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城市交通网络拓扑结构复杂性研究

2010-08-05
城市交通,复杂网络,级联失效,鲁棒性,复杂性研究
城市交通网络拓扑结构复杂性研究

论文中英文摘要
  作者姓名:吴建军
  论文题目:城市交通网络拓扑结构复杂性研究
  作者简介:吴建军,男, 1973年5月出生,2004年9月师从于北京交通大学高自友教授,于2008年6月获博士学位。现为北京交通大学讲师。
  
城市交通网络拓扑结构复杂性研究中文摘要
  
  城市交通作为交通运输系统的重要组成部分,是承载人类活动的基本构件之一,是城市繁荣、有序和高速发展的主要支撑条件。而日益严重的交通问题,严重影响了城市的经济建设和运行效率,也给人们的工作和生活带来了种种不便与损害,已经成为制约城市可持续发展的主要瓶颈。

  众所周知,城市交通系统是一个典型的、开放的、复杂巨系统,城市交通运行规律极其复杂。在新的形势下,要缓解城市交通问题,构筑和谐交通体系,需要应用复杂系统的研究方法,结合系统科学的原理、多学科交叉的理论体系对城市交通系统复杂性开展深入的理论和应用研究,从整体、宏观的角度去认识整个交通系统,理解城市交通网络演化的内在机理和运行规律。城市交通系统由道路子系统、流量子系统以及管理子系统组成,它的复杂性涉及到方方面面。具体包括以下几点:(1)人-车流以及道路、交叉口、枢纽等交通工程及控制设施众多,且各组分之间联系紧密;(2)系统中的人-车流具有智能性,能够对周围环境变化作出反应,具有自组织、自适应和自驱动等能力;(3)网络中运动的人-车流之间存在强烈的非线性相互作用;(4)交通系统具有动态性和随机性,处于不断地发展变化之中;(5)系统的高度开放性又进一步加深了交通系统的复杂性。因此,与其相关问题的研究极具挑战性,特别是网络结构与出行者博弈行为二者之间的相关关系。

  近几年发展起来的复杂网络方法,为我们研究系统复杂性提供了一个新视角、新方法。小世界效应与无标度特性的科学发现掀起了对复杂网络结构及其动力学特性的研究热潮,提高了人们对现实世界的科学认识。随着研究的深入,对于复杂网络的探讨已经渗透到包括社会学、生物学、物理学、经济学、计算机机科学以及交通运输等各领域中。

  应用复杂网络理论,从理论上分析城市交通网络结构复杂性,是研究复杂交通网络的关键所在,同时也是城市交通网络研究的基础理论问题之一。研究城市交通网络结构复杂性,不仅包括交通网络本身的拓扑特性,更为重要的是要研究不同网络拓扑条件下城市交通所体现出来的特征。城市交通网络具有其它复杂网络相似的一些拓扑特性,但又具有不同于其它复杂网络的显著特点,如自主性和选择性。同时人们逐渐认识到,解决大城市交通问题,必须以路线及道路网络为对象进行全面的分析。而且对本身是动态实体的城市交通网络来说,适应性和动态性也是它具有的基本特性。这意味着城市交通网络拓扑结构不是固定的、成熟的、也不是一成不变的。相反由于外部作用的驱动或者内部元素的作用,允许它随时间进行演化和调节。因此开展此方面的研究可以从宏观角度帮助我们理解城市交通网络演化的内在机理和运行规律,进而为提出解决交通问题的有效方法提供理论基础。对切实提高整个路网承载能力,充分利用现有交通资源,减少我国交通建设设计、管理和控制的盲目性,科学地制定城市交通的发展战略规划,发展先进的交通管理与控制技术打下坚实的理论基础。

  本论文主要基于复杂网络理论和交通出行者行为科学,通过融合城市交通网络自身的一些特点,研究了城市交通网络拓扑结构复杂性。具体来讲,本论文研究工作主要有如下几个方面:

  (1)基于复杂网络及交通出行者行为科学的相关理论,建立了不同路网拓扑结构(无标度、小世界和随机网)与交通流量之间的相关关系,分析了三种路网拓扑结构的交通承载力,发现当交通需求量较小时,随机网络的承载力较大。随着交通需求量的增加,无标度网络反而表现出较大的承载力。因此,对于大规模的城市交通网络,无标度网络是较理想的网络拓扑。在上述结论的基础上,进一步研究了此类拓扑网络中度分布指数、交通需求量与交通阻塞之间的关联关系,进而为解决网络拓扑与流量承载力的关系难题提供了新的视角。此外,基于网络的观点进一步讨论了最优交通网络拓扑,分析了此类拓扑网络中度分布指数、交通需求量与交通阻塞之间的关联关系;

