic instabilities. In order to deepen our understanding of these models, in this paper, we examine the transition from a linear stable stream of cars of one headway into a linear stable stream of a second headway. Numerical results of the governing equations identify a range of transition phenomena, including monotonic and oscillating travelling waves and a time- dependent dispersive adjustment wave. However, for certain conditions, we find that the adjustment takes the form of a nonlinear traveling wave from the upstream headway to a third, intermediate headway, followed by either another traveling wave or a dispersive wave further downstream matching the downstream headway. This intermediate value of the headway is selected such that the nonlinear traveling wave is the fastest stable traveling wave which is observed to develop in the numerical calc...Continue Reading

References

Jul 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B S Kerner, P Konhäuser
Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M BandoY Sugiyama
Nov 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T S Komatsu, S i Sasa
Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P BergA Woods
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Nagatani

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Citations

Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H K LeeD Kim
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ihor LubashevskyReinhard Mahnke

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