基于多子网复合复杂网络模型的互联网拓扑演化模型及相关性质研究
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摘要
目前,复杂网络的理论研究已经被广泛应用于社会学、生物学、交通、计算机和通信等领域。但在各领域中,理论研究成果在实际中的应用还不够深入,因此,将复杂网络理论付诸十具体的应用之中必将成为今后复杂网络的研究热点。
互联网是一个典型的复杂系统,应用复杂网络理论研究互联网拓扑结构、理解互联网演化机制、建立互联网拓扑演化模型将对评估网络抗毁性、优化网络性能、设计高效网络协议等方面具有重要的实际意义。互联网拓扑因划分粒度的粗细,可分为自治系统级拓扑和路由器级拓扑。目前已有的自治系统级或路由器级拓扑演化模型普遍存在模型所生成的网络与实际网络之间在某些网络拓扑特征性质方面差异较大、不能确切反映网络演化内在成因规律等问题。针对互联网中存在着不同类个体间多种关系的特点,本文利用我子网复合复杂网络模型,从网络拓扑特征分的的角度展开研究,对互联网自治系统级拓扑和路由器级拓扑进行了实证分析,根据实证分析结果提出了互联网自治系统级和路由器级拓扑演化模型,并在此基础上对互联网中的级联失效现象进行了研究。本研究为基于复杂网络的互联网的研究提供了理论支撑,具有重要的理论意义与应用价值。论文的主要研究工作如下：
(1)互联网自治系统级拓扑和路由器级拓扑的实证研究。利用权威的CAIDA-Skitter项11拓扑实测数据,对自治系统级互联网拓扑的的度、簇系数等网络特征量度进行分析。通过自主研发的网络拓扑测量软件CERNET-MTR,对中国教育和科研计算机网(CERNET)进行测量并得到其路由器捅扑和网站页面链接的实测数据,对CERNET中路由器级互联网拓扑的度、最短路径长度、介数等基本特征量度进行分析。由上述分析结果,发现了新加入的自治系统节点受地理位置影响、自治系统级互联网中存在服务提供方节点构成的连通骨干子网、实际网络设备性能制约路由器节点的连接度最大值等影响网络拓扑演化的现象,为后续自治系统级和路由器级互联网拓扑演化模型的提出提供可靠依据。
(2)基于多子网复合复杂网络模型的路由器级互联网拓扑演化模型研究。基于(1)中得到的实证分析结果,提出了基于多子网复杂网络模型的路由器级互联网拓扑演化模型,该模型利用多子网复合复杂网络模型的子网加载运算,将网站子网加载到路由器子网中,综合考虑路由器负载、路由器硬件限制等实际影响因素,从网络流量传输优化的角度出发,由路由器间所需流量传输带宽及路由器负载决定新增路由器节点的偏好择优机制。通过计算机仿真实验农明,该模型在度分布、簇系数、平均最短路径、最大连接度、叶子节点数量等网络特征量度与同等规模实际互联网较为吻合,能够较好的体现实际路由器网络拓扑结构的幂律特性、小世界特性层次性等网络特征
(3)基于多子网复合复杂网络模型的自治系统级互联网拓扑演化模型研究。自治系统节点类型、网络的增长和老化、局域世界特性等都是自治系统级互联网演化过程中必须考虑的实际影响因素。针对这些因素,提出了基于多子网复合复杂网络模型的自治系统级互联网拓扑演化模型,在该模型中将互联网中的自治系统节点根据其功能分为两类：服务提供方节点和服务消费方节点,自治系统节点问连边的关系分为网络服务消费方——网络服务提供方关系(C2P)和对等关系(P2P)。借鉴经典的BA演化模型思想,将地理位置、价格和服务质量等因素作为偏好择优机制的影响因子,对不同类型的新增节点采用小同的建立连边的策略,并利用删除节点和和边体现网络老化现象。通过对该模型200次仿真实验结果所取的平均值与实际自治系统级互联网的网络特征值进行对比,结果显示该模型能够较好的模拟出自治系统级互联网的度分布、簇系数、平均最短路径、核数、介数、叶子节点数量等网络拓扑特征量度,准确有效的刻画了实际自治系统级互联网的节点度分布、小世界特性、异配性、聚合性、层次性、富入俱乐部性等网络特征。
(4)基于多子网复合复杂网络模型的级联失效研究。级联失效是网络脆弱性的一个重要表现。基于多子网复合复杂网络模型,提出了一个带有可调参数的级联失效策略,并引入了一种新的度量网络鲁棒性的测度——级联失效阈值。通过仿真和理论分析证明,该策略可以有效地评估网络产生级联失效的阈值,为有限资源下的网络拓扑结构优化,抑制网络拥塞提供有效的建议,可指导实际网络拓扑的负荷分配,从而达到提高网络鲁棒性的目的。该级联失效策略也可应用于随机网络、小世界网络、无标度网络等多种,典型复杂网络拓扑,并通过仿真实验证明相对于上述3种典型复杂网络拓扑结构,基于多子网复合复杂网络模型的路由器级互联网演化模型所生成的网络拓扑结构具有更强的鲁棒性。
本文提出的基于多子网复合复杂网络模型的自治系统级和路由器级互联网演化模型解决了现有互联网演化模型无法描述互联网中多类个体间多种关系的问题,体现了由多类个体、个体间多种关系共同决定互联网演化的思想,能够较为真实的揭示互联网的形成机理和演化规律,所生成的网络拓扑结构与同规模实际网络拓扑特征较为吻合。
At present, the theoretical study of complex networks has been widely used in the fields of sociology, biology, communications, computer and communication. But in those fields, theoretical research results are not enough deep in practice, therefore, complex network theory is applied into specific application, which will become the research focus in the future.
