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Novel direct algorithm for computing simultaneous all-level reliability of multistate flow networks

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  • Yeh, Wei-Chang

Abstract

Different types of networks, such as, Internet of Things, social networks, wireless sensor networks, transportation networks, and 4g/5G serve to benefit and help our daily lives. The multistate flow network (MFN) is used to model the network structures and applications. The level d reliability, Rd, of the MFN is the success probability of sending at least d units of integer flow from the nodes 1 to n and is a popular index for designing, managing, controlling, and evaluating MFNs. The traditional indirect algorithms must have all d-MPs (special connected vectors) or (d-1)-MCs (special disconnected vectors) first, and then use inclusion-exclusion technique (IET) or sum-of-disjoint product (SDP) in terms of found d-MPs or (d-1)-MCs to calculate Rd. The above four procedures are all NP-Hard and #P-Hard and cannot calculate Rd for d = 1, 2, …, dMAX simultaneously, that is, they can only calculate R1, R2, …, and RdMAX sequentially. Thus, in this study a novel algorithm is proposed to calculate the Rd directly for all d simultaneously, eliminating the need of using the above four procedures. The time complexity and demonstration of the proposed algorithm were analyzed with suitable examples. Furthermore, an experiment was conducted on 12 benchmark networks to validate the proposed algorithm.

Suggested Citation

  • Yeh, Wei-Chang, 2022. "Novel direct algorithm for computing simultaneous all-level reliability of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    • Handle: RePEc:eee:reensy:v:225:y:2022:i:c:s0951832022002630
    DOI: 10.1016/j.ress.2022.108623
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    References listed on IDEAS

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    1. Yeh, Wei-Chang & Tan, Shi-Yi & Zhu, Wenbo & Huang, Chia-Ling & Yang, Guang-yi, 2022. "Novel binary addition tree algorithm (BAT) for calculating the direct lower-bound of the highly reliable binary-state network reliability," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
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    3. Yeh, Wei-Chang & Hao, Zhifeng & Forghani-elahabad, Majid & Wang, Gai-Ge & Lin, Yih-Lon, 2021. "Novel Binary-Addition Tree Algorithm for Reliability Evaluation of Acyclic Multistate Information Networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
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    5. Hao, Zhifeng & Yeh, Wei-Chang & Tan, Shi-Yi, 2021. "One-batch preempt deterioration-effect multi-state multi-rework network reliability problem and algorithms," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
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    Cited by:

    1. Kozyra, Paweł Marcin, 2023. "The usefulness of (d,b)-MCs and (d,b)-MPs in network reliability evaluation under delivery or maintenance cost constraints," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    2. Gao, Dawei & Zhu, Yongsheng & Yan, Ke & Soares, C. Guedes, 2024. "Deep learning–based framework for regional risk assessment in a multi–ship encounter situation based on the transformer network," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    3. Niu, Yi-Feng & Zhao, Xia & Xu, Xiu-Zhen & Zhang, Shi-Yun, 2023. "Reliability assessment of a stochastic-flow distribution network with carbon emission constraint," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    4. Xu, Xiu-Zhen & Zhou, Run-Hui & Wu, Guo-Lin & Niu, Yi-Feng, 2024. "Evaluating the transmission distance-constrained reliability for a multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    5. Yeh, Wei-Chang, 2024. "A new hybrid inequality BAT for comprehensive all-level d-MP identification using minimal paths in Multistate Flow Network reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 244(C).

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