Cascading failures in interconnected networks with dynamical redistribution of loads

Cascade-robustness optimization of coupling preference in interconnected networks

Cascading failures of loads in isolated networks under random failures or intentional attacks have been studied in the past decade. The corresponding results for interconnected networks remain missing. In this paper we extend the cascading failure model used in isolated networks to the case of interconnected networks, and study cascades of failures in a data-packet transport scenario. We find that for sparse coupling, enhancing the coupling probability can make interconnected networks more robust against intentional attacks, but keeping increasing the coupling probability has the opposite effect for dense coupling. Additionally, the optimal coupling probability is largely affected by the coupling preference. Finally, assortative coupling is more helpful to resist the cascades compared to disassortative or random coupling. These results can be useful for the design and optimization of interconnected networks such as communication networks, power grids and transportation systems.

In network security, how to use efficient response methods against cascading failures of complex networks is very important. In this paper, concerned with the highest-load attack (HL) and random attack (RA) on one edge, we define five kinds of weighting strategies to assign the external resources for recovering the edges from cascading failures in heterogeneous scale-free (SF) networks. The influence of external resources, the tolerance parameter, and the different weighting strategies on SF networks against cascading failures is investigated carefully. We find that, under HL attack, the fourth kind of weighting method can more effectively improve the integral robustness of SF networks, simultaneously control the spreading velocity, and control the outburst of cascading failures in SF networks than other methods. Moreover, the third method is optimal if we only knew the local structure of SF networks and the uniform assignment is the worst. The simulations of the real-world autonomous system in, Internet have also supported our findings. The results are useful for using efficient response strategy against the emergent accidents and controlling the cascading failures in the real-world networks.

Research on cascading failure in multilayer network with different coupling preference

RETRACTED: Vulnerability analysis of road network for dangerous goods transportation considering intentional attack: Based on Cellular Automata

The robustness of infrastructure networks has attracted great attention in recent years. Scholars have studied the robustness of complex networks against cascading failures from different aspects. In this paper, a new capacity allocation strategy is proposed to reduce cascading failures and improve network robustness without changing the network structure. Compared with the typical strategy proposed in Motter–Lai (ML) model, the new strategy can reduce the scale of cascading failure. The new strategy applied in scale-free network is more efficient. In addition, to reasonably evaluate the two strategies, we introduce contribution rate of unit capacity to network robustness as evaluation index. Results show that our new strategy works well, and it is more advantageous in the rational utilization of capacity in scale-free networks. Furthermore, we were surprised to find that the efficient utilization of capacity costs declined as costs rose above a certain threshold, which indicates that it is not wise to restrain cascading failures by increasing capacity costs indefinitely.

Road vulnerability is crucial for enhancing the robustness of urban road networks and urban resilience. In medium or large cities, road failures in the face of unexpected events, such as heavy rainfall, can affect regional traffic efficiency and operational stability, which can cause high economic losses in severe cases. Conventional studies of road cascading failures under unexpected events focus on dynamic traffic flow, but the significant drop in traffic flow caused by urban flooding does not accurately reflect road load changes. Meanwhile, limited studies analyze the spatiotemporal pattern of cascading failure of urban road networks under real rainstorms and the correlation of this pattern with road vulnerability. In this study, road vulnerability is calculated using a network’s global efficiency measures to identify locations of high and low road vulnerability. Using the between centrality as a measure of road load, the spatiotemporal patterns of road network cascading failure during a real rainstorm are analyzed. The spatial association between road network vulnerability and cascading failure is then investigated. It has been determined that 90.09% of the roads in Zhengzhou city have a vulnerability of less than one, indicating a substantial degree of spatial heterogeneity. The vulnerability of roads adjacent to the city ring roads and city center is often lower, which has a significant impact on the global network’s efficiency. In contrast, road vulnerability is greater in areas located on the urban periphery, which has little effect on the global network’s efficiency. Five hot spots and three cold spots of road vulnerability are identified by using spatial autocorrelation analysis. The cascading failure of a road network exhibits varied associational characteristics in distinct clusters of road vulnerability. Road cascading failure has a very minor influence on the network in hot spots but is more likely to cause widespread traffic congestion or disruption in cold spots. These findings can help stakeholders adopt more targeted policies and strategies in urban planning and disaster emergency management to build more resilient cities and promote sustainable urban development.

