基于感知流量算法的复杂网络拥塞问题研究

研究了在具有感知流量的路由策略下,复杂网络的拓扑结构对网络中传输流量的影响.为了描述数据包传输过程的有效性,通过引入一个状态参数,利用由稳态到拥塞的指标流量相变值来刻画网络的吞吐量.基于每个节点的数据包处理能力与该节点的度或介数成比例提出两种模型并进行仿真.仿真结果表明,平均度相同的情况下,模型Ⅰ中,WS小世界网络比ER随机网络和BA无标度网络更容易产生拥塞;模型Ⅱ中,所有网络容量都得到较大的提高,尤其是WS小世界网络.但当网络的基本连接参数改变时,哪种模型更利于网络的流量传输,还要依据网络本身的结构特性 关键词： 复杂网络 无标度网络 感知流量 拥塞     

Optimal structure of complex networks for minimizing traffic congestion

To design complex networks to minimize traffic congestion, it is necessary to understand how traffic flow depends on network structure. We study data packet flow on complex networks, where the packet delivery capacity of each node is not fixed. The optimal configuration of capacities to minimize traffic congestion is derived and the critical packet generating rate is determined, below which the network is at a free flow state but above which congestion occurs. Our analysis reveals a direct relation between network topology and traffic flow. Optimal network structure, free of traffic congestion, should have two features: uniform distribution of load over all nodes and small network diameter. This finding is confirmed by numerical simulations. Our analysis also makes it possible to theoretically compare the congestion conditions for different types of complex networks. In particular, we find that network with low critical generating rate is more susceptible to congestion. The comparison has been made on the following complex-network topologies: random, scale-free, and regular.     

Properties of Bottleneck on Complex Networks

The traffic bottleneck plays a key role in most of the natural and artificial network. Here we present a simply model for bottleneck dynamical characteristics consideration the reliability on the complex network by taking into account the network topology characteristics and system size. We find that there is a critical rate of flow generation below which the network traffic is free but above which traffic congestion occurs. Also, it is found that random networks have larger critical flow generating rate than scale free ones. Analytical results may be practically useful for designing networks, especially for the urban traffic network.     

Congestion analysis of traffic networks with direction-dependant heterogeneity

Traffic flow directionality and network weight asymmetry are widespread notions in traffic networks. This paper investigates the influence of direction-dependant heterogeneity on traffic congestion. To capture the effect of the link directionality and link weight asymmetry, the heterogeneity indexes of complex networks and the traffic flow model are introduced. The numerical results show that the critical value of heterogeneity determines congestion transition processes. The congestion degree increases with heterogeneity when the network heterogeneity is at a subcritical region. A network is more tolerant of congestion if the heterogeneity of the network is smaller or larger than the critical value. Furthermore, when heterogeneity reaches the critical value, the average number of accumulated vehicles arrives at the maximum and the traffic flow is under a serious congestion state. A significant improvement on the tolerance to congestion of traffic networks can be made if the network heterogeneity is controlled within a reasonable range.     

基于节点相关性的网络不动点理论研究

现代复杂的通信网络内部存在着广泛的幂律现象，网络节点之间存在相关特性. 根据这种相关特性，提出了网络不动点理论. 将Banach不动点理论引入网络模型，证明了网络不动点理论的正确有效性. 证明过程是把通信网络看作由路径预测算法产生的似马尔可夫链的路由节点迭代序列形成的网络空间. 由节点相关性可知，此空间中的节点序列相对越长就越能折射出搜索的目标所在，预测准确率也会逐步增加，可以更好地进行目标定位、数据挖掘等. 通过某种路由准则的算子从源节点最终映射到的目的节点与Banach空间的不动点相对应，即为网络空间的不动点. 当网络发展到能为用户提供真正的无处不在的连接时，网络不动点理论的物理特性将非常明显. 因为网络规模越大，节点间的群体作用越显著，就越能显现网络不动点理论的物理特性. 关键词： 计算机网络 长程相关 不动点 幂律     

