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Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints

Author

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  • Majid Forghani-elahabad

    (Center of Mathematics, Computing, and Cognition, Federal University of ABC, Santo André 09210-580, SP, Brazil)

  • Omar Mutab Alsalami

    (Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

Abstract

The quickest path problem in multistate flow networks, which is also known as the quickest path reliability problem (QPRP), aims at calculating the probability of successfully sending a minimum of d flow units/data/commodity from a source node to a destination node via one minimal path (MP) within a specified time frame of T units. Several exact and approximative algorithms have been proposed in the literature to address this problem. Most of the exact algorithms in the literature need prior knowledge of all of the network’s minimal paths (MPs), which is considered a weak point. In addition to the time, the budget is always limited in real-world systems, making it an essential consideration in the analysis of systems’ performance. Hence, this study considers the QPRP under cost constraints and provides an efficient approach based on a node–child matrix to address the problem without knowing the MPs. We show the correctness of the algorithm, compute the complexity results, illustrate it through a benchmark example, and describe our extensive experimental results on one thousand randomly generated test problems and well-established benchmarks to showcase its practical superiority over the available algorithms in the literature.

Suggested Citation

  • Majid Forghani-elahabad & Omar Mutab Alsalami, 2023. "Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4889-:d:1295171
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    References listed on IDEAS

    as
    1. Forghani-elahabad, Majid & Mahdavi-Amiri, Nezam, 2015. "An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 472-481.
    2. Alkaff, Abdullah & Qomarudin, Mochamad Nur & Bilfaqih, Yusuf, 2021. "Network reliability analysis: matrix-exponential approach," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    3. Forghani-elahabad, Majid & Yeh, Wei-Chang, 2022. "An improved algorithm for reliability evaluation of flow networks," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    4. Bai, Guanghan & Tian, Zhigang & Zuo, Ming J., 2016. "An improved algorithm for finding all minimal paths in a network," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 1-10.
    5. Jiangbin Zhao & Mengtao Liang & Rongyu Tian & Zaoyan Zhang & Xiangang Cao, 2023. "Reliability Optimization of Hybrid Systems Driven by Constraint Importance Measure Considering Different Cost Functions," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    6. Michael Hart Moore, 1976. "On the Fastest Route for Convoy-Type Traffic in Flowrate-Constrained Networks," Transportation Science, INFORMS, vol. 10(2), pages 113-124, May.
    7. Yeh, Wei-Chang, 2007. "An improved sum-of-disjoint-products technique for the symbolic network reliability analysis with known minimal paths," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 260-268.
    8. 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).
    9. Forghani-elahabad, Majid & Francesquini, Emilio, 2023. "Usage of task and data parallelism for finding the lower boundary vectors in a stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 238(C).
    10. Niu, Yi-Feng & Gao, Zi-You & Lam, William H.K., 2017. "A new efficient algorithm for finding all d-minimal cuts in multi-state networks," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 151-163.
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