Fault-tolerant routing and wavelength assignment algorithm for multiple link failures in wavelength-routed all-optical WDM networks

In this paper, we investigate the problem of enhancing multiple-fault restorability in the path protected wavelength-routed all-optical WDM networks. The system architecture considered is circuit-switched with dynamic arrival of session requests. We propose a mechanism, which is used to combat multiple link failures. A routing and wavelength assignment algorithm has been proposed with the name of fault-tolerant routing and wavelength assignment algorithm. The comparison of this algorithm has also been made with the best-fit and first-fit algorithms. This algorithm deals with the optical networks with multiple faults and is effective for the varying load applied to nodes. This algorithm works well for the load applied to the nodes varying from low to high.     

基于相继故障信息的网络节点重要度演化机理分析

分析了过载机制下节点重要度的演化机理.首先,在可调负载重分配级联失效模型基础上,根据节点失效后其分配范围内节点的负载振荡程度,提出了考虑级联失效局域信息的复杂网络节点重要度指标.该指标具有两个特点:一是值的大小可以清晰地指出节点的失效后果;二是可以依据网络负载分配范围、负载分配均匀性、节点容量系数及网络结构特征分析节点重要度的演化情况.然后,给出该指标的仿真算法,并推导了最近邻择优分配和全局择优分配规则下随机网络和无标度网络节点重要度的解析表达式.最后,实验验证了该指标的有效性和可行性,并深入分析了网络中节点重要度的演化机理,即非关键节点如何演化成影响网络级联失效行为的关键节点.     

Optimal intentional islanding to enhance the robustness of power grid networks

Intentional islanding of a power system can be an emergency response for isolating failures that might propagate and lead to major disturbances. Some of the islanding techniques suggested previously do not consider the power flow model; others are designed to minimize load shedding only within the islands. Often these techniques are computationally expensive. We aim to find approaches to partition power grids into islands to minimize the load shedding not only in the region where the failures start, but also in the topological complement of the region. We propose a new constraint programming formulation for optimal islanding in power grid networks. This technique works efficiently for small networks but becomes expensive as size increases. To address the scalability problem, we propose two grid partitioning methods based on modularity, properly modified to take into account the power flow model. They are modifications of the Fast Greedy algorithm and the Bloom algorithm, and are polynomial in running time. We tested these methods on the available IEEE test systems. The Bloom type method is faster than the Fast Greedy type, and can potentially provide results in networks with thousands of nodes. Our methods provide solutions which retain at least 40–50% of the system load. Overall, our methods efficiently balance load shedding and scalability.     

K-dimensional protection structure (KDPS) for multi-link failure in data center optical networks

Currently, data center has become one of the most important application resources. Meanwhile, there is huge amount of data streams within a data center or among different data centers, which requires the transmission channel with high bandwidth and good reliability. Optical networks become the essential solution for the data center interconnection. Especially for intra data center networks, there are too many links for a limited number of nodes, which make the network so complex and vulnerable. A K-dimensional protection structure (KDPS) is proposed against multi-link failure in data center optical networks, and 3DPS is mainly introduced and analyzed in the paper. Two greedy algorithms are proposed to construct KDPS in static and dynamic optical networks respectively. Numerical results show that 3DPS can be constructed with more difficulty in dynamic optical networks, and the greedy algorithm can find the 3DPS much easier under three-link failures than under dual-link failures.     

Robustness analysis of network controllability

Structural controllability, which is an interesting property of complex networks, attracts many researchers from various fields. The maximum matching algorithm was recently applied to explore the minimum number of driver nodes, where control signals are injected, for controlling the whole network. Here we study the controllability of directed Erdös–Rényi and scale-free networks under attacks and cascading failures. Results show that degree-based attacks are more efficient than random attacks on network structural controllability. Cascade failures also do great harm to network controllability even if they are triggered by a local node failure.     

Proactive robustness control of heterogeneously loaded networks

A proactive measure to increase the robustness of heterogeneously loaded networks against cascades of overload failures is proposed. It is based on load-dependent weights. Compared to simple hop weights, respective shortest flow paths turn a previously heterogeneous load distribution into a more homogeneous one for the nodes and links of the network. The use of these flow paths increases the networks robustness and at the same time reduces the investment costs into the networks capacity layout. These findings are of relevance for critical infrastructures like communication and transportation networks.     