Network science has attracted much attention in recent years due to its interdisciplinary applications. We witnessed the revolution of network science in 1998 and 1999 started with small-world and scale-free networks having now thousands of high-profile publications, and it seems that since 2010 studies of ‘network of networks’ (NON), sometimes called multilayer networks or multiplex, have attracted more and more attention. The analytic framework for NON yields a novel percolation law for n interdependent networks that shows that percolation theory of single networks studied extensively in physics and mathematics in the last 50 years is a specific limit of the rich and very different general case of n coupled networks. Since then, properties and dynamics of interdependent and interconnected networks have been studied extensively, and scientists are finding many interesting results and discovering many surprising phenomena. Because most natural and engineered systems are composed of multiple subsystems and layers of connectivity, it is important to consider these features in order to improve our understanding of such complex systems. Now the study of NON has become one of the important directions in network science. In this paper, we review recent studies on the new emerging area—NON. Due to the fast growth of this field, there are many definitions of different types of NON, such as interdependent networks, interconnected networks, multilayered networks, multiplex networks and many others. There exist many datasets that can be represented as NON, such as network of different transportation networks including flight networks, railway networks and road networks, network of ecological networks including species interacting networks and food webs, network of biological networks including gene regulation network, metabolic network and protein–protein interacting network, network of social networks and so on. Among them, many interdependent networks including critical infrastructures are embedded in space, introducing spatial constraints. Thus, we also review the progress on study of spatially embedded networks. As a result of spatial constraints, such interdependent networks exhibit extreme vulnerabilities compared with their non-embedded counterparts. Such studies help us to understand, realize and hopefully mitigate the increasing risk in NON.

The local-world (LW) evolving network model shows a transition for the degree distribution between the exponential and power-law distributions, depending on the LW size. Cascading failures under intentional attacks in LW network models with different LW sizes were investigated using the cascading failures load model. We found that the LW size has a significant impact on the network’s robustness against deliberate attacks. It is much easier to trigger cascading failures in LW evolving networks with a larger LW size. Therefore, to avoid cascading failures in real networks with local preferential attachment such as the Internet, the World Trade Web and the multi-agent system, the LW size should be as small as possible.

Core infrastructure systems like water, electricity, transport, and communication are fundamental to modern cities, supporting vital services and everyday societal operations. However, their resilience is increasingly threatened by the occurrence and severity of compound hazards, such as floods that occurs concurrently with power system outages. These risks increase systemic risks that go far beyond the original source of disruption and frequently cause cascade failures throughout interconnected networks. With an emphasis on the dynamics of interdependencies and cascading consequences, this study investigates the resilience of urban lifeline networks under compound hazard situations. To capture the multi-layered vulnerabilities of lifeline systems, the study combines functional dependencies, performance indicators, and hazard scenarios using a network-based modelling technique. The results demonstrate how interruptions in one industry may quickly spread to others, worsening service outages and impairing emergency response capabilities. Key resilience measures—robustness, redundancy, and recovery time—are evaluated to identify vulnerable nodes and routes under compound hazards. The paper also explores mitigation strategies such as advanced monitoring, decentralized energy systems, and adaptive infrastructure design. By linking hazard modelling with resilience assessment, the study advances knowledge and offers practical insights for policymakers and engineers to strengthen urban lifeline resilience. This review uniquely synthesizes recent advances in understanding the interdependencies and cascading dynamics of urban lifeline systems exposed to compound hazards. It provides a comprehensive framework that integrates systemic risk concepts with resilience assessment approaches, offering new insights for urban resilience research and practice. This review contributes to the current body of knowledge by synthesizing existing research on cascading failures and systemic risks affecting urban lifeline systems under compound hazards, and by proposing a conceptual framework to enhance urban resilience planning and risk-informed decision-making.

Exploring the robustness of urban bus network: A case from Southern China

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 show that scale-free networks are more robust against cascading overload failures than Erdős-Rényi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works, which neglect the effect of fluctuations of loads.

High-performance supercomputers generally comprise millions of CPUs in which interconnection networks play an important role to achieve high performance. New design paradigms of dynamic on-chip interconnection network involve a) topology b) synthesis, modeling and evaluation c) quality of service, fault tolerance and reliability d) routing procedures. To construct a dynamic highly fault tolerant interconnection networks requires more disjoint paths from each source-destination node pair at each stage and dynamic rerouting capability to use the various available paths effectively. Fast routing and rerouting strategy is needed to provide reliable performance on switch/link failures. This paper proposes two new architecture designs of fault tolerant interconnection networks named as reliable interconnection networks (RIN-1 and RIN-2). The proposed layouts are multipath multi-stage interconnection networks providing four disjoint paths for all the source-destination node pairs with dynamic rerouting capability. The designs can withstand switch failures in all the stages (including input and output stages) and provide more reliability. Reliability analysis of various MIN architectures is evaluated. On comparing the results with some existing MINs it is evident that the proposed designs provides higher reliability values and fault tolerance.

The effects of natural disasters, pandemic‐induced lockdowns, and other disruptions often cascade across networks. In this work, we use minimum cost of resilience (MCOR) and operation‐based resilience metrics to quantify network performance against single‐connectivity failures and identify critical connections in interconnected networks. MCOR corresponds to the minimum additional infrastructure investment that is required to achieve a certain level of resilience. To guarantee MCOR, we incorporate the metrics in a multi‐scenario mixed‐integer linear program (MILP) that accounts for resilience in the design phase of interconnected networks. The goal is to obtain optimal generation and transportation capacities with flexible operation under all single‐connectivity disruption scenarios. We demonstrate the applicability of our resilience‐aware framework on a water‐energy nexus (WEN) example focusing on grass‐root design and retrofitting. We further apply the framework to analyze a regional WEN and observe that it is possible to achieve “full” resilience in the expense of additional regional investments.

An efficient local cascade defense method in complex networks