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Robustness of subsystem-based reliability for complete-transposition network

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Abstract

System reliability assessment is of great significance since it determines whether the system can perform properly or not. As an effective metric, subsystem-based reliability is defined to be the probability that at least one of the fault-free subsystems of a given size remains available in the event of node failure. In this work, we propose two distinct strategies to measure the subsystem reliability of complete-transposition network \(CT_n\) and investigate the robustness of its reliability bounds. Specifically, by virtue of the probability fault model, we establish the upper and lower bounds of subsystem reliability for \(CT_n\) in terms of at most four subgraphs intersecting. Subsequently, the approximation of subsystem reliability for \(CT_n\) is derived by ignoring the intersection among subgraphs. Furthermore, we investigate the robustness of subsystem reliability bounds for \(CT_n\) and determine the critical time point such that the bounds are valid. Numerical simulations are performed to verify the established analytic inference, which shows that the approximation of subsystem reliability is sufficient to characterize the exact value of subsystem reliability.

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Acknowledgements

The authors would like to express their sincere gratitude to all reviewers for valuable suggestions, which are helpful in improving and clarifying the original manuscript. We thank the National Institute of Education, Nanyang Technological University, where part of this research was performed. This work was partly supported by the National Natural Science Foundation of China (Nos. 61977016, 61572010), Natural Science Foundation of Fujian Province (Nos. 2020J01164, 2017J01738). This work was also partly supported by Fujian Alliance of Mathematics (No. 2023SXLMMS04) and China Scholarship Council (CSC No. 202108350054).

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  1. Shuming Zhou, Hong Zhang and Qifan Zhang have contributed equally to this work.

Authors and Affiliations

  1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, Fujian, China

    Baohua Niu, Shuming Zhou, Hong Zhang & Qifan Zhang

  2. Key Laboratory of Analytical Mathematics and Applications (Ministry of Education), Fujian Normal University, Fuzhou, 350117, China

    Shuming Zhou

  3. Center for Applied Mathematics of Fujian Province (Fujian Normal University), Fuzhou, 350117, China

    Shuming Zhou

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  1. Baohua Niu
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Correspondence to Shuming Zhou.

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Niu, B., Zhou, S., Zhang, H. et al. Robustness of subsystem-based reliability for complete-transposition network. J. Appl. Math. Comput. 69, 4717–4737 (2023). https://doi.org/10.1007/s12190-023-01948-7

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  • DOI: https://doi.org/10.1007/s12190-023-01948-7

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