### Abstract

A consecutive-k-n network is a generalization of the well-known consecutive-k-out-of-n system, and has many practical applications. This network consists of n + 2 nodes (node 0, the source, nodes 1, 2 ..., n, and node n + 1, the target) and directed links from node i to node j (0 ≤ i < j ≤ n + 1, j - i ≤ k). Because all nodes except the source and target, and all links are fallible, the network works if and only if there exists a working path from the source to the target. For the k = 2 case, based on identical node reliabilities and some assumptions on link reliabilities, Chen, Hwang and Li (1993) gave a recursive algorithm for the reliability of the consecutive-2-n network. In this paper we give a closed form equation for the reliability of the general consecutive-k-n network by means of a novel Markov chain method. Based on the equation, we propose an algorithm which is more efficient than other published ones for the reliability of the consecutive-k-n network.

Original language | English |
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Pages (from-to) | 159-166 |

Number of pages | 8 |

Journal | Journal of Information Science and Engineering |

Volume | 19 |

Issue number | 1 |

State | Published - 1 Jan 2003 |

### Keywords

- Algorithm
- Complexity
- Consecutive-k-n network
- Consecutive-k-out-of-n system
- Reliability

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## Cite this

*Journal of Information Science and Engineering*,

*19*(1), 159-166.