Cascading failures are a critical vulnerability of complex information or infrastructure networks. Here we investigate the properties of load-based cascading failures in real and synthetic spatially-embedded network structures, and propose mitigation strategies to reduce the severity of damages caused by such failures. We introduce a stochastic method for optimal heterogeneous distribution of resources (node capacities) subject to a fixed total cost. Additionally, we design and compare the performance of networks with N-stable and (N-1)-stable network-capacity allocations by triggering cascades using various real-world node-attack and node-failure scenarios. We show that failure mitigation through increased node protection can be effectively achieved against single node failures. However, mitigating against multiple node failures is much more difficult due to the combinatorial increase in possible failures. We analyze the robustness of the system with increasing protection, and find that a critical tolerance exists at which the system undergoes a phase transition, and above which the network almost completely survives an attack. Moreover, we show that cascade-size distributions measured in this region exhibit a power-law decay. Finally, we find a strong correlation between cascade sizes induced by individual nodes and sets of nodes. We also show that network topology alone is a weak factor in determining the progression of cascading failures.
Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behavior of cascading overload failures analytically and numerically. The cascading overload failures are found to spread radially from the c…
Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method shows that scale-free networks are more robust against cascading overload failure…
Most risk analysis models systematically underestimate the probability and impact of catastrophic events (e.g., economic crises, natural disasters, and terrorism) by not taking into account interconnectivity and interdependence of risks. To address this weakness, we propose the Cascading Alternating Renewal Process (CARP) to forecast interconnected global risks. However, assessments of the model's prediction precision are limited by lack of sufficient ground truth data. Here, we establish prediction precision as a function of input data size by using alternative long ground truth data generate…
In this paper we study the Motter-Lai model of cascading failures induced by overloads in both isotropic and anisotropic spatial networks, generated by placing nodes in a square lattice and using various distributions of link lengths and angles. Anisotropy has not been earlier considered in the Motter-Lai model and is a real feature that may affect the cascading failures. This could reflect the existence of a preferred direction in which a given attribute of the system manifests, such as power lines that follow a city built parallel to the coast. We show that the anisotropy causes a greater sp…
We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade $p_f$ as function of the strength of the initial attack, measured by the fraction of nodes $p$, which survive the initial attack for different values of tolerance $α$ in random regular and Erdös-Renyi graphs. We find the existence of first order phase transition line $p_t(α)$ on a $p-α$ plane, such that if $p <p_t$ the cascade of failures lead to a very small fracti…
We investigate the effect of a specific edge weighting scheme $\sim (k_i k_j)^β$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter $β$ and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different co…
We study the propagation of cascading failures in complex supply networks with a focus on nonlocal effects occurring far away from the initial failure. It is shown that a high clustering and a small average path length of a network generally suppress nonlocal overloads. These properties are typical for many real-world networks, often called small-world networks, such that cascades propagate mostly locally in these networks. Furthermore, we analyze the spatial aspects of countermeasures based on the intentional removal of additional edges. Nonlocal actions are generally required in networks whi…
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially meet the load demands imposed on the network. Every single line failure changes the load distribution in the surviving network, possibly causing further lines to become overloaded and trip as well. An initial single line failure can therefore potentially trigger massive cascading effects, and in this paper we measure the risk of such cascading events by the pr…
We study the robustness of flow networks against cascading failures under a partial load redistribution model. In particular, we consider a flow network of $N$ lines with initial loads $L_1, \ldots, L_N$ and free-spaces (i.e., redundant space) $S_1, \ldots, S_N$ that are independent and identically distributed with joint distribution $P_{LS}(x,y)=\mathbb{P}(L \leq x, S \leq y)$. The capacity $C_i$ is the maximum load allowed on line $i$, and is given by $C_i=L_i + S_i$. When a line fails due to overloading, it is removed from the system and $(1-\varepsilon)$-fraction of the load it was carryin…
