公交客流加权复杂网络结构及动力学行为研究
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摘要
摘要：城市公共交通系统是一个由静态拓扑网络子系统和动态流量子系统相互作用、相互影响而形成的复杂、动态巨系统,也是一个在长期的发展过程中,受城市社会经济活动、空间结构、地理特征甚至文化习俗等多重因素影响的演化产物。对于城市公交系统的复杂性,近年来兴起的复杂网络理论为研究公交系统内部和外部的耦合作用和组织机理提供了一个新视角、新方法。随着复杂网络理论在国内外学术界掀起的研究热潮不断高涨,人们对复杂网络的研究更多地关注在网络构成要素和信息的不断变化以及网络的演化过程和动力学行为上。城市公交网络是一个具有技术网络和社会网络特征混合而成的复合型复杂网络,具有时空动态复杂性,研究城市公交网络结构的复杂性,不仅要研究公交网络本身的静态拓扑特性,更重要的是要研究加载了动态客流量信息的加权网络所体现出来的特性。而目前,对基于客流动态行为的公交加权网络研究几乎没有,为更好地把握公交系统的组织结构和整体特性,需要用公交网络的影响要素动态变化的观点来重新认识网络,建立模型来模拟公交网络的演化过程以再现网络结构属性,并分析公交网络这一复杂系统的动力学行为。这些问题的研究对于从复杂网络理论角度优化和调整城市公交线网具有重要的理论及现实指导意义。
本文以加载了客流动态行为的城市公共交通系统作为研究对象,基于复杂网络理论和公交系统规划理论,对城市公交加权复杂网络的结构特征及动力学行为进行了研究。首先提出了加权复杂网络特征度量指标和模型构建方法,利用统计分析与比较分析相结合的方法,对城市公交无权和有权复杂网络结构的统计特性进行了实证研究；其次在总结公交加权网络系统特性的基础上,探索形成这些网络结构的演化机理,针对不同的公交网络抽象形式构建了加权网络演化模型,研究了有、无承载力约束下的公交网络演化特性；最后提出公交网络稳定性概念和分析指标,考虑网络上的流量分布特性,研究了不同外部影响条件下公交加权网络的动力学行为,为提高公交网络稳定性提供理论依据。
具体来讲,本文的研究工作主要有如下几个方面：
1.提出了基于客流的城市公交加权复杂网络模型构造方法。考虑公交网络上的客流特征,将现实城市公交系统抽象构建为三类加权复杂网络模型,突破了传统公交复杂网络理论研究以静态物理统计特性为出发点的局限。系统梳理了复杂网络加权特征度量指标,并结合网络流量特征提出了一些加权度量指标,丰富了加权复杂网络的统计指标。
2.对基于客流量的城市公交无权和加权复杂网络进行了统计分析实证研究。在对北京公交客流数据收集与处理的基础上,采用统计物理学、计算机模拟等方法分别针对北京地面公交系统、轨道交通系统以及融合地面公交和轨道交通的双方式公交系统进行了三类复杂加权网络、7个子系统维度的统计分析,通过无权静态拓扑结构与加权动态网络结构的复杂网络特征比对分析,多角度、多维度地挖掘了公交系统的结构组织特征和功能,探讨了公交系统演化的机理。
3.研究了有、无承载力约束的城市公交加权复杂网络演化模型,以真实合理地再现公交网络的演化过程。在综合考虑公交系统演化过程中的乘客利益、公交公司利益、地理空间位置等影响因素基础上,通过理论解析与数值模拟的方法,分别研究构造了基于客流分布及扰动影响动态变化的公交线路、公交站点以及公交换乘加权网络演化模型,探讨了演化过程中的流量动态行为。通过解析公交网络存在客流承载能力限制的机理,本文进一步研究了在网络点强度、边权承载能力有限的条件下,公交加权网络演化模型的网络结构和流量分布特性,探讨了公交网络的承载力约束阈值,挖掘出了实际公交加权网络结构统计特性的产生机制。
4.研究了城市公交加权复杂网络的动力学行为,对加载了流量信息的公交网络稳定性进行了分析。本文提出了公交加权网络的稳定性概念和分析指标,分别采用交通动力学和级联失效两种方法来研究公交加权网络的动态稳定性,即考虑网络上流量具有自主性和选择性行为,采用公交OD配流理论来研究公交换乘网络上的动力学行为；构建面向加权网络的耦合映像格子(CML)稳定性分析模型,通过考虑流量的局域再分配动态行为,研究具有混沌动力系统特征的网络无权和加权要素的相互耦合作用而导致的公交站点加权网络级联失效行为。
ABSTRACT:Urban public transit network (PTN) is a complex and dynamic system, which is the interaction result between topology and dynamic flow distribution. It is also the evolution result of many factors during the long-term development, such as socio-economic activities, spatial structure, geographical features, cultural customs, etc. As to the complexity of PTN, a new method is provided by the complex network (CN) theory for studying its mechanism and the coupling function in recent years. With more and more research on CN theory at home and abroad, the study on its evolution process and dynamic behavior is paid more close attention. PTN, as a mixture of technic and social network, is a compound complex network with spatiotemporally dynamic complexity.In the study on its complexity, not only the characteristics of topology but also the ones of weighted network loaded with dynamic passenger flow should be studied. However, there is little research on the weighted PTN based on passenger flow at present. In order to explore the PTN's organizational structure and characteristics, it should be rediscovered in the view of dynamic changes of its impact factors, and the evolutionary process should be simulated. It is significant to research these issues, which has important theoretical and practical value on the optimization PTN in the view of CN theory.