  (2)交通网络上的级联失效问题是研究其复杂性的一个热点问题。在实际的交通网络中,由于受到路段阻抗的影响,从而改变人们的出行路径选择行为,因此城市交通网络上的级联失效过程较其它网络更加复杂。本论文研究了用户平衡条件下城市交通网络中的级联失效问题,建立了不同去除策略下的级联失效模型、边-点-边级联失效模型和点能力动态更新的级联失效模型,分析了级联失效的过程及机理,探讨了相关的控制措施及缓解方法;建立了基于介数的能力分配模型以提高网络的鲁棒性,并把模型扩展到交通网络上,提出了考虑有效性的路段重要性度量方法。在上述基础上提出了有限资源条件下的能力分配模型和抵抗网络级联失效的利润函数,分析了路段重要性分布的幂律特性以及利润与能力分配系数之间的关系,从而降低了城市交通网络产生级联失效的风险;

  (3)城市交通中蕴涵着许多经济学问题,例如用户均衡的效率损失上界以及缓解交通阻塞的经济方法。结合交通出行行为科学和复杂网络理论,论文研究了不同网络拓扑和个体路径选择行为条件下城市交通网络上的统计特性及其一般规律。分析了非线性阻抗函数时用户均衡效率损失上界,发现不同拓扑上的用户均衡效率损失是有界和有序的,均匀网络具有较好的抗自由竞争能力,而高聚类高集群的非均匀网络这种能力较差。此外,通过研究最小支撑树上的流量分布规律,发现最小支撑树上流量占总系统流量的比例接近于一个常数。进一步研究表明,交通网络上的阻塞与OD流量之间存在某种幂律关系。这些一般规律对进行交通网络规划与设计具有科学的理论意义;

  (4)通过分析典型组元上的统计特性,提出了用以缓解交通阻塞的三种策略,结论表明提高最小费用权重支撑树上的一小部分路段能力就可以有效的改善整个交通系统的阻塞程度;而提高最小支撑聚类上的一小部分路段能力就可以有效改善局部交通拥堵;

  (5)最后通过构建两种公交网络拓扑抽象,发现当不考虑中间站点时,北京市公交网络度分布具有幂律特性,而当考虑中间站点时,北京市公交网络却具有明显的小世界特性。此外,在上述基础上对北京市公交网络的鲁棒性问题进行了模拟攻击实验,发现北京市公交网络具有较好的局部有效性,但其全局有效性较差。在实证统计分析的基础上,研究了国家高速公路网络拓扑特性及其鲁棒性,并对2008年春节南方雪灾事件进行了模拟攻击实验。

  关键词:城市交通;复杂网络;级联失效;鲁棒性

Studies on the Complexity of Topology Structure in the Urban Traffic Network
Wu Jianjun
ABSTRACT
  
  As an important component of traffic systems, urban traffic is not only a basic part to bear the human activities, but also the main supporting condition for the city prosperity, ordered and high-speed developments. However, increasing traffic problems have affected the city’s economic construction and the operating efficiency, even do much harm and inconvenience to our life and work. Therefore, traffic problems have become a great bottleneck of the urban sustainable development.

  It is well known, the urban traffic is a classic, exoteric and complex system, and its running rule is also intricate. Under the new situation, in order to alleviate traffic problems in large cities and build a harmonious transportation system, it is necessary to develop theoretical and applied research with complex systems methods through combining the principle of system sciences and the interdisciplinary theoretical system. On the other hand, we should recognize and understand the evolution and internal operating mechanism of urban traffic network from the whole and macro viewpoints. Urban traffic system consists of road sub-system, flow sub-system and management sub-system, in which every aspect is very complexity. It has the following features: (1) There are large number of traffic engineering and control facilities with a close links between the various components, such as people-vehicle flow, road, intersection, and hub, and so on. (2) People-vehicle flow in the traffic system has the intelligence, able to respond to changes in the surrounding environment. Additionally, the system has the self-organizing, adaptive and self-drive capacity, etc. (3) There has a strong nonlinear interaction between the people and vehicle flow in the traffic system. (4) The traffic system with dynamic and stochastic is constantly development. (5) A high degree of openness is further deepened the complexity of the transport system.
Therefore, it is a challenging for us to study the related problem, especially for the correlation between network structure and traveler game behavior.

  Complex networks theory provides a new view and method for studying the system complexity. The finding of small-world effects and scale-free property has attracted a great deal of attention to the complex network structure and dynamics in recent years, which raises the science awareness of the real world. With the in-depth research for complex networks, it has infiltrated including sociology, biology, physics, economics, computer science, as well as transport and other areas.

