Nonlinear analysis of traffic flow on a gradient highway
Nonlinear analysis of traffic flow on a gradient highway
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DOI：
10.1016/j.physa.2011.09.026
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发表时间：
2012-02
影响因子：
3.3
通讯作者：
Wen-xing Zhu;Rui-Ling Yu
中科院分区：
文献类型：
--
作者：
Wen-xing Zhu;Rui-Ling Yu
本文通过分析和数值计算研究了单车道坡度（上坡/下坡）公路上坡度对交通流的影响。利用线性稳定性理论，得到了系统的稳定性条件、中性稳定性条件和不稳定性条件。结果表明，坡度不同，交通流的稳定性也不同。导出了分别描述稳定区、亚稳定区和不稳定区三角激波、孤子波和扭结-反扭结波的Burgers方程、Korteweg-de弗里斯方程（KdV）和修正的Korteweg-de弗里斯方程（mKdV）。对三角形激波、扭结-反扭结波和孤子波进行了模拟。结果表明，三角形激波和扭结-反扭结波的振幅随坡度变化，当平均车头时距小于安全距离时，孤立波以向上的形式出现，当平均车头时距大于安全距离时，孤立波以向下的形式出现.此外，扭结-反扭结波和孤立波都向后传播。数值模拟结果与解析结果吻合较好。
We investigate the slope effects upon traffic flow on a single lane gradient (uphill/downhill) highway analytically and numerically. The stability condition, neutral stability condition and instability condition are obtained by the use of linear stability theory. It is found that stability of traffic flow on the gradient varies with the slopes. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, meta-stable and unstable region respectively. A series of simulations are carried out to reproduce the triangular shock waves, kink–antikink waves and soliton waves. Results show that amplitudes of the triangular shock waves and kink–antikink waves vary with the slopes, the soliton wave appears in an upward form when the average headway is less than the safety distance and a downward form when the average headway is more than the safety distance. Moreover both the kink–antikink waves and the solitary waves propagate backwards. The numerical simulation shows a good agreement with the analytical result.