【作者】 赵晖；

【导师】 高自友；

【作者基本信息】 北京交通大学 ， 交通运输规划与管理， 2007， 博士

【摘要】 网络的结构复杂性、演化机制及动力学行为是一般输运网络研究的基础性科学问题,对认识大规模交通运输网络具有重要意义。本文从统计物理的观点,运用理论解析及数值模拟等手段,对一般输运网络的演化模型及动力学特征进行了若干探讨和研究。首先,本文对一般输运网络的加权模型做了一系列的相关研究。根据一般输运网络度、强度、权重分布、强度-度相关性、聚类特性以及相配性等相关统计特征,并结合考虑网络演化的某些特殊规律,提出了若干加权网络模型。这些模型通过引入不同演化机制,不仅可以再现实际输运网络中的多种统计规律,还能够再现小变量饱和、指数甩尾等较为细致的网络统计特征。在复杂网络科学的研究初期,人们主要关注的是小世界效应、无标度现象、层次性、模块性等网络拓扑结构特征。随着研究的不断深入,人们开始注意到网络的隐含特性和框架结构。本文通过对若干实际网络和模型网络中不同重要程度Hub结点统计规律的研究,从节点重要度的角度研究了输运网络的主要框架。传播动力学是网络科学中的一类重要的研究分支。本文通过考虑一般输运网络的模块性和小世界特性,分析了模块结构对传播动力学的影响。研究表明网络的模块结构对拥堵传播的传播速度、范围以及传播中出现的同步现象都有较为明显的作用,这在一定程度上揭示了网络模块结构和传播之间的某些内在规律。级联失效在大规模输运网络上时有发生,且对整个系统的破坏性巨大。如何应对级联失效所引起的大规模故障一直是网络科学的重要课题之一。本文通过对级联失效产生机制较为深入的分析,并结合无标度网络的拓扑特征,提出了利用导航策略来控制级联失效的方法。研究表明,采用合适的导航策略能够有效提高网络稳健性,避免级联失效的发生。此外,本文通过考虑交通平衡状态下不同拓扑结构输运网络上的流量分配状态,研究了规则网络、随机网络、小世界网络以及无标度网络上流量分布的规律性。认识这些一般输运网络上的流量分布规律,对理解现实世界中的各种交通现象有重要理论价值和实际意义。更多还原

【Abstract】 To characterize the structure complexity, evolutionary mechanisms and dynamic behaviors of network is the key in researching transportation network. In this paper, by using the theoretical analysis and numerical simulations, we studied the evolution and dynamical behaviors on general transportation networks in the statistical mechanics point of view.Firstly, we made a series researches on the weighted models of general transportation networks. By considering the statistical properties of transportation networks, such as degree distribution, strength distribution, weight distribution, correlation of strength and degree, clustering coefficient and assortativity, and so on, we evolved some weighted networks models. The different evolution processes can give various statistical features of real transportation systems successfully. Especially, the models can reproduce features such as saturation for small variables, exponential decay, etc.At the beginning of the research on the complex network science, people focus on the small world effect, scale free phenomena, hierarchy architecture, modularity structure, and so on. With the deeper insight into this field, people begin to realize the hidden features and structures of networks. In this paper, we studied the statistical characteristics of Hub nodes in various important levels, and to reveal the main structures of transportation networks in the nodes’ importance point of view.Epidemic dynamic is one of the most important problems in transpiration network science. By considering the modular structure and small world property of real transportation system, we study the effect of modularity on the epidemic behaviors on networks. It is found that the modularity prevent the rate, extent and the synchronization behavior of the propagation. It reveals some implicit regularities of the relationship between the modularity and the epidemic spreading dynamics.Cascading failures can take place in large transportation networks, such as power grid, Internet, etc, sometimes. It may bring catastrophe of the whole system. How to defend the cascade break down is one of the most important problems in researching network science. In this paper, we investigate the cascading failure by considering the degree based navigation strategy. It is found that by using the proper navigation strategy, it can reduce the risk of cascading failure considerably.In addition, we investigate the statistical properties of the traffic dynamics in equilibrium state on transportation networks with different topology, including regular,random, small world and scale free networks. To understand the properties in trafficequilibrium state is important in realizing the traffic phenomena of real transportationsystems.更多还原