### Abstract

The design of reliable communications networks is an interesting and important topic. Perhaps the most common measure of reliability is a probabilistic one: the probability that a network is connected given the possibility of statistically independent line failures. In general, this is not efficiently computable. In this article, we develop a formula for the reliability of the most reliable maximal series-parallel networks. The most reliable maximal series-parallel networks are those maximal series-parallel networks with the minimum number of vertices of degree 2, independent of many of the simpler reliability estimates. A two-dimensional recurrence relating networks of varying sizes and edge deficiencies provides a generating function which in turn is exploited to give a simple closed expression for reliability.

Original language | English (US) |
---|---|

Pages (from-to) | 27-32 |

Number of pages | 6 |

Journal | Networks |

Volume | 15 |

Issue number | 1 |

State | Published - Mar 1985 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Networks*,

*15*(1), 27-32.

**MOST RELIABLE SERIES-PARALLEL NETWORKS.** / Neufeld, Eric M.; Colbourn, Charles.

Research output: Contribution to journal › Article

*Networks*, vol. 15, no. 1, pp. 27-32.

}

TY - JOUR

T1 - MOST RELIABLE SERIES-PARALLEL NETWORKS.

AU - Neufeld, Eric M.

AU - Colbourn, Charles

PY - 1985/3

Y1 - 1985/3

N2 - The design of reliable communications networks is an interesting and important topic. Perhaps the most common measure of reliability is a probabilistic one: the probability that a network is connected given the possibility of statistically independent line failures. In general, this is not efficiently computable. In this article, we develop a formula for the reliability of the most reliable maximal series-parallel networks. The most reliable maximal series-parallel networks are those maximal series-parallel networks with the minimum number of vertices of degree 2, independent of many of the simpler reliability estimates. A two-dimensional recurrence relating networks of varying sizes and edge deficiencies provides a generating function which in turn is exploited to give a simple closed expression for reliability.

AB - The design of reliable communications networks is an interesting and important topic. Perhaps the most common measure of reliability is a probabilistic one: the probability that a network is connected given the possibility of statistically independent line failures. In general, this is not efficiently computable. In this article, we develop a formula for the reliability of the most reliable maximal series-parallel networks. The most reliable maximal series-parallel networks are those maximal series-parallel networks with the minimum number of vertices of degree 2, independent of many of the simpler reliability estimates. A two-dimensional recurrence relating networks of varying sizes and edge deficiencies provides a generating function which in turn is exploited to give a simple closed expression for reliability.

UR - http://www.scopus.com/inward/record.url?scp=0022034518&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022034518&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022034518

VL - 15

SP - 27

EP - 32

JO - Networks

JF - Networks

SN - 0028-3045

IS - 1

ER -