Internet is a typical complex system, complex network theory is used to study the topology and evolution mechanism of Internet, establishment of the network topology evolution model will has important practical significance for estimating network security and survivability, optimizing network performance, designing an efficient network protocol. According to different granularity, Internet topology can be divided into autonomy system-level topology and router-level topology. For the existing autonomy system-level or router-level topology evolution model, there are a lots of problems that some network topological characteristics are different between network generated by model and actual network, and network evolution inherent causes and laws are not accurately reflected. In this dissertation, for the characteristics of different kinds entities and their relationships in Internet, Internet autonomy system-level topology and router-level topology are studied by multi-subnet composited complex network model. Based on these, the cascading failure of Internet is studied. The above studies could improve the development of complex system, which having theoretical and applied significance. The main works in this dissertation include:
(1) Empirical research of Internet autonomy system-level topology and router-level topology. Through obtaining authoritative CAIDA-Skitter project topology measured data, from the perspective of network characteristics analysis, the basic characteristics, such as degree, clustering coefficient and so on, of autonomy system-level Internet topology is analyzed. Through self-developed network topology measurement software CERNET-MTR, the measured data of router topology and website page link of the China Education and Research Network (CERNET) are obtained. Using the theory of Multi-subnet Composited Complex Network, the basic characteristics such as degree, shortest path length, betweenness and so on, of topology of CERNET router-level Internet are analyzed. Based on these, accurate understanding of Internet autonomy system-level and router-level topology and its evolution law are obtained. The above studies could act as the theoretical foundation for follow-up Internet autonomy system-level and router-level topology evolution models.
(2) Research of router-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model. Based on the basic characteristics of topology and its evolution law from empirical research of Internet router-level topology, using the theory of Multi-subnet Composited Complex Network, through loading router subnet to website subnet, a Internet router-level topology evolution model is proposed. The actual impact of factors, such as. router load and limitations of router hardware are considered into the model, from the point of view of network performance optimization, router nodes and network traffic transmitted between nodes are taken into consider together. Through network characteristics contrast between a large number of simulation results and the same scale actual network, it shows that the model can simulate the basic characteristics of the actual router network topology.