Robustness of Cyber-Physical Supply Networks in Cascading Failures

A cyber-physical supply network is composed of an undirected cyber supply network and a directed physical supply network. Such interdependence among firms increases efficiency but creates more vulnerabilities. The adverse effects of any failure can be amplified and propagated throughout the network. This paper aimed at investigating the robustness of the cyber-physical supply network against cascading failures. Considering that the cascading failure is triggered by overloading in the cyber supply network and is provoked by underload in the physical supply network, a realistic cascading model for cyber-physical supply networks is proposed. We conducted a numerical simulation under cyber node and physical node failure with varying parameters. The simulation results demonstrated that there are critical thresholds for both firm’s capacities, which can determine whether capacity expansion is helpful; there is also a cascade window for network load distribution, which can determine the cascading failures occurrence and scale. Our work may be beneficial for developing cascade control and defense strategies in cyber-physical supply networks.     

Mitigation strategies on scale-free networks against cascading failures

According to the dynamic characteristics of the cascading propagation, we introduce a mitigation mechanism and propose four mitigation methods on four types of nodes. By the normalized average avalanche size and a new measure, we demonstrate the efficiencies of the mitigation strategies on enhancing the robustness of scale-free networks against cascading failures and give the order of the effectiveness of the mitigation strategies. Surprisingly, we find that only adopting once mitigation mechanism on a small part of the overload nodes can dramatically improve the robustness of scale-free networks. In addition, we also show by numerical simulations that the optimal mitigation method strongly depends on the total capacities of all nodes in a network and the distribution of the load in the cascading model. Therefore, according to the protection strength for scale-free networks, by the distribution of the load and the protection price of networks, we can reasonably select how many nodes and which mitigation method to efficiently protect scale-free networks at the lower price. These findings may be very useful for avoiding various cascading-failure-induced disasters in the real world and for leading to insights into the mitigation of cascading failures.     

一种基于势博弈的无线传感器网络拓扑控制算法

在实际的应用中,无线传感器网络常常由大量电池资源有限的传感器节点组成.如何降低网络功耗,最大化网络生存时间,是传感器网络拓扑控制技术的重要研究目标.随着传感节点的运行,节点的能量分布可能越来越不均衡,需要在考虑该因素的情况下,动态地调整节点的网络负载以均衡节点的能耗,达到延长网络生存时间的目的.该文引入博弈理论和势博弈的概念,综合考虑节点的剩余能量和节点发射功率等因素,设计了一种基于势博弈的拓扑控制模型,并证明了该模型纳什均衡的存在性.通过构造兼顾节点连通性和能耗均衡性的收益函数,以确保降低节点功耗的同时维持网络的连通性.通过提高邻居节点的平均剩余能量值以实现将剩余能量多的节点选择作为自身的邻居节点,提高节点能耗的均衡性.在此基础上,提出了一种分布式的能耗均衡拓扑控制算法.理论分析证明了该算法能保持网络的连通性.与现有基于博弈理论的DIA算法和MLPT算法相比,本算法形成的拓扑负载较重、剩余能量较小的瓶颈节点数量较少,节点剩余能量的方差较小,网络生存时间更长.     

一种全局同质化相依网络耦合模式

相依网络的相依模式(耦合模式)是影响其鲁棒性的重要因素之一.本文针对具有无标度特性的两个子网络提出一种全局同质化相依网络耦合模式.该模式以子网络的总度分布均匀化为原则建立相依网络的相依边,一方面压缩度分布宽度,提高其对随机失效的抗毁性,另一方面避开对度大节点(关键节点)的相依,提高其对蓄意攻击的抗毁性.论文将其与常见的节点一对一的同配、异配及随机相依模式以及一对多随机相依模式作了对比分析,仿真研究其在随机失效和蓄意攻击下的鲁棒性能.研究结果表明,本文所提全局同质化相依网络耦合模式能大大提高无标度子网络所构成的相依网络抗级联失效能力.本文研究成果能够为相依网络的安全设计等提供指导意义.     

复杂网络牵制控制优化选点算法及节点组重要性排序

本文研究复杂网络动力学模型的无向网络牵制控制的优化选点及节点组重要性排序问题.根据牵制控制的同步准则,网络的牵制控制同步取决于网络的Laplacian删后矩阵的最小特征值.因此,通过合理选择受控节点集得到一个较大的Laplacian删后矩阵最小特征值,是牵制控制优化选点问题的核心所在.基于Laplacian删后矩阵最小特征值的图谱性质,本文提出了多个受控节点选取的递归迭代算法,该算法适用于任意类型的网络.通过BA无标度网络、NW小世界网络及一些实际网络中的仿真实验表明:该算法在控制节点数较少时,能有效找到最优受控节点集.最后讨论了在复杂网络牵制控制背景下节点组重要性排序问题,提出节点组的重要性排序与受控节点的数目有关.     

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.     