In this paper, the PTN loaded with passenger flow is taken as the research object to study its dynamic behaviors and structure characteristics based on CN theory and PTN planning theories. Firstly, the modeling approaches of weighted complex PTN and measures of its structure characteristics are proposed; secondly, based on the systematic characteristics of weighted complex PTN, the evolution mechanisms of these networks are explored, and the evolution models are presented according to different abstract forms of weighted complex PTN. The evolution characteristics of these models are also analyzed with and without capacity constraints. Lastly, the concept of PTN's stability and related indicators are proposed, and the dynamic behaviors are studied under different faults or attacks with considering flow distribution, which provides theory bases for improving the PTN. Specifically, the main content of this dissertation and innovation are summarized as follows:
1. Firstly, models for constructing the weighted complex PTN are proposed. The realistic urban public transit system is abstracted to three kinds of weighted complex network models, which integrates the dynamic flow information into the static topology. The measuring indexes for weighted complex network are introduced systematically and some new ones are proposed based on the characteristics of passenger flow in the network, which enriches the measuring indexes of weighted complex network.
2. Secondly, weighted PTN based on passenger flow and topologic network are statistically analyzed and empirically studied. Based on the passenger flow data collected and disposed from Beijing PTN, related theories, such as statistical physics, computer simulation and so on, are used to analyze Beijing bus system, subway system, multimode public transit system and their seven subsystems. The characteristics and functions of PTN's structure are explored from multi-view and multi-dimension through comparative analysis of the topology and weighted dynamic network.
3. Thirdly, the evolution models of weighted PTNs with and without capacity constraints are studied to reproduce the evolution process. Based on the overall consideration of benefits of passengers and transportation companies, and factors of geographical space and spatial position, etc., the evolution models of weighted PTNs for route, station and transfer are built and studied respectively through the methods of theoretical analysis and numerical simulation, and the dynamic behaviors of the flow in the evolution process are also discussed. In addition, through the analysis of flow constraint mechanism in PTN, the structure and characteristics of flow distribution in the evolution models are presented further under the limited capacity of node strength and edge weight, the capacity thresholds are investigated, and the production mechanism of statistical characteristics in realistic weighted PTN is explored.
4. Finally, the stability of weighted PTN loaded with passenger flow is analyzed. In this section, the concept of weighted PTN's stability and its analysis indexes are presented, and the dynamic stability of Beijing PTN is studied by the methods of traffic dynamics and cascading failures respectively. Namely, considering the autonomous and selective behaviors of the flow distribution in the whole network, the dynamic behaviors of PTN are studied based on theory of OD flow distribution; a Coupled Map Lattices model for weighted network is proposed, through the local flow redistribution, the cascading failures caused by the coupling of weighted and topologic network factors, which are with the characteristics of chaos dynamic system, are analyzed.
本文以加载了客流动态行为的城市公共交通系统作为研究对象,基于复杂网络理论和公交系统规划理论,对城市公交加权复杂网络的结构特征及动力学行为进行了研究。首先提出了加权复杂网络特征度量指标和模型构建方法,利用统计分析与比较分析相结合的方法,对城市公交无权和有权复杂网络结构的统计特性进行了实证研究；其次在总结公交加权网络系统特性的基础上,探索形成这些网络结构的演化机理,针对不同的公交网络抽象形式构建了加权网络演化模型,研究了有、无承载力约束下的公交网络演化特性；最后提出公交网络稳定性概念和分析指标,考虑网络上的流量分布特性,研究了不同外部影响条件下公交加权网络的动力学行为,为提高公交网络稳定性提供理论依据。
具体来讲,本文的研究工作主要有如下几个方面：
1.提出了基于客流的城市公交加权复杂网络模型构造方法。考虑公交网络上的客流特征,将现实城市公交系统抽象构建为三类加权复杂网络模型,突破了传统公交复杂网络理论研究以静态物理统计特性为出发点的局限。系统梳理了复杂网络加权特征度量指标,并结合网络流量特征提出了一些加权度量指标,丰富了加权复杂网络的统计指标。
2.对基于客流量的城市公交无权和加权复杂网络进行了统计分析实证研究。在对北京公交客流数据收集与处理的基础上,采用统计物理学、计算机模拟等方法分别针对北京地面公交系统、轨道交通系统以及融合地面公交和轨道交通的双方式公交系统进行了三类复杂加权网络、7个子系统维度的统计分析,通过无权静态拓扑结构与加权动态网络结构的复杂网络特征比对分析,多角度、多维度地挖掘了公交系统的结构组织特征和功能,探讨了公交系统演化的机理。
3.研究了有、无承载力约束的城市公交加权复杂网络演化模型,以真实合理地再现公交网络的演化过程。在综合考虑公交系统演化过程中的乘客利益、公交公司利益、地理空间位置等影响因素基础上,通过理论解析与数值模拟的方法,分别研究构造了基于客流分布及扰动影响动态变化的公交线路、公交站点以及公交换乘加权网络演化模型,探讨了演化过程中的流量动态行为。通过解析公交网络存在客流承载能力限制的机理,本文进一步研究了在网络点强度、边权承载能力有限的条件下,公交加权网络演化模型的网络结构和流量分布特性,探讨了公交网络的承载力约束阈值,挖掘出了实际公交加权网络结构统计特性的产生机制。
4.研究了城市公交加权复杂网络的动力学行为,对加载了流量信息的公交网络稳定性进行了分析。本文提出了公交加权网络的稳定性概念和分析指标,分别采用交通动力学和级联失效两种方法来研究公交加权网络的动态稳定性,即考虑网络上流量具有自主性和选择性行为,采用公交OD配流理论来研究公交换乘网络上的动力学行为；构建面向加权网络的耦合映像格子(CML)稳定性分析模型,通过考虑流量的局域再分配动态行为,研究具有混沌动力系统特征的网络无权和加权要素的相互耦合作用而导致的公交站点加权网络级联失效行为。
