A new car-following model with consideration of the traffic interruption probability

In this paper, we present a new car-following model by taking into account the effects of the traffic interruption probability on the car-following behaviour of the following vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flows in the headway sensitivity space-stable, metastable, and unstable--are classified. Both the analytical and simulation results show that the traffic interruption probability indeed has an influence on driving behaviour, and the consideration of traffic interruption probability in the car-following model could stabilize traffic flow.     

Kinetic description of bottleneck effects in traffic flow

This paper deals with the effects of traffic bottlenecks using an extended Lighthill-Whitham-Richards （LWR） model. The solution structure is analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a δ-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fun-damental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions.     

守恒高阶交通流模型的相平面分析

在Lagrange坐标下,运用微分方程定性理论中的相平面分析方法,研究一个近期所提出的守恒高阶交通流模型的行波解,讨论系统的平衡点类型及其稳定性状态,分析相平面中的轨线全局分布结构,验证数值解与解析解的一致性.从而,能够较好地解释现实交通中的时停时走波和瓶颈处的振荡现象,表明所讨论的模型能够描述复杂的拥挤交通.     

交通流流体力学模型与非线性波

介绍了交通流问题中的流体力学描述方法,分析了交通流在受压力和自驱动力等因素作用下所产生的非线性波动现象.这些描述包括LWR运动学模型,考虑动力学效应的高阶模型,考虑超车效应的多车种LWR(Lighthill-Whitham-Richards)模型,以及考虑流通量间断的模型方程.此外,还介绍了LWR网络推广模型在交叉口的Riemann问题求解;提出了描述二维行人流问题的Navier-Stokes-Eikon方程模型并描述了确定行人流运动期盼方向的基本思想.     

交通流瓶颈效应的运动学描述.

采用一个推广的LWR模型研究交通瓶颈效应.通过求解流通量间断的Riemann问题,得到关于模型解结构的解析结果,由此导出了描述在瓶颈上游车流的排队现象及其队列长度和高度(密度)的一个典型解,并能够构造模型方程的一种δ-映射算法.更有意义的是,表明了通过采用三角形基本图,这一运动学模型能够描述时走时停波.通过数值模拟,验证丁数值结果与解析结果的一致性,从而支撑了文章的理论结果.     

Characteristic Parameters of a Wide Cluster in a Higher-Order Traffic Flow Model

Nonlinear weak solution theory is applied to determine the parameters of a wide cluster in an ＂anisotropic＂ higher-order traffic flow model. These parameters are the maximal and minimal densities and the travelling wave speed in the solution structure, Numerical experiments show that the convergent simulation results arc in good agreement with those obtaincd from the analytical expressions.     

Helbing流体力学交通流模型的守恒形式

得到了Helbing交通流流体力学模型的标准守恒形式,并证明了模型的双曲性,这对研究模型的解析性质和数值格式至关重要.基于给出的守恒形式,设计了高效求解模型方程的LDG(lo-cal discontinuous Galerkin)格式,并模拟了由不稳定平衡态到稳定的时停时走波的演化.数值模拟也表明,通过扩散系数校正确实使模型得到改进,避免了车辆碰撞和出现极端高密度.