Modelling Interdependencies Between the Electricity and Information Infrastructures

Laprie, Jean-Claude; Kanoun, Karama; Kaâniche, Mohamed

doi:10.1007/978-3-540-75101-4_5

Cited by 115 publications

(68 citation statements)

References 27 publications

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“…where L † represents the Moore-Penrose pseudoinverse of L. At the threshold a rough lower bound for λ 2 …”

Section: If and Only If C Cmentioning

confidence: 99%

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Maximizing algebraic connectivity in interconnected networks

Shakeri¹,

Albin²,

Sahneh³

et al. 2016

Phys. Rev. E

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Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks operate together with interlayer links among them. In order to have a well-connected multilayer structure, it is necessary to optimally design these interlayer links considering realistic constraints. In this work, we solve the problem of finding an optimal weight distribution for one-to-one interlayer links under budget constraint. We show that for the special multiplex configurations with identical layers, the uniform weight distribution is always optimal. On the other hand, when the two layers are arbitrary, increasing the budget reveals the existence of two different regimes. Up to a certain threshold budget, the second eigenvalue of the supra-Laplacian is simple, the optimal weight distribution is uniform, and the Fiedler vector is constant on each layer. Increasing the budget past the threshold, the optimal weight distribution can be nonuniform. The interesting consequence of this result is that there is no need to solve the optimization problem when the available budget is less than the threshold, which can be easily found analytically. DOI: 10.1103/PhysRevE.93.030301Real-world networks are often connected together and therefore influence each other [1]. Robust design of interdependent networks is critical to allow uninterrupted flow of information, power, and goods in spite of possible errors and attacks [2][3][4]. The second eigenvalue of the Laplacian matrix, λ 2 (L), is a good measure of network robustness [5]. Fiedler shows that algebraic connectivity increases by adding links [6]. Moreover, it is harder to bisect a network with higher algebraic connectivity [7]. The second eigenvalue of the Laplacian matrix is also a measure of the speed of mixing for a Markov process on a network [8]. Boyd et al. maximize the mixing rate by assigning optimum link weights in the setting of a single layer (see Refs. [9,10]).For multiplex networks (see Fig. 1), a natural question is the following. Given fixed network layers, how should the weights be assigned to interlayer links in order to maximize algebraic connectivity?The behavior of λ 2 , in the case of identical weights, i.e., with a fixed coupling weight p for every interlayer link, has been studied recently. networks by choosing from a set of interlayer links with predefined weights [16].In this Rapid Communication we remove the constraint of identical interlinking weights and pose the problem of finding the maximum algebraic connectivity for a one-toone interconnected structure between different layers in the presence of limited resources. We show that up to the threshold budget p * N (where p * is the same threshold studied in Refs. [11,13,14]) the uniform distribution of identical weights is actually optimal. For larger budgets, the optimal distribution of weights is generally not uniform.Let G = (V,E) represent a network a...

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“…where L † represents the Moore-Penrose pseudoinverse of L. At the threshold a rough lower bound for λ 2 …”

Section: If and Only If C Cmentioning

confidence: 99%

“…Robust design of interdependent networks is critical to allow uninterrupted flow of information, power, and goods in spite of possible errors and attacks [2][3][4]. The second eigenvalue of the Laplacian matrix, λ 2 (L), is a good measure of network robustness [5].…”

mentioning

confidence: 99%

Maximizing algebraic connectivity in interconnected networks

Shakeri¹,

Albin²,

Sahneh³

et al. 2016

Phys. Rev. E

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“…However, despite the high significance and relevance of the subject, only a few studies on interdependent networks exist and these usually focus on the analyses of specific real network data [2][3][4][5][6]. The limited progress is mainly due to the absence of theoretical tools for analyzing interdependent systems.…”

