混合交通流动力学建模研究
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摘要
交通流理论是研究交通特性的一门边缘科学,交通流模型则是用来简化分析交通流及评估假定的交通控制策略的重要方式,为交通管理者和使用者提供包括路网规划设计、交通管理等理论依据。但中国特有的混合交通流形式,使得国外的交通流理论与方法在中国不能完全适用。因此,针对中国的交通流特点,研究由不同车型形成的混合交通流的作用机理,建立能描述混合交通流的动力学模型,对提高混合交通流的可控性,改善日益严重的交通拥挤状况具有重要的理论意义,同时更具有实际意义。
论文在现有连续交通流模型研究基础上,针对由不同机动车型构成的混合车流建立了新的动力学模型,包括模型的推导、参数的标定、模型的离散、模型的性能分析及效用验证。主要内容包括：
介绍交通流理论国内外研究现状,分析交通流动力学一阶模型及高阶模型后,指出现有交通流动力学模型的特点和亟待解决完善之处,并总结出交通流基本参数间的关系模型和常用的数值方法。综合分析了交通流的构成及交通特性、交通流的分类、混合交通流的形成及交通流的基本特征。
分析传统车辆跟驰模型推导过程,将传统跟驰模型推导过程的简化项定义为车辆间的干扰,分析其在混合交通流中不能简化的机理,并导出混合交通流中的粘性项,建立了新的车辆跟驰模型；提出新的速-密函数和弛豫时间函数；采用动力学建模方法,建立了新的交通流动力学模型；给出模型的迎风差分和Lax差分数值解；通过编制的优化程序对模型参数进行标定。
针对现有动力学高阶模型存在的问题,对模型做了数学特性及性能分析,证实新模型在理论上能解决困扰现有高阶模型的几个问题：特征根问题、车辆倒退问题、线性稳定性问题、间断的传递、拥堵的消散、簇的传递及状态的转换问题。
重新定义了交通拥挤,并以此来定义一个无量纲量来量化交通拥挤度,建立模型。该模型考虑了车型比例、交通条件及交通环境等因素,通过设定阈值,以交通拥挤度值大小来划分交通状态。通过实例验证,证实模型能够真实、客观的描述交通拥挤状态,有良好的通用性。
最后,本文设计试验,采集交通实测数据,模型进行定性和定量的效用验证,并将其与模型仿真数据进行对比,包括与其它典型的高阶连续流模型的仿真数据间的对比,试验结果说明本模型不仅能合理解释交通现象,而且仿真数据能够与实测数据较好的拟合,仿真速度也很快。
Traffic flow theory is a frontier subject that describes the characteristic and formation mechanism of traffic, and traffic flow model is the important method which is used to simplify the analysis of traffic flow and assessment of traffic control strategies including road network planning and designing, traffic management and so on, which can provide traffic managers and users with theoretical foundation. However, in China, it is not practical to apply the same theory and method on car flow using in the developed countries because of our specific mixed traffic flow. Therefore, it is important to indicate the formation mechanism of the traffic flow between with different vechicle styles, build mixed traffic flow model by dynamics, control the traffic system, and improve the worsening traffic congestion situation the traffic status according to the nature of the mixed traffic flow in China. So, this work not only has important theoretical significance, but also has practical significance.
The paper sets up the traffic flow model by means of dynamics for different vehicle types, based on the study of continuous traffic flow model. The main work includes model derivation, parameter calibration, discretization of model, performance analysis of model and effectiveness verification. Details are as following.
First, after introducing the study status of traffic flow theory in China and developed coutried, analyzing the first-order and high-order traffic flow models, the thesis pointes out that the characteristics of the existing traffic flow model and problems which demanded prompt solution perfectly, and summs up the basic relationship of parameters and commonly numerical methods. Then the composition of traffic flow, traffic characteristics, traffic flow classification, the formation of mixed traffic flow and traffic flow basic features are described.
Analyzing the derivation process of the traditional car-following model, summing up the previous work, the simplified term in the traditional car-following model is defined as the interference between vehicles, which is the viscous term in high-order traffic flow model. And a new car-following model, new speed-density function and relaxation time function are presented; the new high-order continuous traffic flow model is set up by dynamics; then, the upwind difference numerical solution and Lax difference numerical solution are given. Paper provides an optimization procedure for calibration of the model parameters.
Paper analyzes the mathematical properties and performance of the new model, the analysis conclusion shows that the new model can solve the following problems in theory, which include:eigenvalue problem, the negative speed problem, the linear stability, discontinuous transmission, dissipation of congestion, the transmission and state conversion of cluster. And these issues once plagued most of the existing high-order models.