  The key problem of complex traffic networks is to analyze their structure complexity including the topology complexity and the characteristics in different topologies, which is also a foundational theory of the urban traffic. The urban traffic network has some similar topology characteristics as other complex networks. However, many different properties are found in the urban system, such as autonomous and selective behaviors. Moreover, it has become a commonsense that we should study the urban traffic systematically from road lane to road network. In addition, adaptability and dynamic characteristics are also important properties, which mean that their topology structures are not fixed and unchangeable, and they will evolve with time under the external and internal force drive.

  Therefore, the related study can help us to understand the evolution of urban traffic networks within the mechanism and operation rules from a macro perspective, and then propose the effective way to alleviate the traffic problems. Meanwhile, it can provide a solid theoretical basis to increase the capacity of road network efficiently, full use of existing transportation resources, reduce the blindness in the traffic design, management and control, scientifically formulate urban transport development strategy planning and development of advanced traffic management and control technology to lay a solid theoretical basis.

  This dissertation, from the points of complex network theory and traveler behavioral sciences, studies the complexity of topology structure for the urban traffic network with the consideration of some features in the traffic system. The main contents of this dissertation are summarized as follows:

  (1) Based on complex network and traveler behavioral science theory, the correlation is proposed between the road network topologies (scale free, small world and random networks) and the traffic flow. We analyse the traffic bearing capacity in three kinds of road network topology. It is found that when the traffic demand is small, random networks can bear a larger traffic flow. As the traffic demand increases, scale-free network shows a greater carrying capacity. Therefore, for large-scale urban traffic network, scale-free network is an ideal network topology. Based on the above findings, the relationship between the degree distribution exponent, traffic demand and traffic congestion is further studied. It provides a new perspective for us to study the problem between the network topology and the traffic carrying capacity. In addition, we further discuss the optimal transportation network topology with the network-based point of view, and give an analysis of the degree distribution exponent, traffic demand and traffic congestion in this topology.

  (2) Cascading failure is a hot issue to study the complexity on the transport network. In the real traffic network, due to the impact of link cost, people will change their travel route choice behavior. So in the urban traffic network, the process of cascading failure is more complex than the other networks. This dissertation examines this problem with the consideration of the user equilibrium, proposes three models, e.g., different removal strategies cascading failures model, edge-node-edge cascading failure model and dynamical node-capacity update cascading failure model, to capture the dynamics of cascading failures in the urban traffic network, and analyse the cascading failure process and mechanism. Based on these models, we give the relevant control strategies and alleviate methods. Additionally, a capacity assignment model is established to improve the network’s robustness. Then, we extend the model to traffic networks and propose a new method to measure the link importance by considering the efficiency of traffic networks. The link-importance-based capacity assignment model with limited resources and profits functions to resist the cascading failures are given. The power-law form of link-importance distribution and the relationship between the profit function and assignment parameter are analysed. The results can be used to decrease the risk of cascading failures of traffic network.

  (3) Thirdly, many economic problems exist in the urban traffic, e.g., the upper bound of the efficiency loss for user equilibrium and the economical method to alleviate the traffic congestion. The efficiency loss for user equilibrium in different topologies with nonlinear cost functions and the general law under the traffic congestion condition are investigated. Results show that the upper bound of the loss is limited and ordered. And there exists a higher resistance to the free competition for homogeneous networks than that of heterogeneous networks. Based on these results, the bottleneck identification and the strategy to alleviate the traffic congestion are proposed. In addition, by studying the traffic flow distribution rule in the minimum spanning tree, it is found that the proportion of the minimum spanning tree in the total system is close to a constant. Further studies have shown that the relationship between the traffic congestion on the network and the OD flow exhibits the power-law form. These general rules have scientific theoretical significance in the traffic network planning and design.

  (4) By analyzing the statistical properties in the typical components, three strategies to relieve traffic congestion is proposed. The conclusion shows that raising a small section of link capacity in the minimum cost weight spanning tree can effectively improve the overall traffic system congestion level. While, increased a small portion of road capacity in the minimum spanning cluster is effective in improving local traffic congestion.

  (5) Finally, two kinds of public transit network topology are constructed. It is found that when not considering the middle of the site, the Beijing public transit network has a power-law degree distribution property. But when considering the middle of the site, the Beijing public transit network has obvious characteristics of a small world effects. In addition, based on the above-mentioned methods, Beijing's public transit network robustness is investigated by a simulated attack experiment. We found that Beijing public transit network has a good local effectiveness, but the overall effectiveness is poor. Based on the statistical analysis, the national highway network topology characteristics and robustness is researched. Additionally, an attack experiment is simulated for the 2008 South Spring the snowstorm events.
Key words: Urban traffic; Complex network; Cascading failures; Robustness
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本栏目主要介绍科学技术方面,包括现代科学研究成果、现代科技、现代科学技术、城市交通网络拓扑结构复杂性研究等。特别关注有关人与文化的价值方面的研究。

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