交通流中的自持非线性波
Self-sustained nonlinear waves in traffic flow
摘要：
在类比气体动力爆轰波，其中包括一个附加的放热反应区的冲击，我们认为在这里的非线性行波解决方案，称为“jamitons”，双曲（“无粘”）连续交通方程。通用的存在性标准的背景下，检查的Lax熵条件。我们的分析自然排除了行波解决方案，其中冲击传播下游更迅速比个别车辆。与最近从周期性道路（Sugiyama等人，New Journal of Physics，10，2008），我们的数值计算表明，在适当的道路条件下，jamitons吸引解决方案，系统的时间演化收敛到jamiton主导的配置。堵塞的特点是在相对紧凑的路段密度急剧增加的道路。通过一个详细的例子，我们的分析，交通建模和控制的应用程序进行检查。
英文摘要：
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, termed "jamitons," 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 (Sugiyama et al., New Journal of Physics, 10, 2008), our numerical calculations show that, under appropriate road conditions, jamitons are attracting solutions, with the time evolution of the system converging towards a jamiton-dominated configuration. Jamitons are characterized by a sharp increase in density over a relatively compact section of the roadway. Applications of our analysis to traffic modeling and control are examined by way of a detailed example.
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