Interdependent multi-layer networks: modeling and survivability analysis with applications to space-based networks

On the Rising Interdependency between the Power Grid, ICT Network, and E-Mobility: Modeling and Analysis

Boosting critical infrastructures’ (CIs) preparedness to threats, including natural disasters and manmade attacks, is a global imperative. The intrinsic dependencies and interdependencies between CIs hinder their resiliency. Moreover, the evolution of CIs is, in many cases, en routè to tighten those interdependencies. The goal of this paper is to uncover and analyze the rising interdependency between the electric power grid, information and communication technology (ICT) networks, and transportation systems that are heavily reliant on electric-power drivetrains, collectively referred to hereafter as electro-mobility (e-mobility). E-mobility includes electric vehicles (EVs) and electric railway systems. A new influence graph-based model is introduced, as a promising approach to model operational interdependencies between CIs. Each of the links of the influence graph represents the probability of failure of the sink node following a failure of the source node. A futuristic scenario has been analyzed assuming increased dependency of the power grid on ICT for monitoring and control, and high penetration levels of EVs and distributed energy resources (DERs) in an urban region. Inspecting the influence graph shows that the impact of interdependency between the power grid, the ICT network, and the transportation network, for the case study analyzed in this paper, does not lead to failures during normal operation with proper design; however, it is severe during emergency conditions since it leads to failure propagation among the three CIs. This paper sets the stage for more research on this topic, and calls for more attention to interdependency analysis.

Modeling joint restoration strategies for interdependent infrastructure systems

Life in the modern world depends on multiple critical services provided by infrastructure systems which are interdependent at multiple levels. To effectively respond to infrastructure failures, this paper proposes a model for developing optimal joint restoration strategy for interdependent infrastructure systems following a disruptive event. First, models for (i) describing structure of interdependent infrastructure system and (ii) their interaction process, are presented. Both models are considering the failure types, infrastructure operating rules and interdependencies among systems. Second, an optimization model for determining an optimal joint restoration strategy at infrastructure component level by minimizing the economic loss from the infrastructure failures, is proposed. The utility of the model is illustrated using a case study of electric-water systems. Results show that a small number of failed infrastructure components can trigger high level failures in interdependent systems; the optimal joint restoration strategy varies with failure occurrence time. The proposed models can help decision makers to understand the mechanisms of infrastructure interactions and search for optimal joint restoration strategy, which can significantly enhance safety of infrastructure systems.

The structure and dynamics of multilayer networks

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

Robustness of network of networks under targeted attack

The robustness of a network of networks (NON) under random attack has been studied recently [Gao et al., Phys. Rev. Lett. 107, 195701 (2011)]. Understanding how robust a NON is to targeted attacks is a major challenge when designing resilient infrastructures. We address here the question how the robustness of a NON is affected by targeted attack on high- or low-degree nodes. We introduce a targeted attack probability function that is dependent upon node degree and study the robustness of two types of NON under targeted attack: (i) a tree of n fully interdependent Erdős-Rényi or scale-free networks and (ii) a starlike network of n partially interdependent Erdős-Rényi networks. For any tree of n fully interdependent Erdős-Rényi networks and scale-free networks under targeted attack, we find that the network becomes significantly more vulnerable when nodes of higher degree have higher probability to fail. When the probability that a node will fail is proportional to its degree, for a NON composed of Erdős-Rényi networks we find analytical solutions for the mutual giant component P(∞) as a function of p, where 1-p is the initial fraction of failed nodes in each network. We also find analytical solutions for the critical fraction p(c), which causes the fragmentation of the n interdependent networks, and for the minimum average degree k[over ¯](min) below which the NON will collapse even if only a single node fails. For a starlike NON of n partially interdependent Erdős-Rényi networks under targeted attack, we find the critical coupling strength q(c) for different n. When q>q(c), the attacked system undergoes an abrupt first order type transition. When q≤q(c), the system displays a smooth second order percolation transition. We also evaluate how the central network becomes more vulnerable as the number of networks with the same coupling strength q increases. The limit of q=0 represents no dependency, and the results are consistent with the classical percolation theory of a single network under targeted attack.