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Journal of Information Science and Engineering, Vol.19 No.1, pp.159-166 (January 2003)


An Efficient Algorithm for the Reliability of
Consecutive-k-n Networks

Jen-Chun Chang, Rong-Jaye Chen* and Frank K. Hwang+
Department of Information Management
Ming Hsin Institute of Technology
Hsinchu, 304 Taiwan
E-mail: jimmy@mis.mhit.edu.tw
*Department of Computer Science and Information Engineering
+Department of Applied Mathematics
National Chiao Tung Univeristy
Hsinchu, 300 Taiwan
E-mail: rjchen@csie.nctu.edu.tw
E-mail: fhwang@math.nctu.edu.tw

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, K, 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.

Keywords: consecutive-k-n network, consecutive-k-out-of-n system, algorithm, reliability, complexity

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Received February 15, 2000; revised July 15, 2000; accepted July 31, 2000.
Communicated by Gen-Huey Chen.