(3) Research of autonomy system-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model. Autonomy system node types, the growth and aging of the network, local-world characteristics must be taken into account the actual impact of autonomy system-levellntemet evolution. A Internet autonomy system-level topology evolution model is proposed. According to their respective functions, autonomy system nodes in the Internet are divided into two categories:service provider node and service customer node, the relationship of line between autonomy system nodes in the Internet are divided into two categories:service provider to service customer relationship and peer to peer relationship. The model is based on the classic BA model, the location, price and service quality act as impact factor of the preferred attachment mechanism, and different strategy of establish connection is used for two different types of nodes, network aging is reflected by deleting nodes and edges. Through theoretical analysis and network characteristics contrast between200times simulation results and the same scale actual network, it shows that the model can simulate the basic characteristics of the actual autonomy system network topology and effectively and accurately portray the actual autonomy system-level Internet network characteristics.
(4) Research of cascading failure based on Multi-subnet Composited Complex Network. Cascade failure is an important symbol of network vulnerability. A cascading failure ploy with an adjustable parameter based on Multi-subnet Composited Complex Network Model is proposed, and a new measure of network robustness is introduced. Through simulation and theoretical analysis, the ploy can effectively estimate the threshold of the network generated by cascading failure, effective recommendations for network topology optimization under limited resources and for suppressing network congestion are provided. The research can guide the actual network topology and load distribution for achieving the purpose to improve network robustness. The cascading failure model can be applied to a variety of typical complex network topologies, such as ER random networks, small-world networks, scale-free networks, the simulation results show that network topology generated by router-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model are more robust than the three typical complex network topology.