mentioning

confidence: 99%

Inter-similarity between coupled networks

Parshani¹,

Rozenblat²,

Ietri³

et al. 2010

EPL

306

245

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Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of dependent nodes are coupled according to some regularity which we coin inter-similarity. For example, we study a system composed from an interdependent world wide port network and a world wide airport network and show that well connected ports tend to couple with well connected airports. We introduce two quantities for measuring the level of inter-similarity between networks (i) Inter degree-degree correlation (IDDC) (ii) Inter-clustering coefficient (ICC). We then show both by simulation models and by analyzing the port-airport system that as the networks become more inter-similar the system becomes significantly more robust to random failure.Recently, an American Congressional Committee highlighted the intensified risk in an attack on national infrastructures, due to the growing interdependencies between different infrastructures [1]. However, despite the high significance and relevance of the subject, only a few studies on interdependent networks exist and these usually focus on the analyses of specific real network data [2][3][4][5][6]. The limited progress is mainly due to the absence of theoretical tools for analyzing interdependent systems. Very recent studies [7,8] present for the first time a framework for studying interdependency between networks and show that such interdependencies significantly increases the vulnerability of the networks to random attack. In these studies, the dependencies between the networks are assumed to be completely random, i.e., a randomly selected node from network A is connected and depends on a randomly selected node from network B and vice versa. Due to the dependencies an initial failure of even a small fraction of nodes from one network can lead to an iterative process of failures that can completely fragment both networks.However, the restriction of random interdependencies is a strong assumption that usually does not occur in many real interdependent systems. As a first example consider the two infrastructures that are mentioned both in the committee report [1] and in the studies discussed above [2,7,8]: The Italian power grid and SCADA communication networks. A power node depends on a communication node for control while a communication node depends on a power node for electricity. It is highly unlikely that a central (high degree) communication node will depend on a small (low degree) power node. Rather, it is much more common that a central communication node depends on a central power station. Moreover, coupled networks usually also poses some similarity in structure, for instance, an area that is overpopulated is bound to have many power stations as well as many communication nodes. Another real example is the world wide port and airport networks that we study in this manuscript.We find that well connected ports tend to couple to wel...

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“…Infrastructure interdependency has specifically been described as both a distinctly bidirectional relationship (Laprie et al, 2007;Rinaldi et al, 2001) and elsewhere in such a way that includes both bidirectional and non-reciprocal dependency in the form of an influence from one element on another (HM Treasury and Infrastructure UK, 2011; Pederson et al, 2006). Others have made this distinction by referring to 'input' only and 'mutual' interdependencies (Eusgeld et al, 2011).…”

Section: Directionalitymentioning

confidence: 99%

A framework for characterising infrastructure interdependencies

Carhart¹,

Rosenberg²

2016

IJCAST

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Abstract:The interdependencies within and between infrastructure systems can produce benefits and risks. The perception and value of these relationships can vary significantly depending on the viewpoint of the actors within the system. The current methods for describing these relationships do not necessarily account for these different perspectives, and tend to focus on reducing the risks and vulnerabilities associated with interdependency. By taking a holistic, multi-stakeholder approach of the infrastructure system it is possible to also identify the proactive opportunities for improving efficiency, effectiveness and resilience that can emerge from the relationships. A taxonomy is presented which allows for the characterisation of infrastructure relationships in multiple dimensions, with particular focus on identifying opportunities in a way that is therefore complementary to current methods. An application of this taxonomy to the identification of potentially beneficial relationships within the UK infrastructure system is described.Keywords: infrastructure interdependency; system-of-systems; systems architecture framework.Reference to this paper should be made as follows: Carhart, N. and Rosenberg, G. (2016) His research has included the development and implementation of new accident modelling techniques and process to enhance socio-technical resilience within high-hazard industries. Under ICIF he is involved in researching the planning and management of emergent properties within the infrastructure system-of-systems in order to enhance the value proposition and ensure the sustainable delivery of the valued society outcomes it facilitates. This has looked at supporting resilience at all levels of the system from the individual user to the governance structures and the critical role that learning and education play in managing the complex challenges of the future. He is also the editor of the Hazards Forum Newsletter. Ges Rosenberg is a Research Fellow in the Engineering Systems and DesignResearch Group at the University of Bristol focussed on systems-based, interdisciplinary approaches to engineering. His key themes include uncertainty management, evidence-based decision making, sustainability, resilience and 36 N. Carhart and G. Rosenberg creating value through co-design of innovative business models. His research includes co-developing the interdependency planning and management framework for UK Treasury's Green Book supplementary guidance: valuing infrastructure spend. He is the Network Manager for the EPSRC-funded project 'Redistributed Manufacturing | Resilient Sustainable City'. His prior background is in aerospace engineering including mathematical modelling, simulation and analysis of linear and nonlinear dynamic systems, and controls-structures interaction. This paper is a revised and expanded version of a paper entitled 'Establishing a common language of infrastructure interdependency' presented at the

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Modelling Interdependencies Between the Electricity and Information Infrastructures

Cited by 115 publications

References 27 publications

Maximizing algebraic connectivity in interconnected networks

Maximizing algebraic connectivity in interconnected networks

Inter-similarity between coupled networks

A framework for characterising infrastructure interdependencies

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