Nonlinear analysis of traffic jams in an anisotropic continuum model

This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence.In order to establish traffic flow stability criterion or to know the critical parameters that lead,on one hand,to a stable response to perturbations or disturbances or,on the other hand,to an unstable response and therefore to a possible congestion,a nonlinear stability criterion is derived by using a wavefront expansion technique.The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter.It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods.Moreover,the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.     

一种改进的两车道交通流格子模型

通过引入新的流量转移函数，改进了两车道交通流格子模型，克服了现有模型隐含的车辆向后运动缺陷.推导了模型的线性稳定性条件.数值模拟结果显示，对于轻度车流扰动，改进的模型可以满意地描述车辆换道过程和趋势. 关键词： 两车道交通流 交通流格子模型 稳定性条件     

弯道交通流跟驰建模与稳定性分析

为发现弯道道路条件下交通流的演化特性及稳定条件,在全速度差最优模型的基础上,研究了弯道情况下的交通流跟驰模型表达式,并以状态空间法和控制系统的稳定性判据对其进行了稳定性分析,得到弯道情况下交通流的稳定条件,最后进行了数值模拟,验证了模型稳定条件的正确性.研究结果表明在相同的初始交通流密度情况下,弯道道路随着道路弧度的增大,交通流稳定性逐渐降低.     

Nonlinear analysis of an improved continuum model considering mean-field velocity difference

Based on the velocity gradient model, an extended continuum model with consideration of the mean-field velocity difference is proposed in this paper. By using the linear stability theory, the linear stability criterion of the new model is gained, which proved that mean-field velocity difference has significant influence on stability of traffic flow. The KdV–Burgers equation is derived by using non-linear analysis method and the evolution of density wave near the neutral stability line is explored. Numerical simulations are carried out how mean-field velocity difference affect the stability of traffic flow, and energy consumption is also studied for this new macro model. At the same time, complicated traffic phenomena such as local cluster effects, shock waves and rarefaction waves can be reproduced in the new model by numerical simulation. Numerical results are consistent with the theoretical analysis, which indicates that the mean-field velocity difference not only suppresses traffic jam, but also depresses energy consumption.     

A viscous continuum traffic flow model with consideration of the coupling effect for two-lane freeways

In this paper, the viscous continuum traffic flow model for a single lane is extended to the traffic flow for two-lane freeways. The proposed model is a higher-order continuum model considering the coupling and lane changing effects of the vehicles on two adjacent lanes. It results from integrating the Taylor series expansion of the viscous continuum traffic flow model proposed by Ge (2006 Physica A 371 667) into the multi-lane model presented by Daganzo (1997 Transpn. Res. B 31 83). Our proposed model may be used to describe non-anisotropic behaviour because of lane changing in multi-lane traffic. A linear stability analysis is given and the neutral stability condition is obtained. Also, issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are investigated through a simulation experiment. The simulation results show that the proposed model is capable of explaining some particular traffic phenomena commonly observable in real world traffic flow.     

Earthquake model describes traffic jams caused by imperfect driving styles

The wide modeling potential of the classical spring-block type system is illustrated by an interdisciplinary application. A simple one-dimensional spring-block chain with asymmetric spring forces is used to model idealized single-lane highway traffic and the emergence of phantom traffic jams. Based on the stop-time statistics of one car in the row, a proper order parameter is defined. By extensive computer simulations the parameter space of the model is explored, analyzed and interpreted. Existence of free and congested flow phases is confirmed and the transition between them is analyzed.     

单通道高速公路车流的相互作用力模型研究

交通流的研究对于城市化进程非常重要.文章以一个实际例子,阐明了交通物理学研究的主要方式.从交通动力学中的车辆跟随模型出发,综合交通流中车辆依据道路交通情况来调整车辆的运行,以保持在安全前提下的一个较快的速度和合适的车辆间距,建立了适用于单轨道高速公路的相互作用力的微观模型．在单轨道交通条件下,通过解析和数字模拟两种方法来研究该模型的平衡解,并讨论了其在微扰下的稳定性．同时,文章还试图模拟一些已知的交通相,并通过与实际交通现象中的一些特征比较来说明其可行性．此外,还通过建立相应的宏观流体力学模型,与微观模型进行比较,并肯定了其适用性．     

Stabilisation analysis of multiple car-following model in traffic flow

An improved multiple car-following model is proposed by considering the arbitrary number of preceding cars, which includes both the headway and the velocity difference of multiple preceding cars. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg--de Vries equation is derived to describe the traffic behaviour near the critical point by applying the nonlinear analysis. Traffic flow can be also divided into three regions: stable, metastable and unstable regions. Numerical simulation is accordance with the analytical result for the model. And numerical simulation shows that the stabilisation of traffic is increasing by considering the information of more leading cars and there is unavoidable effect on traffic flow from the multiple leading cars' information.     

Feedback control scheme of traffic jams based on the coupled map car-following model

Based on the pioneering work of Konishi et al. [Phys. Rev. E （1999） 60 4000], a new feedback control scheme is presented to suppress traffic jams based on the coupled map car-following model under the open boundary condition. The effect of the safe headway on the traffic system is considered. According to the control theory, the condition under which traffic jams can be suppressed is analyzed. The results are compared with the previous results concerning congestion control. The simulations show that the suppression performance of our scheme on traffic jams is better than those of the previous schemes, although all the schemes can suppress traffic jams. The simulation results are consistent with theoretical analyses.     