ABSTRACT:Urban public transit network (PTN) is a complex and dynamic system, which is the interaction result between topology and dynamic flow distribution. It is also the evolution result of many factors during the long-term development, such as socio-economic activities, spatial structure, geographical features, cultural customs, etc. As to the complexity of PTN, a new method is provided by the complex network (CN) theory for studying its mechanism and the coupling function in recent years. With more and more research on CN theory at home and abroad, the study on its evolution process and dynamic behavior is paid more close attention. PTN, as a mixture of technic and social network, is a compound complex network with spatiotemporally dynamic complexity.In the study on its complexity, not only the characteristics of topology but also the ones of weighted network loaded with dynamic passenger flow should be studied. However, there is little research on the weighted PTN based on passenger flow at present. In order to explore the PTN's organizational structure and characteristics, it should be rediscovered in the view of dynamic changes of its impact factors, and the evolutionary process should be simulated. It is significant to research these issues, which has important theoretical and practical value on the optimization PTN in the view of CN theory.
In this paper, the PTN loaded with passenger flow is taken as the research object to study its dynamic behaviors and structure characteristics based on CN theory and PTN planning theories. Firstly, the modeling approaches of weighted complex PTN and measures of its structure characteristics are proposed; secondly, based on the systematic characteristics of weighted complex PTN, the evolution mechanisms of these networks are explored, and the evolution models are presented according to different abstract forms of weighted complex PTN. The evolution characteristics of these models are also analyzed with and without capacity constraints. Lastly, the concept of PTN's stability and related indicators are proposed, and the dynamic behaviors are studied under different faults or attacks with considering flow distribution, which provides theory bases for improving the PTN. Specifically, the main content of this dissertation and innovation are summarized as follows:
1. Firstly, models for constructing the weighted complex PTN are proposed. The realistic urban public transit system is abstracted to three kinds of weighted complex network models, which integrates the dynamic flow information into the static topology. The measuring indexes for weighted complex network are introduced systematically and some new ones are proposed based on the characteristics of passenger flow in the network, which enriches the measuring indexes of weighted complex network.
2. Secondly, weighted PTN based on passenger flow and topologic network are statistically analyzed and empirically studied. Based on the passenger flow data collected and disposed from Beijing PTN, related theories, such as statistical physics, computer simulation and so on, are used to analyze Beijing bus system, subway system, multimode public transit system and their seven subsystems. The characteristics and functions of PTN's structure are explored from multi-view and multi-dimension through comparative analysis of the topology and weighted dynamic network.
3. Thirdly, the evolution models of weighted PTNs with and without capacity constraints are studied to reproduce the evolution process. Based on the overall consideration of benefits of passengers and transportation companies, and factors of geographical space and spatial position, etc., the evolution models of weighted PTNs for route, station and transfer are built and studied respectively through the methods of theoretical analysis and numerical simulation, and the dynamic behaviors of the flow in the evolution process are also discussed. In addition, through the analysis of flow constraint mechanism in PTN, the structure and characteristics of flow distribution in the evolution models are presented further under the limited capacity of node strength and edge weight, the capacity thresholds are investigated, and the production mechanism of statistical characteristics in realistic weighted PTN is explored.
4. Finally, the stability of weighted PTN loaded with passenger flow is analyzed. In this section, the concept of weighted PTN's stability and its analysis indexes are presented, and the dynamic stability of Beijing PTN is studied by the methods of traffic dynamics and cascading failures respectively. Namely, considering the autonomous and selective behaviors of the flow distribution in the whole network, the dynamic behaviors of PTN are studied based on theory of OD flow distribution; a Coupled Map Lattices model for weighted network is proposed, through the local flow redistribution, the cascading failures caused by the coupling of weighted and topologic network factors, which are with the characteristics of chaos dynamic system, are analyzed.
引文
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