Recently, there has been a growing concern about the overload status of the power grid networks, and the increasing possibility of cascading failures. Many researchers have studied these networks to provide design guidelines for more robust power grids. Topological analysis is one of the components of system analysis for its robustness. This paper presents a complex systems analysis of power grid networks. First, the cascading effect has been simulated on three well known networks: the IEEE 300 bus test system, the IEEE 118 bus test system, and the WSCC 179 bus equivalent model. To extend the …
MATCASC: A tool to analyse cascading line outages in power grids
Faculty of Technology, Policy and Management, Delft University of Technology（代尔夫特理工大学技术、政策与管理学院）；Computational Physics for Engineering Materials, ETH Zurich（苏黎世联邦理工学院工程材料计算物理）
In complex networks, the failure of one or very few nodes may cause cascading failures. When this dynamical process stops in steady state, the size of the giant component formed by remaining un-failed nodes can be used to measure the severity of cascading failures, which is critically important for estimating the robustness of networks. In this paper, we provide a cascade of overload failure model with local load sharing mechanism, and then explore the threshold of node capacity when the large-scale cascading failures happen and un-failed nodes in steady state cannot connect to each other to f…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure (triggering event). It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. We obtain {\em upper} and {\em lower} limits to network robust…
One of the serious threats related to climate change is an increase in the number and severity of extreme weather events. A prominent example are hurricanes, which result from rising coastal temperatures. Such extreme weather events can cause extensive damages in infrastructure systems and, potentially, destroy components in electricity transmission networks, which in turn can lead to major blackouts. In our recent work, we study the risk of hurricane-induced cascading failures in power systems of the U.S. East Coast using historical wind field data sets. For this purpose, we model the destruc…
Motivated by reliability of networks in critical infrastructures, we consider optimal robustness of a class of flow networks against a \textit{targeted} attack, namely max-load targeted attack, that triggers cascading failures due to removal of largest load carrying portion of lines. The setup involves a network of $N$ lines with initial loads $L_1, \ldots, L_N$, drawn from independent and identical uniform distribution, and free-spaces or redundancies $S_1, \ldots, S_N$ to be allocated. In the failure propagation mechanism, a line fails initially due to attack and later due to overloading. Th…
In today's global economy, supply chain (SC) entities have become increasingly interconnected with demand and supply relationships due to the need for strategic outsourcing. Such interdependence among firms not only increases efficiency but also creates more vulnerabilities in the system. Natural and human-made disasters such as floods and transport accidents may halt operations and lead to economic losses. Due to the interdependence among firms, the adverse effects of any disruption can be amplified and spread throughout the systems. This paper aims at studying the robustness of SC networks a…
We study how large functional networks can grow stably under possible cascading overload failures and evaluated the maximum stable network size above which even a small-scale failure would cause a fatal breakdown of the network. Employing a model of cascading failures induced by temporally fluctuating loads, the maximum stable size $n_{\text{max}}$ has been calculated as a function of the load reduction parameter $r$ that characterizes how quickly the total load is reduced during the cascade. If we reduce the total load sufficiently fast ($r\ge r_{\text{c}}$), the network can grow infinitely. …
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems $A$ and…
Using the linearized DC power flow model, we study cascading failures and their spatial and temporal properties in the US Western Interconnect (USWI) power grid. We also introduce the preferential Degree And Distance Attachment (DADA) model, with similar degree distributions, resistances, and currents to the USWI. We investigate the behavior of both grids resulting from the failure of a single line. We find that the DADA model and the USWI model react very similarly to that failure, and that their blackout characteristics resemble each other. In many cases, the failure of a single line can cau…
We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between in…
Large cascades can develop in online social networks as people share information with one another. Though simple reshare cascades have been studied extensively, the full range of cascading behaviors on social media is much more diverse. Here we study how diffusion protocols, or the social exchanges that enable information transmission, affect cascade growth, analogous to the way communication protocols define how information is transmitted from one point to another. Studying 98 of the largest information cascades on Facebook, we find a wide range of diffusion protocols - from cascading reshare…
ISC-CNR Physics Dept., Univ. dir Roma "La Sapienza"（罗马第一大学）；IMT Alti Studi Lucca（卢卡高等研究院）；LIMS London Institute of Mathematical Sciences（伦敦数学科学研究所）；Gubkin Russian State University of Oil and Gas（古比雪夫俄罗斯国立石油天然气大学）；ENEA: Italian National Agency for New Technologies, Energy and Sustainable Economic Development（意大利国家新能源与可持续发展技术署）