复杂交通运输网络上的拥挤与效率问题研究

本文研究复杂交通运输网络上的拥挤与效率问题. 在无标度网络、随机网络以及小世界网络等不同拓扑结构中, 探讨了不同的能力分配方式和不同的OD (Origin-Destination) 交通需求分布对网络拥挤度和效率的影响. 随着平均交通需求的增加, 分析无标度网络、随机网络以及小世界网络从自由流状态到交通拥堵状态的变化规律. 为便于比较, 本文侧重研究网络拥挤度的倒数, 并将其定义为通畅度. 研究发现网络中的通畅度与效率之间存在线性相关关系, 并且不同网络中的线性比例系数 (或斜率)是不同的, 从而体现了不同网络具有不同的运输性能. 关键词： 复杂网络 拥挤 效率     

结合可视图的多状态交通流时间序列特性分析

交通流时间序列的研究主要采用数据挖掘和机器学习的方法,这些"黑箱"挖掘方法很难直观反映序列特性.为增强交通流时间序列及其特征分析的可视化性,结合可视图理论来构建交通流时间序列的关联网络,从复杂网络角度实现交通流时间序列的特性分析.在网络构建的过程中,考虑到不同交通状态下交通流表征具有的差异性,首先利用交通流参量的相关性对交通流状态进行分类,然后构建不同交通状态下的时间序列复杂网络,并对这些网络的特征属性给出统计分析,如度分布、聚类系数、网络直径、模块化等.研究表明,可视图法可为交通流时间序列映射到网络提供有效途径,并且不同状态下交通流时间序列构建的复杂网络的模块化、聚类系数和度分布等统计特征呈现一定的变化规律,为交通流运行态势的研究提供了可视化的分析角度.     

Effective usage of shortest paths promotes transportation efficiency on scale-free networks

With rapid economic and social development, the problem of traffic congestion is getting more and more serious. Accordingly, network traffic models have attracted extensive attention. In this paper, we introduce a shortest-remaining-path-first queuing strategy into a network traffic model on Barabási–Albert scale-free networks under efficient routing protocol, where one packet’s delivery priority is related to its current distance to the destination. Compared with the traditional first-in-first-out queuing strategy, although the network capacity has no evident changes, some other indexes reflecting transportation efficiency are significantly improved in the congestion state. Extensive simulation results and discussions are carried out to explain the phenomena. Our work may be helpful for the designing of optimal networked-traffic systems.     

Efficient packet routing strategy in complex networks

We investigate a new efficient packet routing strategy which mitigates traffic congestion on complex networks. In order to avoid congestion, we minimize the maximum betweenness, which is a measure for concentration of routing paths passing through a node in the network. Danila et al. propose a packet routing strategy in which, instead of shortest paths, they used efficient paths, which are the paths with the minimum total summations of weights assigned to nodes in the respective paths. They use a heuristic algorithm in which the weights are updated step by step by using the information of betweenness of each node in every step and the respective total summations of weights for paths through the nodes with large degrees become comparatively large. Thus passage through such nodes, where congestion almost occurs, is likely to be avoided in their algorithm. The convergence time by their algorithm is, however, quite long. In this paper, we propose a new efficient heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in the much smaller number of iteration steps for convergence than that by the algorithm of Danila et al.     

基于通信序列熵的复杂网络传输容量

网络的传输性能在一定程度上依赖于网络的拓扑结构.本文从结构信息的角度分析复杂网络的传输动力学行为,寻找影响网络传输容量的信息结构测度指标.通信序列熵可以有效地量化网络的整体结构信息,为了表征网络整体传输能力,把通信序列熵引入到复杂网络传输动力学分析中,研究网络的通信序列熵与传输性能之间的关联特性,分析这种相关性存在的内在机理.分别在BA无标度和WS小世界网络模型上进行仿真,结果显示:网络的通信序列熵与其传输容量存在密切关联性,随着通信序列熵的增加,网络拓扑结构的均匀性随之增强,传输容量明显增加.网络的传输容量是通信序列熵的单调递增函数,与通信序列熵成正关联关系.通信序列熵可有效评估网络的传输容量,本结论可为设计高传输容量网络提供理论依据.     

