低维宏观交通流模型的稳定性和分岔分析

交通流模型的分岔点对应临界的交通状态,对研究交通流的稳定性具有重要的理论意义.为了分析宏观交通流模型的分岔特征,通过对低维宏观交通流模型的求解得到两个平衡点,并讨论了其稳定性,发现该模型存在一个跨临界分岔点.数值仿真验证了结论的正确性,并且在一定条件下,通过改变响应时间会影响到最终的平衡状态.     

离散交通流模型的反馈线性化与拥堵控制

在自动化高速公路环境下,提出一种改进的宏观离散交通流模型密度控制方法.利用反馈线性化方法,将宏观离散交通流模型转换为一般容易处理的线性系统模型,简化了密度控制器的设计.利用线性系统中具有输入变换的跟踪反馈控制方法,对线性化后的系统模型设计控制律.通过控制该线性系统的状态变量,间接稳定离散交通流模型中的交通流密度,达到对道路交通流拥堵的控制.同时给出设计方法和步骤,仿真实例说明了方法的实用性.     

基于多源监测数据的道路交通流状态重构研究

根据给定区域多源监测的道路交通流数据对实际道路交通状况进行评估.通过对多源数据的清洗与融合,获得描述交通流状况的基本参数.将参数应用于偏微分方程模型及仿真模拟中,分别从宏观和微观的角度对区域内交通流变化情况进行预测.依据预测结果,为交通问题的科学管理提出了建议.     

具有时滞和周期特征的短时交通流灰建模及其应用

针对短时交通流的延迟性、随机性和周期性特征,采用灰关联分析和分数阶累加生成方法建立了带时滞和周期特征的分数阶累加灰色新模型.针对短时交通流的延迟性,将短时交通流数据拆分成参考时间序列和对应的比较时间序列,进行关联度分析,得到计算时滞值的方法.针对短时交通流的随机性和周期性,利用分数阶累加生成方法,并引入tan(kp)为发展系数,sin(kp)为输入变量,建立了短时交通流的分数阶GM(1,1|tan(kp),sin(kp))模型,给出了模型参数的最小二乘估计和周期性参数与分数阶阶数的优化求解算法.最后将模型应用于长沙市芙蓉区某交叉路口的交通流建模及预测中,并与常规的五种模型进行了对比分析,结果表明,模型能较为准确地反映交通流的实际情况,且有较高的预测精度和较为稳定的结果.     

各向异性交通流动力学模型的波动特性

对姜锐等人最近提出的一种新的交通流动力学模型的波动特性进行了分析.该模型中,不存在大于宏观车流速度的特征速度,从而满足交通流各向异性的要求.线性稳定性分析发现,新模型在一定条件下保持稳定,文中给出了稳定条件判定标准.分析指出,这一模型的波由一阶波和二阶波两种层次构成,既允许交通光滑波的存在,也充许交通激波的存在,但是其激波条件与其它相关模型有明显区别.正是这种区别,使得新模型在处理某些交通问题(如车辆倒退现象)上更加符合实际车流情况.     

短时交通流混沌预测模型的比较研究

短时交通流预测是实现交通流诱导的关键技术之一.针对目前短时交通混沌预测模型预测结果差异较大的问题,归纳了4种基于混沌理论的短时交通流预测模型:RBF神经网络模型、最大Lyapunov指数模型、局域线性模型和Volterra滤波器自适应预测模型,并对这4种预测模型进行了比较研究.应用4种预测模型对几个典型的非线性系统进行预测,验证了算法的准确性.然后用这4种预测模型对微观实测交通流的时间序列进行实证分析.仿真结果表明,4种预测模型对典型混沌时间序列具有很好的预测效果;而对实测交通流预测,其预测精度和稳定性较差,但可以满足实时交通流预测的需要.     

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.     

关于δ初值的Chaplygin压交通流AR模型的Riemann问题

研究Chaplygin压交通流AR模型初值含Dirac δ函数的Riemann问题.在广义Rankine-Hugoniot条件和熵条件下,构造性地获得了包含δ激波的整体广义解,明确地显示出四种不同的结构.结果表明,在Riemann初值这里构造的扰动下,Riemann解是稳定的.     

交通流非参数回归模型

交通流宏观参数流量、速度和占有率在交通工程和管理中具有非常重要的作用 ,对这三者关系的刻划反映了道路本身特性和交通流的规律。到目前为止 ,基本上采用线性或非线性的参数模型来描述 ,此类模型在应用中具有一定的局限性 ,并交通变量时间序列进行预测 ,数据拟合表明 ,选择适当的核函数或邻近数以及窗宽 ,可以达到比较满意的效果     

信号交叉口车辆的延误分析

针对路段上交通流的特性,以及信号交叉口交通流的动态流通特征,分析了车辆到达信号交叉口的规律以及车辆越过停车线的特点,从而建立了停车延误模型;又分析了单个相位停车线的长度与交叉口几何特征的关系,及车辆在通过信号交叉口之间的路段过程中的运行特性,建立了相位延误模型;从而得到一个在信号交叉口处适用任何饱和度的排队延误模型,使得结果更贴近车辆在信号交叉口的实际延误时间.     

Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach

This paper proposes a macroscopic model to describe the operations of cooperative adaptive cruise control (CACC) traffic flow, which is an extension of adaptive cruise control (ACC) traffic flow. In CACC traffic flow a vehicle can exchange information with many preceding vehicles through wireless communication. Due to such communication the CACC vehicle can follow its leader at a closer distance than the ACC vehicle. The stability diagrams are constructed from the developed model based on the linear and nonlinear stability method for a certain model parameter set. It is found analytically that CACC vehicles enhance the stabilization of traffic flow with respect to both small and large perturbations compared to ACC vehicles. Numerical simulation is carried out to support our analytical findings. Based on the nonlinear stability analysis, we will show analytically and numerically that the CACC system better improves the dynamic equilibrium capacity over the ACC system. We have argued that in parallel to microscopic models for CACC traffic flow, the newly developed macroscopic will provide a complete insight into the dynamics of intelligent traffic flow.     

Modeling the asymmetry in traffic flow (a): Microscopic approach

The asymmetric characteristic of a vehicle’s ability in deceleration and acceleration, as well as its impact to micro- and macroscopic traffic flow has caused increased attention from both theoretical and practical sides. However, how to realistically model this property remains a challenge to researchers. This paper is one of the two studies on this topic, which is focused on the modeling at the microscopic level from the investigation of car-following behavior. The second part of the study [H. Liu, H. Xu, H. Gong, Modeling the asymmetry in traffic flow (b): macroscopic approach, Appl. Math. Model. (submitted for publication)] is focused on the modeling of this asymmetric property from the macroscopic scale. In this paper, we first present an asymmetric full velocity difference car-following approach, in which a higher order differential equation is developed to take into account the effect of asymmetric acceleration and deceleration in car-following. Then, efforts are dedicated to calibrate the sensitivity coefficients from field data to complete the theoretical approach. Using the data recorded from the main lane traffic and ramp traffic of a segment of the US101 freeway, the two sensitivity coefficients have been successfully calibrated from both congested and light traffic environments. The experimental study reveals that in the studied traffic flow, the intensity of positive velocity difference term is significantly higher than the negative velocity difference term, which agrees well with the results from studies on vehicle mechanics.     

An explicitly solvable kinetic model for vehicular traffic and associated macroscopic equations

In the present paper, a kinetic model for vehicular traffic is presented and investigated in detail. For this model, the stationary distributions can be determined explicitly. A derivation of associated macroscopic traffic flow equations from the kinetic equation is given. The coefficients appearing in these equations are identified from the solutions of the underlying stationary kinetic equation and are given explicitly. Moreover, numerical experiments and comparisons between different macroscopic models are presented.     

An ODE traffic network model

We are interested in models for vehicular traffic flow based on partial differential equations and their extensions to networks of roads. In this paper, we simplify a fluidodynamic traffic model and derive a new traffic flow model based on ordinary differential equations (ODEs). This is obtained by spatial discretization of an averaged density evolution and a suitable approximation of the coupling conditions at junctions of the network. We show that the new model inherits similar features of the full model, e.g., traffic jam propagation. We consider optimal control problems controlled by the ODE model and derive the optimality system. We present numerical results on the simulation and optimization of traffic flow in sample networks.     

Simulating vehicular traffic in a network using dynamic routing

We present a new numerical code which solves the Lighthill – Whitham model, the classic macroscopic model for vehicular traffic flow, in a network with multi-destinations. We use a high-resolution shock-capturing scheme with approximate Riemann solver to solve the partial differential equations of the Lighthill – Whitham theory. These schemes are very efficient, robust and moreover well adapted to simulations of traffic flows. We develop a theory of dynamic routing including a procedure for traffic flow assignment at junctions which reproduces the correct propagation of irregularities and ensures at the same time conservation of the number of vehicles.     

On the convective Cahn-Hilliard equation with degenerate mobility

In this paper, we study the existence of weak solutions for the convective Cahn-Hilliard equation with degenerate mobility. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.     

Propagation of Perturbations of Solutions for a Doubly Degenerate Nonlinear Parabolic Equation

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Spatial distribution complexities of traffic congestion and bottlenecks in different network topologies

Recently, urban traffic congestion has become a popular social problem. The generation and the propagation of congestion has close relation with the network topology, the traffic flow, etc. In this study, based on the traffic flow propagation method, we investigate the time and space distribution characteristics of the traffic congestion and bottlenecks in different network topologies (e.g., small world, random and regular network). The simulation results show that the random network is an optimal traffic structure, in which the traffic congestion is smaller than others. Moreover, the regular network is the worst topology which is prone to be congested. Additionally, we also prove the effects of network with community structure on the traffic system and congestion bottlenecks including its generation, propagation and time–space complexities. Results indicate that the strong community structure can improve the network performance and is effective to resist the propagation of the traffic congestion.