Autonomy system-level and router-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model proposed in this dissertation solve the problem that existing Internet evolution models can not describe different kinds entities and their relationships in Internet, reflec the method that Internet evolution is jointly decided by different kinds entities and their relationships in Internet. They can reveal the evolution mechanism of Internet, and the network topology characteristics generated by evolution models are consistent with the same scale actual network.
互联网是一个典型的复杂系统,应用复杂网络理论研究互联网拓扑结构、理解互联网演化机制、建立互联网拓扑演化模型将对评估网络抗毁性、优化网络性能、设计高效网络协议等方面具有重要的实际意义。互联网拓扑因划分粒度的粗细,可分为自治系统级拓扑和路由器级拓扑。目前已有的自治系统级或路由器级拓扑演化模型普遍存在模型所生成的网络与实际网络之间在某些网络拓扑特征性质方面差异较大、不能确切反映网络演化内在成因规律等问题。针对互联网中存在着不同类个体间多种关系的特点,本文利用我子网复合复杂网络模型,从网络拓扑特征分的的角度展开研究,对互联网自治系统级拓扑和路由器级拓扑进行了实证分析,根据实证分析结果提出了互联网自治系统级和路由器级拓扑演化模型,并在此基础上对互联网中的级联失效现象进行了研究。本研究为基于复杂网络的互联网的研究提供了理论支撑,具有重要的理论意义与应用价值。论文的主要研究工作如下：
(1)互联网自治系统级拓扑和路由器级拓扑的实证研究。利用权威的CAIDA-Skitter项11拓扑实测数据,对自治系统级互联网拓扑的的度、簇系数等网络特征量度进行分析。通过自主研发的网络拓扑测量软件CERNET-MTR,对中国教育和科研计算机网(CERNET)进行测量并得到其路由器捅扑和网站页面链接的实测数据,对CERNET中路由器级互联网拓扑的度、最短路径长度、介数等基本特征量度进行分析。由上述分析结果,发现了新加入的自治系统节点受地理位置影响、自治系统级互联网中存在服务提供方节点构成的连通骨干子网、实际网络设备性能制约路由器节点的连接度最大值等影响网络拓扑演化的现象,为后续自治系统级和路由器级互联网拓扑演化模型的提出提供可靠依据。
(2)基于多子网复合复杂网络模型的路由器级互联网拓扑演化模型研究。基于(1)中得到的实证分析结果,提出了基于多子网复杂网络模型的路由器级互联网拓扑演化模型,该模型利用多子网复合复杂网络模型的子网加载运算,将网站子网加载到路由器子网中,综合考虑路由器负载、路由器硬件限制等实际影响因素,从网络流量传输优化的角度出发,由路由器间所需流量传输带宽及路由器负载决定新增路由器节点的偏好择优机制。通过计算机仿真实验农明,该模型在度分布、簇系数、平均最短路径、最大连接度、叶子节点数量等网络特征量度与同等规模实际互联网较为吻合,能够较好的体现实际路由器网络拓扑结构的幂律特性、小世界特性层次性等网络特征
(3)基于多子网复合复杂网络模型的自治系统级互联网拓扑演化模型研究。自治系统节点类型、网络的增长和老化、局域世界特性等都是自治系统级互联网演化过程中必须考虑的实际影响因素。针对这些因素,提出了基于多子网复合复杂网络模型的自治系统级互联网拓扑演化模型,在该模型中将互联网中的自治系统节点根据其功能分为两类：服务提供方节点和服务消费方节点,自治系统节点问连边的关系分为网络服务消费方——网络服务提供方关系(C2P)和对等关系(P2P)。借鉴经典的BA演化模型思想,将地理位置、价格和服务质量等因素作为偏好择优机制的影响因子,对不同类型的新增节点采用小同的建立连边的策略,并利用删除节点和和边体现网络老化现象。通过对该模型200次仿真实验结果所取的平均值与实际自治系统级互联网的网络特征值进行对比,结果显示该模型能够较好的模拟出自治系统级互联网的度分布、簇系数、平均最短路径、核数、介数、叶子节点数量等网络拓扑特征量度,准确有效的刻画了实际自治系统级互联网的节点度分布、小世界特性、异配性、聚合性、层次性、富入俱乐部性等网络特征。
(4)基于多子网复合复杂网络模型的级联失效研究。级联失效是网络脆弱性的一个重要表现。基于多子网复合复杂网络模型,提出了一个带有可调参数的级联失效策略,并引入了一种新的度量网络鲁棒性的测度——级联失效阈值。通过仿真和理论分析证明,该策略可以有效地评估网络产生级联失效的阈值,为有限资源下的网络拓扑结构优化,抑制网络拥塞提供有效的建议,可指导实际网络拓扑的负荷分配,从而达到提高网络鲁棒性的目的。该级联失效策略也可应用于随机网络、小世界网络、无标度网络等多种,典型复杂网络拓扑,并通过仿真实验证明相对于上述3种典型复杂网络拓扑结构,基于多子网复合复杂网络模型的路由器级互联网演化模型所生成的网络拓扑结构具有更强的鲁棒性。
本文提出的基于多子网复合复杂网络模型的自治系统级和路由器级互联网演化模型解决了现有互联网演化模型无法描述互联网中多类个体间多种关系的问题,体现了由多类个体、个体间多种关系共同决定互联网演化的思想,能够较为真实的揭示互联网的形成机理和演化规律,所生成的网络拓扑结构与同规模实际网络拓扑特征较为吻合。
At present, the theoretical study of complex networks has been widely used in the fields of sociology, biology, communications, computer and communication. But in those fields, theoretical research results are not enough deep in practice, therefore, complex network theory is applied into specific application, which will become the research focus in the future.
