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How to Model and Enumerate Geographically Correlated Failure Events in Communication Networks

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Guide to Disaster-Resilient Communication Networks

Part of the book series: Computer Communications and Networks ((CCN))

Abstract

Several works shed light on the vulnerability of networks against regional failures, which are failures of multiple pieces of equipment in a geographical region as a result of a natural or human-made disaster. This chapter overviews how this information can be added to the existing network protocols through defining shared risk link groups (SRLGs) and probabilistic SRLGs (PSRLGs). The output of this chapter can be the input of later chapters to design and operate the networks to enhance the preparedness against disasters and regional failures in general. In particular, we are focusing on the state-of-the-art algorithmic approaches for generating lists of (P)SRLGs of the communication networks protecting different sets of disasters.

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Notes

  1. 1.

    A point of presence (PoP) is an artificial demarcation point or interface point between communicating entities.

  2. 2.

    For infinite sets, one can use discretization and consider only finite number of sets, albeit with a small error.

  3. 3.

    Some papers like [6, 20, 40, 42, 43] are loosely related to the regional (P)SRLG generating problem, however, our goal is presenting the most relevant works in this field.

    A list of (P)SRLGs can be used as a pre-computed input for various problems [3, 11, 14, 17].

  4. 4.

    This is true for communication networks but not for networks in which there is no monotonicity in failures.

    When attaching probability to the SRLGs, this no longer holds.

  5. 5.

    If there are more than one equal-size sets that satisfy the condition, one is chosen arbitrarily.

  6. 6.

    Polygonal chains can be dismantled to a set of line segments; the method can be applied, and then, the sets of line segments can be joined.

  7. 7.

    Reference [18] offers a mistaken heuristic for computing \(M_r\). It claims the disc failures having nodes of the network as their centre point represent the worst case of failures of radius r, which is clearly not the case. Consider, e.g. a network being an equilateral triangle with side length 3, and \(r=1\); here, \(M_r\) consists of a single SRLG containing all the 3 links instead of the 3 link-pairs claimed by [18].

  8. 8.

    Refreshing in Algorithm 4.1 means that \(M'\) is the set of maximal failures among which are already checked, and if f is maximal amongst them, it is added to \(M'\) and all f’s subsets are eliminated from \(M'\); or if f is not maximal in\(M'\), nothing happens.

  9. 9.

    Under certain conditions, the complexity of the algorithm presented in [29] is optimal.

  10. 10.

    Probabilistic refinements are presented in Sect. 4.3.4.1.

  11. 11.

    Similarly to the precise algorithms, refreshing in Algorithm 4.2 means that \(M_r^g\) is the set of maximal failures among which are already checked, and if \(e(P)_{\text {hit}}\) is maximal amongst them, it is added to \(M_r^g\) and all \(e(P)_{\text {hit}}\)’s subsets are eliminated from \(M_r^g\); or if\(e(P)_{\text {hit}}\) is not maximal in \(M'\), nothing happens.

  12. 12.

    In other words, the degree of over-approximation (Definition 4.9) tends to (1, 0) as \(d_{\mathcal {P}}\rightarrow 0\).

  13. 13.

    Reference [35] tackles a similar problem.

  14. 14.

    An R-tree is an efficient tree data structure for storing spatial objects. Objects are grouped based on their minimum bounding rectangle.

  15. 15.

    The investigated measures are: (1) the total expected capacity of the intersected links, (2) the fraction of pairs of nodes that remain connected, (3) the maximum flow between a given pair of nodes, (4) the average value of maximum flow between all pairs of nodes.

  16. 16.

    Algorithm 4.3 is polynomial assuming the SRLG enumeration and calculating the metric value runs in polynomial time.

  17. 17.

    In contrast, Sect. 4.3.2.5 depicts the non-probabilistic version of this regional failure model.

  18. 18.

    In particular, we may assume that the probability f(e, p) that link e fails if a disaster with epicentre p happens is independent of p as long as it is in \(c\). We denote this common value by \(f(e,c)\).

  19. 19.

    In Sect. 4.4.1.2, we could see how CFPs (and thus all kind of PSRLGs) can be used for calculating the availability of services. To leverage the probabilistic information stored in PSRLGs in case of resilient routing, one needs to calculate a list of SRLGs based on a PSRLG input.

  20. 20.

    Of course, in a non-practical extreme case of R being greater than half of the network diameter, it is possible that \(M_T=\{E\}\), meaning \(|M_T|=1\).

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Acknowledgements

This chapter is based on work from COST Action CA15127 (“Resilient communication services protecting end-user applications from disaster-based failures—RECODIS”) supported by European Cooperation in Science and Technology (COST). Part of this work is supported by the Hungarian Scientific Research Fund (grant No. OTKA K124171, K128062), by the BME-Artificial Intelligence FIKP grant of EMMI (BME FIKP-MI/SC), and the HUJI Cyber Security Center together with the Israel National Cyber Directorate in the Prime Minister’s Office.

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Authors and Affiliations

  1. High-Speed Networks Laboratory (HSNLab), MTA-BME Future Internet Research Group, Budapest University of Technology and Economics, Budapest, Hungary

    Balázs Vass & János Tapolcai

  2. School of Engineering and Computer Science, Hebrew University, Jerusalem, Israel

    David Hay

  3. Delft University of Technology, Delft, The Netherlands

    Jorik Oostenbrink & Fernando Kuipers

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  1. Balázs Vass
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  2. János Tapolcai
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  3. David Hay
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  4. Jorik Oostenbrink
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  5. Fernando Kuipers
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Correspondence to Balázs Vass .

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Editors and Affiliations

  1. Department of Computer Communications, Gdańsk University of Technology, Gdańsk, Poland

    Jacek Rak

  2. School of Computing and Communications, Lancaster University, Lancaster, UK

    David Hutchison

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Vass, B., Tapolcai, J., Hay, D., Oostenbrink, J., Kuipers, F. (2020). How to Model and Enumerate Geographically Correlated Failure Events in Communication Networks. In: Rak, J., Hutchison, D. (eds) Guide to Disaster-Resilient Communication Networks. Computer Communications and Networks. Springer, Cham. https://doi.org/10.1007/978-3-030-44685-7_4

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  • DOI: https://doi.org/10.1007/978-3-030-44685-7_4

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