Modeling wireless sensor networks using random graph theory

A critical issue in wireless sensor networks (WSNs) is represented by limited availability of energy within network nodes. Therefore, making good use of energy is necessary in modeling sensor networks. In this paper we proposed a new model of WSNs on a two-dimensional plane using site percolation model, a kind of random graph in which edges are formed only between neighbouring nodes. Then we investigated WSNs connectivity and energy consumption at percolation threshold when a so-called phase transition phenomena happen. Furthermore, we proposed an algorithm to improve the model; as a result the lifetime of networks is prolonged. We analyzed the energy consumption with Markov process and applied these results to simulation.     

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes

Based on the model of the same degree of all nodes we proposed before, a new algorithm, the so-called “spread all over vertices” (SAV) algorithm, is proposed for generating small-world properties from a regular ring lattices. During randomly rewiring connections the SAV is used to keep the unchanged number of links. Comparing the SAV algorithm with the Watts-Strogatz model and the “spread all over boundaries” algorithm, three methods can have the same topological properties of the small world networks. These results offer diverse formation of small world networks. It is helpful to the research of some applications for dynamics of mutual oscillator inside nodes and interacting automata associated with networks.     

Transforming a complex network to an acyclic one

Acyclic networks are a class of complex networks in which links are directed and do not have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an acyclic network allows one to find the structural properties of the network. With our approach one can find the communities and key nodes in complex networks. Also we propose a new parameter of complex networks which can mark the most vulnerable nodes of the system. The proposed algorithm can be applied to finding communities and bottlenecks in general complex networks.     

A new information dimension of complex networks

The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.     

Identifying Influential Nodes in Complex Networks Based on Multiple Local Attributes and Information Entropy

Identifying influential nodes in complex networks has attracted the attention of many researchers in recent years. However, due to the high time complexity, methods based on global attributes have become unsuitable for large-scale complex networks. In addition, compared with methods considering only a single attribute, considering multiple attributes can enhance the performance of the method used. Therefore, this paper proposes a new multiple local attributes-weighted centrality (LWC) based on information entropy, combining degree and clustering coefficient; both one-step and two-step neighborhood information are considered for evaluating the influence of nodes and identifying influential nodes in complex networks. Firstly, the influence of a node in a complex network is divided into direct influence and indirect influence. The degree and clustering coefficient are selected as direct influence measures. Secondly, based on the two direct influence measures, we define two indirect influence measures: two-hop degree and two-hop clustering coefficient. Then, the information entropy is used to weight the above four influence measures, and the LWC of each node is obtained by calculating the weighted sum of these measures. Finally, all the nodes are ranked based on the value of the LWC, and the influential nodes can be identified. The proposed LWC method is applied to identify influential nodes in four real-world networks and is compared with five well-known methods. The experimental results demonstrate the good performance of the proposed method on discrimination capability and accuracy.     

复杂网络中带有应急恢复机理的级联动力学分析

提出带有应急恢复机理的网络级联故障模型,研究模型在最近邻耦合网络,Erdos-Renyi随机网络,Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为.给出了应急恢复机理和网络效率的定义,并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响.结果表明,模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度,并且提高了网络的恢复能力.而且网络中节点负载容量越大,网络效率降低速度和节点故障率的增长速度越慢.同时,随着节点过载故障概率的减小,网络效率的降低速度和节点故障率的增长速度也逐渐减缓.此外,对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析,结果发现网络拓扑节点度分布的异质化程度的增大,提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度.以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为,为实际网络中级联故障现象的控制和防范提供了参考.     

Blocking probability analysis of survivable routing in WDM optical networks with/without sparse-wavelength conversion

In this paper, a new algorithm for wavelength assignment has been proposed and its performance is evaluated in terms of blocking probability and fairness. It has been shown that the proposed algorithm offers the least blocking probability. The blocking performance of wavelength division multiplexing (WDM) network has been analyzed for the network having 10 nodes and for varying loads. As the load per link (in Erlangs) increases, the blocking probability increases. The result shows that the performance of first-fit algorithm is better than random algorithm whereas the proposed algorithm offers the least blocking.     

Model for cascading failures with adaptive defense in complex networks

<正>This paper investigates cascading failures in networks by considering interplay between the flow dynamic and the network topology,where the fluxes exchanged between a pair of nodes can be adaptively adjusted depending on the changes of the shortest path lengths between them.The simulations on both an artificially created scale-free network and the real network structure of the power grid reveal that the adaptive adjustment of the fluxes can drastically enhance the robustness of complex networks against cascading failures.Particularly,there exists an optimal region where the propagation of the cascade is significantly suppressed and the fluxes supported by the network are maximal. With this understanding,a costless strategy of defense for preventing cascade breakdown is proposed.It is shown to be more effective for suppressing the propagation of the cascade than the recent proposed strategy of defense based on the intentional removal of nodes.