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MARKOV CHAIN METHOD FOR COMPUTING THE RELIABILITY OF HAMMOCK NETWORKS

Published online by Cambridge University Press:  20 November 2020

Marilena Jianu Open the ORCID record for Marilena Jianu [Opens in a new window] ,
Daniel Ciuiu ,
Leonard Dăuş  and
Mihail Jianu
Marilena Jianu
Affiliation:
Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, Blvd. Lacul Tei, 124, 020396Bucharest, Romania E-mail: marilena.jianu@utcb.ro; E-mail: daniel.ciuiu@utcb.ro; E-mail: leonard.daus@utcb.ro
Daniel Ciuiu
Affiliation:
Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, Blvd. Lacul Tei, 124, 020396Bucharest, Romania E-mail: marilena.jianu@utcb.ro; E-mail: daniel.ciuiu@utcb.ro; E-mail: leonard.daus@utcb.ro
Leonard Dăuş
Affiliation:
Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, Blvd. Lacul Tei, 124, 020396Bucharest, Romania E-mail: marilena.jianu@utcb.ro; E-mail: daniel.ciuiu@utcb.ro; E-mail: leonard.daus@utcb.ro
Mihail Jianu
Affiliation:
St Catherine's College, University of Oxford, Manor Rd, OxfordOX1 3UJ, UK E-mail: mihail.jianu@stcatz.ox.ac.uk
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Abstract

In this paper, we develop a new method for evaluating the reliability polynomial of a hammock network. The method is based on a homogeneous absorbing Markov chain and provides the exact reliability for networks of width less than 5 and arbitrary length. Moreover, it produces a lower bound for the reliability polynomial for networks of width greater than or equal to 5. To investigate how sharp this lower bound is, we compare our method with other approximation methods and it proves to be the most accurate in terms of absolute as well as relative error. Using the fundamental matrix, we also calculate the average time to absorption, which provides the mean length of a network that is expected to work.

Keywords

graph polynomialshammock networksMarkov chainsnetwork reliability
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 276 - 293
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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