Modelling Interdependent Cascading Failures in Real World Complex Networks using a Functional Dependency Model

Infrastructure systems are becoming increasingly complex and interdependent. As a result our ability to predict the likelihood of large-scale failure of these systems has significantly diminished and the consequence of this is that we now have a greatly increased risk of devastating impacts to society. Traditionally these systems have been analysed using physically-based models. However, this approach can only provide information for a specific network and is limited by the number of scenarios that can be tested. In an attempt to overcome this shortcoming, many studies have used network graph theory to provide an alternative analysis approach. This approach has tended to consider infrastructure systems in isolation, but has recently considered the analysis of interdependent networks through combination with percolation theory. However, these studies have focused on the analysis of synthetic networks and tend to only consider the topology of the system. In this paper we develop a new analysis approach, based upon network theory, but accounting for the hierarchical structure and functional dependency observed in real world infrastructure networks. We apply this method to two real world networks, to show that it can be used to quantify the impact that failures within an electricity network have upon a dependent water network

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

How motifs condition critical thresholds for tipping cascades in complex networks: Linking Micro- to Macro-scales

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erd\"os-R\'enyi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole

The failure tolerance of mechatronic software systems to random and targeted attacks

This paper describes a complex networks approach to study the failure tolerance of mechatronic software systems under various types of hardware and/or software failures. We produce synthetic system architectures based on evidence of modular and hierarchical modular product architectures and known motifs for the interconnection of physical components to software. The system architectures are then subject to various forms of attack. The attacks simulate failure of critical hardware or software. Four types of attack are investigated: degree centrality, betweenness centrality, closeness centrality and random attack. Failure tolerance of the system is measured by a 'robustness coefficient', a topological 'size' metric of the connectedness of the attacked network. We find that the betweenness centrality attack results in the most significant reduction in the robustness coefficient, confirming betweenness centrality, rather than the number of connections (i.e. degree), as the most conservative metric of component importance. A counter-intuitive finding is that "designed" system architectures, including a bus, ring, and star architecture, are not significantly more failure-tolerant than interconnections with no prescribed architecture, that is, a random architecture. Our research provides a data-driven approach to engineer the architecture of mechatronic software systems for failure tolerance.Comment: Proceedings of the 2013 ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA (In Print

Structural Vulnerability Analysis of Electric Power Distribution Grids

Power grid outages cause huge economical and societal costs. Disruptions in the power distribution grid are responsible for a significant fraction of electric power unavailability to customers. The impact of extreme weather conditions, continuously increasing demand, and the over-ageing of assets in the grid, deteriorates the safety of electric power delivery in the near future. It is this dependence on electric power that necessitates further research in the power distribution grid security assessment. Thus measures to analyze the robustness characteristics and to identify vulnerabilities as they exist in the grid are of utmost importance. This research investigates exactly those concepts- the vulnerability and robustness of power distribution grids from a topological point of view, and proposes a metric to quantify them with respect to assets in a distribution grid. Real-world data is used to demonstrate the applicability of the proposed metric as a tool to assess the criticality of assets in a distribution grid