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Statistical and Probabilistic Models in Reliability pp 279–294Cite as

Birkhäuser

Exact Methods to Compute Network Reliability

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Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

In this chapter we present and compare some exact methods to resolve network reliability problems. These problems concern all kinds of networks, such as computer, communication or power networks. When components of the network are subject to random failures, the network may or may not continue functioning after the failures of some components. The probability that the network will function is its reliability. Networks are modeled by a graph G = (V, E) composed of elements that fail independently one another with known probabilities. The K-terminal reliability problem has been studied extensively. It consists in evaluating the probability that a given subset of vertices, denoted K, is connected. This problem is NP-hard. We propose here to present the main methods, developed since the 1970s. We first consider the enumeration methods using elementary states, paths or cuts. Then we explain the factoring method performed by reductions. These allow to handle series-parallel graphs to be processed in linear time. Finally, we present the decomposition method implemented as a table-based reduction algorithm allowing to resolve the reliability problem in linear time for graphs with bounded pathwidth.

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Author information

Authors and Affiliations

  1. Université de Technologie de Compiègne, Compiègne, France

    Corinne Lucet & Jean-François Manouvrier

Authors
  1. Corinne Lucet
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  2. Jean-François Manouvrier
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Editor information

Editors and Affiliations

  1. Power Engineering Faculty, University Politehnica Bucharest, 77206, Bucharest, Romania

    D. C. Ionescu

  2. Division Mathématiques Appliquées, Université de Technologie de Compiègne, 60205, Compiègne Cedex, France

    N. Limnios

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© 1999 Springer Science+Business Media New York

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Lucet, C., Manouvrier, JF. (1999). Exact Methods to Compute Network Reliability. In: Ionescu, D.C., Limnios, N. (eds) Statistical and Probabilistic Models in Reliability. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1782-4_20

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  • DOI: https://doi.org/10.1007/978-1-4612-1782-4_20

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7280-9

  • Online ISBN: 978-1-4612-1782-4

  • eBook Packages: Springer Book Archive

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