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Inflection points for network reliability

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Abstract

Given a finite, undirected graph G (possibly with multiple edges), we assume that the vertices are operational, but the edges are each independently operational with probability p. The (all-terminal) reliability, \(\operatorname{Rel}(G,p)\), of G is the probability that the spanning subgraph of operational edges is connected. It has been conjectured that reliability functions have at most one point of inflection in (0,1). We show that the all-terminal reliability of almost every simple graph of order n has a point of inflection, and there are indeed infinite families of graphs (both simple and otherwise) with more than one point of inflection.

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Acknowledgement

The first author would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Jason I. Brown

  2. Systems Engineering Group, Delft University of Technology, Delft, The Netherlands

    Yakup Koç

  3. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands

    Robert E. Kooij

  4. TNO (Netherlands Organisation for Applied Scientific Research), Delft, The Netherlands

    Robert E. Kooij

Authors
  1. Jason I. Brown
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  2. Yakup Koç
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  3. Robert E. Kooij
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Correspondence to Jason I. Brown.

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Brown, J.I., Koç, Y. & Kooij, R.E. Inflection points for network reliability. Telecommun Syst 56, 79–84 (2014). https://doi.org/10.1007/s11235-013-9820-0

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