适应性交通流连续性模型

Adaptive Traffic Continuum Model

关键词:  交通流  动理论模型  距方程  Chapman-Enskog方法  Paveri-Fontana等式

Key words:  traffic flow  kinetic model  moment equation  Chapman-Enskog method  Paveri-Fontana equation

摘要:

[目的]考虑人的主动行为在复杂的交通系统所起的作用,从微观机理出发,利用气体动理学理论建立交通流连续性宏观模型,研究交通的拥堵现象。[方法]假定单一司机的期望速度与其局域瞬时速度成正比,考虑司机期望速度随时间的驰豫变化,利用广义Paveri-Fontana等式,通过运用距方程和Chapman-Enskog方法,导出类Naveri-Stokes方程的适应性交通流模型;然后对适应性交通流模型进行线性稳定性分析,并通过数值分析验证适应性模型的合理性。[结果]适应性模型能更好地解释高密度下的时停时走交通现象,描述交通堵塞的消散过程,反映右转车流的"挤压"效应。[结论]引入司机的期望速度的宏观交通流动力学方程能较好模拟高密度的交通拥堵现象。

Abstract:

[Objective] The congestion of traffic flow is studied by establishing kinetic models from microscopic model to macroscopic one.[Methods] Considering that the desired velocity of a single driver changes with the surrounding and is related to local instantaneous velocity of the vehicle in real traffic, the desired velocity is assumed to be proportional to the local instantaneous velocity.The adaptive flux model like Navier-Stokes traffic equation is derived from the extended Paveri-Fontana equation.The steady condition of the model is obtained by the linear stability analysis.[Results] Compared with steady condition of both Kerner-Konhäuser model and Helbing model, it is found that the adaptive model has the ability to illustrate stop- and-go traffic in middle-high density.Numerical solution of the macroscopic traffic equations verifies rationality of our model.[Conclusion] The hydrodynamic traffic model is suitable to simulate the congestion phenomena in middle-high density via introducing the desired velocity of driver.