交通流驱动的含权网络

文章对含权复杂网络研究的最近进展给予了评述，特别报道了文章作者最近提出的一个交通流驱动的含权技术网络模型。这一模型能够同时给出网络连接度分布的幂函数律、网络强度分布的幂函数律、网络权重分布的幂函数律，以及高聚集性和非相称混合性等五大特征，因此成功地刻画了真实技术网络的无尺度性质和小世界效应     

面向成本-收益好的无标度耦合网络构建方法

较大平均路径长度的网络会带来较大的网络延迟, 难以支持时间敏感业务与应用. 通过增加连接可以降低源和目的节点之间的跳数, 进而降低网络平均延迟, 使得更加快速地传播信息, 但是增加连接的同时也增加了网络构建成本. 分层网络是研究网络耦合的一个有效方法, 但目前网络构建过程中将每层网络分别处理并认为每层网络之间没有强相关性. 本文提出了一种面向成本-收益的无标度网络动态构建方法. 此方法将网络分为多层, 基于连续论在高层网络中添加连接, 使得网络演化为无标度网络. 此连续过程包括节点度增加过程和局部网络半径增长两个连续过程, 在增加连接的过程中引入表征网络构建成本和收益的成本-收益指标. 模拟结果表明引入成本-收益指标的无标度耦合网络构建方法能够在合理范围内有效降低网络平均路径长度, 提升网络性能, 并且本文给出了耦合网络的动态业务性能, 通过调整高层网络避免网络拥塞.     

Optimization of transport protocols in complex networks

In this paper, an optimal routing strategy is proposed to enhance the traffic capacity of complex networks. In order to avoid nodes overloading, the new algorithm is derived on the basis of generalized betweenness centrality which gives an estimate of traffic handled by the node for a route set. Since the nodes with large betweenness centrality are more susceptible to traffic congestion, the traffic can be improved, as our strategy, by redistributing traffic load from nodes with large betweenness centrality to nodes with small betweenness centrality in the proceeding of computing collective routing table. Particularly, depending on a parameter that controls the optimization scale, the new routing can not only enlarge traffic capacity of networks more, but also enhance traffic efficiency with smaller average path length. Comparing results of previous routing strategies, it is shown that the present improved routing performs more effectively.     

Optimal traffic networks topology: A complex networks perspective

We investigate and analyse an optimal traffic network structure for resisting traffic congestion with different volumes of traffic. For this aim, we introduce a cost function and user-equilibrium assignment (UE) which ensures the flow balance on traffic systems. Our finding is that an optimal network is strongly dependent on the total system flow. And the random network is most desirable when the system flow is small. But for the larger volume of traffic, the network with power-law degree distribution is the optimal one. Further study indicates, for scale-free networks, that the degree distribution exponent has large effects on the congestion of traffic network. Therefore, the volume of traffic and characteristic of network determine the optimal network structure so as to minimize the side-effect produced by traffic congestion.     