Internet is a typical complex system, complex network theory is used to study the topology and evolution mechanism of Internet, establishment of the network topology evolution model will has important practical significance for estimating network security and survivability, optimizing network performance, designing an efficient network protocol. According to different granularity, Internet topology can be divided into autonomy system-level topology and router-level topology. For the existing autonomy system-level or router-level topology evolution model, there are a lots of problems that some network topological characteristics are different between network generated by model and actual network, and network evolution inherent causes and laws are not accurately reflected. In this dissertation, for the characteristics of different kinds entities and their relationships in Internet, Internet autonomy system-level topology and router-level topology are studied by multi-subnet composited complex network model. Based on these, the cascading failure of Internet is studied. The above studies could improve the development of complex system, which having theoretical and applied significance. The main works in this dissertation include:
(1) Empirical research of Internet autonomy system-level topology and router-level topology. Through obtaining authoritative CAIDA-Skitter project topology measured data, from the perspective of network characteristics analysis, the basic characteristics, such as degree, clustering coefficient and so on, of autonomy system-level Internet topology is analyzed. Through self-developed network topology measurement software CERNET-MTR, the measured data of router topology and website page link of the China Education and Research Network (CERNET) are obtained. Using the theory of Multi-subnet Composited Complex Network, the basic characteristics such as degree, shortest path length, betweenness and so on, of topology of CERNET router-level Internet are analyzed. Based on these, accurate understanding of Internet autonomy system-level and router-level topology and its evolution law are obtained. The above studies could act as the theoretical foundation for follow-up Internet autonomy system-level and router-level topology evolution models.
(2) Research of router-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model. Based on the basic characteristics of topology and its evolution law from empirical research of Internet router-level topology, using the theory of Multi-subnet Composited Complex Network, through loading router subnet to website subnet, a Internet router-level topology evolution model is proposed. The actual impact of factors, such as. router load and limitations of router hardware are considered into the model, from the point of view of network performance optimization, router nodes and network traffic transmitted between nodes are taken into consider together. Through network characteristics contrast between a large number of simulation results and the same scale actual network, it shows that the model can simulate the basic characteristics of the actual router network topology.
(3) Research of autonomy system-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model. Autonomy system node types, the growth and aging of the network, local-world characteristics must be taken into account the actual impact of autonomy system-levellntemet evolution. A Internet autonomy system-level topology evolution model is proposed. According to their respective functions, autonomy system nodes in the Internet are divided into two categories:service provider node and service customer node, the relationship of line between autonomy system nodes in the Internet are divided into two categories:service provider to service customer relationship and peer to peer relationship. The model is based on the classic BA model, the location, price and service quality act as impact factor of the preferred attachment mechanism, and different strategy of establish connection is used for two different types of nodes, network aging is reflected by deleting nodes and edges. Through theoretical analysis and network characteristics contrast between200times simulation results and the same scale actual network, it shows that the model can simulate the basic characteristics of the actual autonomy system network topology and effectively and accurately portray the actual autonomy system-level Internet network characteristics.
(4) Research of cascading failure based on Multi-subnet Composited Complex Network. Cascade failure is an important symbol of network vulnerability. A cascading failure ploy with an adjustable parameter based on Multi-subnet Composited Complex Network Model is proposed, and a new measure of network robustness is introduced. Through simulation and theoretical analysis, the ploy can effectively estimate the threshold of the network generated by cascading failure, effective recommendations for network topology optimization under limited resources and for suppressing network congestion are provided. The research can guide the actual network topology and load distribution for achieving the purpose to improve network robustness. The cascading failure model can be applied to a variety of typical complex network topologies, such as ER random networks, small-world networks, scale-free networks, the simulation results show that network topology generated by router-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model are more robust than the three typical complex network topology.
Autonomy system-level and router-level Internet topology evolution model based on Multi-subnet Composited Complex Network Model proposed in this dissertation solve the problem that existing Internet evolution models can not describe different kinds entities and their relationships in Internet, reflec the method that Internet evolution is jointly decided by different kinds entities and their relationships in Internet. They can reveal the evolution mechanism of Internet, and the network topology characteristics generated by evolution models are consistent with the same scale actual network.
引文
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