Model for cascading failures in complex networks

Crucitti, Paolo; Latora, Vito; Marchiori, Massimo

doi:10.1103/physreve.69.045104

Cited by 992 publications

(640 citation statements)

References 22 publications

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“…At this point we would like to mention other studies in which the resistance against cascades was studied as a function of geometrical disorder. In models based on critical loads and percolation in interdependent networks it was found that a heterogeneous network is less resistant against higher loads than a homogeneous one [12,13,14]. In our model degree heterogeneity (low γ) appears to strengthen the network at low a but to weaken it at high a.…”

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confidence: 75%

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Ising model for distribution networks

Hooyberghs

Lombeek

Giuraniuc

et al. 2012

Philosophical Magazine

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An elementary Ising spin model is proposed for demonstrating cascading failures (breakdowns, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.Version: April 20, 2018 keywords: Ising model, random fields, complex scale-free distribution network, failure, blackout, breakdown, collapse, avalanche, cascade MotivationStatistical physics studies of cooperative phenomena on random graphs have attracted a lot of new attention and undergone impressive new development since it has become clear that many reallife interconnected structures are well approximated by random scale-free networks [1,2,3,4,5]. One can say that a paradigm shift is occurring from studies of models for critical phenomena on (Bravais) lattices to studies in which such models are defined on random networks. To some extent this paradigm shift resembles that from Euclidean geometry to fractal geometry, in the modeling of various natural phenomena, but scale-free networks are specific in that they are characterized by the presence of a small but important set of hubs. The hubs are highly connected nodes which typically have a large influence on the operation and coherence of the structure.When we are concerned with the distribution of electricity, or the production and sale of material goods by commercial centers to consumers, or the delivery of the daily mail ..., we can * Dedicated to Professor Dr. David Sherrington on the occasion of his 70th birthday. 1 envisage distribution centers as nodes and consumers as links on a network. The consumers have certain demands and the distribution centers certain deliverables. The distribution centers can be active or inactive depending on internal conditions and on external criteria such as the demands of consumers that are linked to them and the status of other nearby centers. The occurrence of hubs in such networks is rathe...

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confidence: 75%

“…[8]. Avalanches in distribution models were also studied using sand piles on networks [9] and in various models based on critical loads [10,11,12,13]. Recently, also models studying percolation in interdependent networks were used [14].…”

Section: Construction Of a General Hamiltonianmentioning

confidence: 99%

Ising model for distribution networks

Hooyberghs

Lombeek

Giuraniuc

et al. 2012

Philosophical Magazine

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“…The question is then under which conditions this failure leads to a cascade of macroscopic size. Applications of this case include power-grid cascade failures [4,5,10], or failures of server infrastructure [6].…”

Section: Results For the Rie Regimementioning

confidence: 99%

“…A fixed relation between fragility and threshold was first used in [4] to describe cascading processes in power grids and Internet (see also [5,9,10]). It basically reflects the situation of many socio-technical systems in which the capacity of agents is usually ad hoc designed to handle the load, because limited by cost, under normal conditions.…”

Section: /23mentioning

confidence: 99%

“…Some modeling framework were recently proposed [1,2,3]. The complex network approach was also used to describe cascading processes in power grids and in Internet services [4,5], and was also applied to data storage services [6]. Importantly, similar agent-based approaches were developed to model avalanche defaults among financial institutions [7,8].…”

Section: Introductionmentioning

confidence: 99%

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How Big Is Too Big? Critical Shocks for Systemic Failure Cascades

et al. 2013

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External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighboring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold θ i determining their capacity to handle a load αθ i with 1 − α being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P (θ), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.

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Structural vulnerability analysis in small‐world power grid networks based on weighted topological model

Panigrahi

Maity

2020

Int Trans Electr Energ Syst

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Model for cascading failures in complex networks

Cited by 992 publications

References 22 publications

Ising model for distribution networks

Ising model for distribution networks

How Big Is Too Big? Critical Shocks for Systemic Failure Cascades

Structural vulnerability analysis in small‐world power grid networks based on weighted topological model

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