两层星形网络的特征值谱及同步能力

多层网络是当今网络科学研究的一个前沿方向.本文深入研究了两层星形网络的特征值谱及其同步能力的问题.通过严格导出的两层星形网络特征值的解析表达式,分析了网络的同步能力与节点数、层间耦合强度和层内耦合强度的关系.当同步域无界时,网络的同步能力只与叶子节点之间的层间耦合强度和网络的层内耦合强度有关;当叶子节点之间的层间耦合强度比较弱时,同步能力仅依赖于叶子节点之间的层间耦合强度;而当层内耦合强度比较弱时,同步能力依赖于层内耦合强度;当同步域有界时,节点数、层间耦合强度和层内耦合强度对网络的同步能力都有影响.当叶子节点之间的层间耦合强度比较弱时,增大叶子节点之间的层间耦合强度会增强网络的同步能力,而节点数、中心节点之间的层间耦合强度和层内耦合强度的增大反而会减弱网络的同步能力;而当层内耦合强度比较弱时,增大层内耦合强度会增强网络的同步能力,而节点数、层间耦合强度的增大会减弱网络的同步能力.进一步,在层间和层内耦合强度都相同的基础上,讨论了如何改变耦合强度更有利于同步.最后,对两层BA无标度网络进行数值仿真,得到了与两层星形网络非常类似的结论.     

基于复杂网络的交通拥堵与传播动力学分析

本文运用改进的中观交通流模型,研究了网络拓扑结构对交通拥堵的影响,进而分析复杂网络上的交通传播动力学特征和传播规律.结论有助于提出消除交通拥堵的有效控制策略以及交通规划的合理方案. 关键词： 复杂网络 交通流 交通拥堵 传播特性     

Cascading dynamics in congested complex networks

Cascading failures often occur in congested complex networks. Cascading failures can be expressed as a three phase process: generation, diffusion and dissipation of congestion. Different from betweenness centrality, we propose a congestion function to represent the extent of congestion on a given node. By introducing the concept of “delay time”, we construct an intergradation between permanent removal and nonremoval. We also build a new evaluation function of network efficiency, based on congestion, which measures the damage caused by cascading failures. Finally, based on Statnet and Webgraph topologies we investigate the effects of network structure and size, delay time, processing ability and traffic generation speed on congestion propagation. Also we uncover cascading process composed of three phases and some factors affecting cascade propagation.     

Hierarchy property of traffic networks

The flourishing complex network theory has aroused increasing interest in studying the properties of real-world networks. Based on the traffic network of Chang--Zhu--Tan urban agglomeration in central China, some basic network topological characteristics were computed with data collected from local traffic maps, which showed that the traffic networks were small-world networks with strong resilience against failure; more importantly, the investigations of assortativity coefficient and average nearest-neighbour degree implied the disassortativity of the traffic networks. Since traffic network hierarchy as an important basic property has been neither studied intensively nor proved quantitatively, the authors are inspired to analyse traffic network hierarchy with disassortativity and to finely characterize hierarchy in the traffic networks by using the n-degree--n-clustering coefficient relationship. Through numerical results and analyses an exciting conclusion is drawn that the traffic networks exhibit a significant hierarchy, that is, the traffic networks are proved to be hierarchically organized. The result provides important information and theoretical groundwork for optimal transport planning.     

Linear Separability of Positive Self-Dual Logical Filters

The threshold logic filter is an important nonlinear filter class, which is defined by a threshold logic function of binary input values. It is proved in this paper that not all positive self-dual logical functions are threshold functions if the number of input variables is 5 or more. The positive self-dual logical filter is a limited class but includes almost all filters for noise removal. Our result means that not all positive self-dual filters can be expressed by one operation of the threshold logic filters. In the sense of the filter expression by neural networks, the two-layer network cannot always optimize even this limited class.     

Traffic dynamics based on a traffic awareness routing strategy on scale-free networks

By incorporating local traffic information into the shortest path routing strategy, we numerically investigate the effectiveness of the traffic awareness routing strategy for scale-free networks with different clustering. In order to characterize the efficiency of the packet-delivery process, we introduce an order parameter and an average transmission time that allow us to measure the network capacity by the critical value of phase transition from free flow to congestion. Compared with the shortest path routing protocol, the network capacity is greatly enhanced by the traffic awareness routing strategy. We also find that there exists an optimum value for the tunable parameter in the congestion awareness strategy. Moreover, simulation results show that the more clustered the network, the less efficient the packet-delivery process.