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。
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。
本论文主要从复杂网络理论和网络优化观点出发,结合城市交通网络自身的特点,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)将用户平衡配流与复杂网络理论相结合,研究了网络拓扑对交通阻塞的影响以及网络拓扑与交通流量的关系,并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)级联失效是研究复杂网络的一个重要分支,本论文应用复杂网络理论研究了城市交通网络上的级联失效问题,建立了三个城市交通网络级联失效模型,即基于不同移除方式的城市交通网络级联失效模型、边-点-边级联失效模型以及点能力动态更新级联失效模型,并在不同网络上进行了模拟实验;
(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。本论文研究了非线性阻抗函数条件下不同网络拓扑上的用户平衡效率损失以及阻塞条件下城市交通网络上呈现的一般规律。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乃,而高聚类高集群的非均匀网络这种能力较差。并以此为基础,研究了基于网络的交通瓶颈识别及改善策略;
(4)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;
(5)最后对北京市公交网络及中国国家高速公路网络拓扑复杂性和鲁棒性进行了实证和攻击实验分析。
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.
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.
This dissertation, from the points of complex network theory and network optimization, studies the complexity of topology structure for the urban traffic network. The main contents of this dissertation are summarized as follows:
(1) Firstly, by combining the user equilibrium assignment with the complex network theory, we study the effects of network topology on the traffic network. Then, the interactions between the network topology and traffic flows are researched. Further, the optimal traffic topology is evaluated based on the complex network perspective, and the relationship among degree distribution, traffic demand and traffic congestion is analyzed.
(2) Secondly, cascading failures are an important branch in the dynamics of the complex network. In the thesis, we firstly propose three models, 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. Moreover, simulation tests are given in different network topologies.
(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 homogenous networks than that of heterogenous networks. Based on these results, the bottleneck identification and the strategy to alleviate the traffic congestion are proposed.
(4) Then, 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.
(5) Finally, the complexity and robustness of Beijing transit network and Chinese highway network are studied through simulating and attacking experiments.
引文
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