Proactive Robustness Control of Heterogeneously Loaded Networks

Schäfer, Mirko; Scholz, J.; Greiner, Martin

doi:10.1103/physrevlett.96.108701

Cited by 81 publications

(68 citation statements)

References 18 publications

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“…Following previous models addressing cascading problems [8,10,13,16,24], each node i in the network has a weight threshold or capacity F i , which is the maximum flow that the node can handle. Conventionally, it is assumed that the threshold of a node is proportional to its weight…”

Section: The Modelmentioning

confidence: 99%

“…, where the constant C > 1 is a threshold parameter characterizing the tolerance of the network [7,8,9,10,13,16,24]. Considering a neighbor j of the node i, if…”

Section: The Modelmentioning

confidence: 99%

“…In fact, understanding how the structure affects the dynamics is regarded as one of the major objectives in the study of complex networks [2]. For this reason, most previous cascading models confined on complex networks, such as the sandpile model [6], the global load based cascading model [7,8,9,10,11,12,13], and the fiber bundle model [14,15,16], have also been subjected to this issue. However, the network weights have not been taken into consideration in these models, regardless of the fact that real networks display a large heterogeneity in the weights which have a strong correlation with the network topology [17,18,19].…”

Section: Introductionmentioning

confidence: 99%

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Cascading failure spreading on weighted heterogeneous networks

Peng

Wang

et al. 2008

J. Stat. Mech.

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Abstract. We study the onset and spreading of cascading failure on weighted heterogeneous networks by adopting a local weighted flow redistribution rule, where the weight and tolerance of a node is correlated with its link degree k as k θ and Ck θ , respectively. The weight parameter θ and tolerance parameter C are positive: θ > 0 and C > 1.0. Assume that a failed node leads only to a redistribution of flow passing through it to its nearest neighboring nodes. We give out theoretical estimations of the onset of the cascading failure for different values of θ. It is found that the cascading failure emerges most difficult on networks with θ = 1.0, while it develops more slowly for larger θ. We furthermore explore the statistical characteristics of the avalanche size on the networks by varying θ, and obtain versatile dynamical scenarios of the cascading processes, which exhibit either "subcritical", or "critical", or "supercritical" behaviors depending on the value of the weight parameter.

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Section: The Modelmentioning

confidence: 99%

“…, where the constant C > 1 is a threshold parameter characterizing the tolerance of the network [7,8,9,10,13,16,24]. Considering a neighbor j of the node i, if…”

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cascading failure spreading on weighted heterogeneous networks

Peng

Wang

et al. 2008

J. Stat. Mech.

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“…In particular, the problem of cascades with load redistribution on networked systems has aroused widespread concern 16,17,18,19 . Some important aspects of cascades have been extensively researched, including the models for describing the cascading failures 20,21,22 , the defense and control strategies for cascades 23,24,25,26 , the cascading models in real networks 27,28,29 . Motter et al 20 put forward a global load-based cascading model.…”

Section: Introductionmentioning

confidence: 99%

Cascades Tolerance of Scale-Free Networks with Attack Cost

Chen¹,

Yin²,

He³

et al. 2017

IJCIS

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Network robustness against cascades is a major topic in the fields of complex networks. In this paper, we propose an attack-cost-based cascading failure model, where the attack cost of nodes is positively related to its degree. We compare four attacking strategies: the random removal strategy (RRS), the low-degree removal strategy (LDRS), the high-degree removal strategy (HDRS) and the genetic algorithm removal strategy (GARS). It is shown that the network robustness against cascades is heavily affected by attack costs and the network exhibits the weakest robustness under GARS. We also explore the relationship between the network robustness and tolerance parameter under these attacking strategies. The simulation results indicate that the critical value of tolerance parameter under GARS is greatly larger than that of other attacking strategies. Our work can supply insight into the robustness and vulnerability of complex networks corresponding to cascading failures.

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“…These graphs may greatly differ in their response to failures. For instance, the 'scale-free' networks (i.e., networks whose node degree distribution is heavytailed [3]) such as World Wide Web, Internet, protein networks, ecological networks or cellular networks, exhibit remarkable robustness to errors , but at the same time, they are very vulnerable to attacks such as the removal of the most highly connected nodes [4] [15], and vulnerability of weighted networks [16] gave us valuable insights into the robustness of complex networks treated as distinct objects. Many of such networks, however, are only a part of larger systems, where a number of coexisting topologies interact and depend on each other [1].…”

mentioning

confidence: 99%

Error and attack tolerance of layered complex networks

2007

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Many complex systems may be described not by one, but by a number of complex networks mapped one on the other in a multilayer structure [1]. The interactions and dependencies between these layers cause that what is true for a distinct single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of three real-life examples of twolayer complex systems that come from the fields of communication (the Internet), transportation (the European railway system) and biology (the human brain). In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multilayer systems are much more vulnerable to errors and intentional attacks than they seem to be from a single layer perspective.

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Proactive Robustness Control of Heterogeneously Loaded Networks

Cited by 81 publications

References 18 publications

Cascading failure spreading on weighted heterogeneous networks

Cascading failure spreading on weighted heterogeneous networks

Cascades Tolerance of Scale-Free Networks with Attack Cost

Error and attack tolerance of layered complex networks

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