A lattice traffic model with consideration of preceding mixture traffic information

In this paper,the lattice model is presented,incorporating not only site information about preceding cars but also relative currents in front.We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution and find that the improvement in the stability of traffic flow is obtained by taking into account preceding mixture traffic information.Direct simulations also confirm that the traffic jam can be suppressed efficiently by considering the relative currents ahead,just like incorporating site information in front.Moreover,from the nonlinear analysis of the extended models,the preceding mixture traffic information dependence of the propagating kink solutions for traffic jams is obtained by deriving the modified KdV equation near the critical point using the reductive perturbation method.     

Effects of the number of on-rampson the ring traffic flow

Since ramp is an important composition of traffic system and there often exist multi ramps in a traffic system, the number of ramps can have great effects on main road traffic and produce some complex phenomena. In this paper, we employ the model presented by Tang \textit{et al}. [2009 {\em Communications in Theoretical Physics} {\bf 51}({1}) 71] to further study the effects of the number of on-ramps on the stability of traffic flow on a ring road. The numerical results show that this model can reproduce some complex traffic phenomena resulting from multi on-ramps on the ring road and the effects of the number of on-ramps on traffic flow, but the phenomena and the effects are both related to the initial density of the main road.     

交通流量序列混沌特性分析及DFPSOVF预测模型

以实际采集的交通流量序列作为研究对象, 分别应用互信息法和虚假邻点法确定其延迟时间和最佳嵌入维数, 完成交通流量序列的相空间重构. 通过计算交通流量序列的饱和关联维数和最大Lyapunov指数判定其混沌特性. 以最小均方(LMS)算法为基础, 构建了一种基于Davidon-Fletcher-Powell方法的二阶Volterra模型(DFPSOVF), 其应用了一种可随输入信号变化而实时变化的基于后验误差假设的可变收敛因子技术. DFPSOVF模型避免了在Volterra模型中采用LMS自适应算法调整系数时参数选择不当引起的问题. 将DFPSOVF模型应用于具有混沌特性的短时交通流量预测, 结果表明: 当模型记忆长度与交通流量序列的嵌入维数选择一致时, 模型的预测精度较高, 可以满足交通诱导和交通控制的需要, 为智能交通控制提供了新方法、新思路及工程应用参考. 关键词： 交通流量 混沌 DFPSOVF模型 预测     

The effect of diffusion in a new viscous continuum traffic model

In this Letter, we propose a new continuum traffic model with a viscous term. The linear stability condition for viscous shock waves is derived. We derive the Korteweg-de Vries (KdV) equation near the neutral stability line. Then we investigate the effect of the viscous term by numerical simulations. The results show that viscosity may induce oscillations and the amplitude of the oscillation increases as the viscosity coefficient increases. This agrees with the linear stability condition. The local clusters are compressed by increasing the viscosity coefficient in the cluster study.     

Stability analysis of traffic flow with extended CACC control models

To further investigate car-following behaviors in the cooperative adaptive cruise control(CACC) strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars' speed differences and headway,variable safety distance(VSD) and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control(VC) model and gap control(GC) model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.     

气体分子动力学交通流模型弛豫时间的改进

对气体分子动力学交通流模型的弛豫时间进行了改进，使之与密度及速度相关.通过算例证明改进后的气体分子动力学交通流模型对于抑制高密度车流状况下的扰动更为有效，具有更强的稳定性. 关键词： 交通流 气体分子动力学 Navier-Stokes方程     

优化车流的交通流格子模型

在一维交通流格子模型的基础上，分别提出考虑最近邻车和次近邻车以及考虑前、后近邻车相互作用进行车流优化的一维交通流格子模型.应用线性稳定性理论和非线性理论进行分析，得出车流的稳定性条件，并导出了描述交通阻塞相变的mKdV方程.用数值模拟验证了mKdV方程的解，数值模拟结果表明考虑最近邻车和次近邻车的优化车流能够增强车流稳定性，而考虑前、后近邻车的优化车流将使稳定性减小. 关键词： 交通流 交通相变 稳定判据 mKdV方程     

元胞自动机混合交通流模型的能耗研究

基于元胞自动机交通流NaSch模型,提出元胞自动机混合交通流能耗公式,对混合交通流的能耗进行研究,通过数值模拟研究不同最大速度、不同车长的混合交通流的能耗;研究表明不同车长、不同最大速度以及混合比对混合交通流能耗均有不同的影响. 关键词： 交通流 元胞自动机 能耗 混合交通     

考虑意外事件对交通流影响的元胞自动机交通流模型

在NaSh模型的基础上,考虑交通事故和养护路段等意外事件对高速公路交通流的影响,建立了有意外事件影响的在车道管制下的高速公路交通流元胞自动机模型,并进行数值模拟. 研究发现:意外事件对高速公路交通流有明显影响,并且意外事件对交通流的影响在某一密度值范围内尤其明显,且意外事件堵塞点在第一车道比在第二车道对交通流的影响小;同时,在该密度值范围内,意外事件堵塞时间和堵塞路段长度越长,对交通流的影响就越大. 关键词： 元胞自动机 交通流 意外事件     

The KdV-Burgers equation in a modified speed gradient continuum model

Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micromacro linkage （Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405）. In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers （KdV-Burgers） equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.     

Effect of multi-velocity-difference in traffic flow

Based on the optimal velocity models, an extended model is proposed, in which multi-veloclty-dllterence aheacl is taken into consideration. The damping effect of the multi-velocity-difference ahead has been investigated by means of analytical and numerical methods. Results indicate that the multi-velocity-difference leads to the enhancement of stability of traffic flow, suppression of the emergence of traffic jamming, and reduction of the energy consumption.