Then, paper redefines the traffic congestion level, and defines a dimensionless parameter to quantify the traffic congestion level. And the traffic congestion level model is set up, which takes into account the proportion of vehicle types, traffic conditions, traffic environment, and other factors. According to the size of the congestion level, the traffic state is divided into five kinds. And the experiments confirm that the model can descript the traffic status really, objectively, moreover, the model has no restrictions on use.
Finally, paper designs several experiments to test the validation of new model in qualitative and quantitative.
论文在现有连续交通流模型研究基础上,针对由不同机动车型构成的混合车流建立了新的动力学模型,包括模型的推导、参数的标定、模型的离散、模型的性能分析及效用验证。主要内容包括：
介绍交通流理论国内外研究现状,分析交通流动力学一阶模型及高阶模型后,指出现有交通流动力学模型的特点和亟待解决完善之处,并总结出交通流基本参数间的关系模型和常用的数值方法。综合分析了交通流的构成及交通特性、交通流的分类、混合交通流的形成及交通流的基本特征。
分析传统车辆跟驰模型推导过程,将传统跟驰模型推导过程的简化项定义为车辆间的干扰,分析其在混合交通流中不能简化的机理,并导出混合交通流中的粘性项,建立了新的车辆跟驰模型；提出新的速-密函数和弛豫时间函数；采用动力学建模方法,建立了新的交通流动力学模型；给出模型的迎风差分和Lax差分数值解；通过编制的优化程序对模型参数进行标定。
针对现有动力学高阶模型存在的问题,对模型做了数学特性及性能分析,证实新模型在理论上能解决困扰现有高阶模型的几个问题：特征根问题、车辆倒退问题、线性稳定性问题、间断的传递、拥堵的消散、簇的传递及状态的转换问题。
重新定义了交通拥挤,并以此来定义一个无量纲量来量化交通拥挤度,建立模型。该模型考虑了车型比例、交通条件及交通环境等因素,通过设定阈值,以交通拥挤度值大小来划分交通状态。通过实例验证,证实模型能够真实、客观的描述交通拥挤状态,有良好的通用性。
最后,本文设计试验,采集交通实测数据,模型进行定性和定量的效用验证,并将其与模型仿真数据进行对比,包括与其它典型的高阶连续流模型的仿真数据间的对比,试验结果说明本模型不仅能合理解释交通现象,而且仿真数据能够与实测数据较好的拟合,仿真速度也很快。
Traffic flow theory is a frontier subject that describes the characteristic and formation mechanism of traffic, and traffic flow model is the important method which is used to simplify the analysis of traffic flow and assessment of traffic control strategies including road network planning and designing, traffic management and so on, which can provide traffic managers and users with theoretical foundation. However, in China, it is not practical to apply the same theory and method on car flow using in the developed countries because of our specific mixed traffic flow. Therefore, it is important to indicate the formation mechanism of the traffic flow between with different vechicle styles, build mixed traffic flow model by dynamics, control the traffic system, and improve the worsening traffic congestion situation the traffic status according to the nature of the mixed traffic flow in China. So, this work not only has important theoretical significance, but also has practical significance.
The paper sets up the traffic flow model by means of dynamics for different vehicle types, based on the study of continuous traffic flow model. The main work includes model derivation, parameter calibration, discretization of model, performance analysis of model and effectiveness verification. Details are as following.
First, after introducing the study status of traffic flow theory in China and developed coutried, analyzing the first-order and high-order traffic flow models, the thesis pointes out that the characteristics of the existing traffic flow model and problems which demanded prompt solution perfectly, and summs up the basic relationship of parameters and commonly numerical methods. Then the composition of traffic flow, traffic characteristics, traffic flow classification, the formation of mixed traffic flow and traffic flow basic features are described.
Analyzing the derivation process of the traditional car-following model, summing up the previous work, the simplified term in the traditional car-following model is defined as the interference between vehicles, which is the viscous term in high-order traffic flow model. And a new car-following model, new speed-density function and relaxation time function are presented; the new high-order continuous traffic flow model is set up by dynamics; then, the upwind difference numerical solution and Lax difference numerical solution are given. Paper provides an optimization procedure for calibration of the model parameters.
Paper analyzes the mathematical properties and performance of the new model, the analysis conclusion shows that the new model can solve the following problems in theory, which include:eigenvalue problem, the negative speed problem, the linear stability, discontinuous transmission, dissipation of congestion, the transmission and state conversion of cluster. And these issues once plagued most of the existing high-order models.
Then, paper redefines the traffic congestion level, and defines a dimensionless parameter to quantify the traffic congestion level. And the traffic congestion level model is set up, which takes into account the proportion of vehicle types, traffic conditions, traffic environment, and other factors. According to the size of the congestion level, the traffic state is divided into five kinds. And the experiments confirm that the model can descript the traffic status really, objectively, moreover, the model has no restrictions on use.
Finally, paper designs several experiments to test the validation of new model in qualitative and quantitative.
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