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Efficient construction of binary decision diagrams for network reliability with imperfect vertices

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  • Kawahara, Jun
  • Sonoda, Koki
  • Inoue, Takeru
  • Kasahara, Shoji

Abstract

This paper discusses evaluation of the network reliability with imperfect vertices, which computes the probability that a subset of nodes is communicable under possible failures of links and nodes. Although the network reliability is efficiently computed utilizing a binary decision diagram (BDD) if assuming link failures only, it can be 10 times slower if considering node failures as well. This is because existing algorithms are designed to repeatedly update a BDD for every node failure in a step-by-step manner. This research proposes an algorithm that creates the final BDD without the redundant repetitions, which greatly improves the computation efficiency. Moreover, this paper presents a better variable order of BDDs among variables corresponding to links and nodes. Under the variable order, the proposed algorithm is compared with existing ones by numerical experiments using various benchmark networks including real communication networks. The results show that the proposed algorithm runs 198.2 times faster than the existing ones for the 10-by-10 grid graph, 1074.6 times faster for the complete graph with 12 vertices, and 65.6 times faster for some well-known benchmark network. For some network instances, the proposed variable order reduces the number of BDD nodes by 15–38% compared with the existing order. This paper reveals that considering imperfect vertices does not impose significant performance overheads.

Suggested Citation

  • Kawahara, Jun & Sonoda, Koki & Inoue, Takeru & Kasahara, Shoji, 2019. "Efficient construction of binary decision diagrams for network reliability with imperfect vertices," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 142-154.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:142-154
    DOI: 10.1016/j.ress.2019.03.026
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    References listed on IDEAS

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    1. Zaitseva, Elena & Levashenko, Vitaly & Kostolny, Jozef, 2015. "Importance analysis based on logical differential calculus and Binary Decision Diagram," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 135-144.
    2. Miroslav Kvassay & Vitaly Levashenko & Elena Zaitseva, 2016. "Analysis of minimal cut and path sets based on direct partial Boolean derivatives," Journal of Risk and Reliability, , vol. 230(2), pages 147-161, April.
    3. Mo, Yuchang & Xing, Liudong & Zhong, Farong & Pan, Zhusheng & Chen, Zhongyu, 2014. "Choosing a heuristic and root node for edge ordering in BDD-based network reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 83-93.
    4. Kang, Won-Hee & Song, Junho & Gardoni, Paolo, 2008. "Matrix-based system reliability method and applications to bridge networks," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1584-1593.
    5. Kim, Youngsuk & Kang, Won-Hee, 2013. "Network reliability analysis of complex systems using a non-simulation-based method," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 80-88.
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    Cited by:

    1. Alkaff, Abdullah & Qomarudin, Mochamad Nur & Bilfaqih, Yusuf, 2021. "Network reliability analysis: matrix-exponential approach," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    2. Alkaff, Abdullah & Qomarudin, Mochamad Nur & Bilfaqih, Yusuf, 2020. "Network reliability analysis: Matrix-exponential approach," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Monfared, M.A.S. & Rezazadeh, Masoumeh & Alipour, Zohreh, 2022. "Road networks reliability estimations and optimizations: A Bi-directional bottom-up, top-down approach," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    4. Davila-Frias, Alex & Yodo, Nita & Le, Trung & Yadav, Om Prakash, 2023. "A deep neural network and Bayesian method based framework for all-terminal network reliability estimation considering degradation," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    5. Vaibhav Gaur & Om Prakash Yadav & Gunjan Soni & Ajay Pal Singh Rathore, 2021. "A literature review on network reliability analysis and its engineering applications," Journal of Risk and Reliability, , vol. 235(2), pages 167-181, April.
    6. Cui, Hongjun & Wang, Fei & Ma, Xinwei & Zhu, Minqing, 2022. "A novel fixed-node unconnected subgraph method for calculating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 226(C).

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