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Reliability evaluation of a stochastic-flow network in terms of minimal paths with budget constraint

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  • Majid Forghani-elahabad
  • Nelson Kagan

Abstract

In a stochastic-flow network with budget constraint, the network reliability for level (d, b), i.e., R(d,b), where d is a given demand value and b is a budget limit, is the probability of transmitting at least d units of flow from a source node to a sink node within the budget of b. The problem of evaluating R(d,b) in terms of Minimal Paths (MPs), which is called the (d, b)-MP problem, has been of considerable interest in the recent decades. Here, presenting some new results, an improved algorithm is proposed for this problem. Some numerical comparisons between our MATLAB implementation of the algorithm proposed in this article and a recently proposed one are made. This way, computational comparative results on some benchmarks and thousands of random test problems are provided in the sense of performance profile introduced by Dolan and Moré. Moreover, complexity results are provided. The complexity and numerical results show the efficiency of our algorithm in comparison with the others. Furthermore, we state how to use the output of the algorithm in order to assess the system reliability. Ultimately, based on the main proposed algorithm, a simple algorithm is stated to evaluate the reliability of some smart grid communication networks.

Suggested Citation

  • Majid Forghani-elahabad & Nelson Kagan, 2019. "Reliability evaluation of a stochastic-flow network in terms of minimal paths with budget constraint," IISE Transactions, Taylor & Francis Journals, vol. 51(5), pages 547-558, May.
    • Handle: RePEc:taf:uiiexx:v:51:y:2019:i:5:p:547-558
    DOI: 10.1080/24725854.2018.1504358
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    Cited by:

    1. Yeh, Wei-Chang, 2020. "A new method for verifying d-MC candidates," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Yeh, Wei-Chang, 2023. "QB-II for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    3. 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).
    4. 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.
    5. Niu, Yi-Feng & Song, Yi-Fan & Xu, Xiu-Zhen & Zhao, Xia, 2022. "Efficient reliability computation of a multi-state flow network with cost constraint," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    6. Yeh, Wei-Chang, 2024. "Time-reliability optimization for the stochastic traveling salesman problem," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    7. Yi-Feng Niu & Can He & De-Qiang Fu, 2022. "Reliability assessment of a multi-state distribution network under cost and spoilage considerations," Annals of Operations Research, Springer, vol. 309(1), pages 189-208, February.
    8. Niu, Yi-Feng & Wan, Xiao-Yu & Xu, Xiu-Zhen & Ding, Dong, 2020. "Finding all multi-state minimal paths of a multi-state flow network via feasible circulations," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    9. Niu, Yi-Feng, 2021. "Performance measure of a multi-state flow network under reliability and maintenance cost considerations," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    10. Xu, Xiu-Zhen & Niu, Yi-Feng & Song, Yi-Fan, 2021. "Computing the reliability of a stochastic distribution network subject to budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    11. Yeh, Cheng-Ta & Lin, Yi-Kuei & Yeng, Louis Cheng-Lu & Huang, Pei-Tzu, 2021. "Reliability evaluation of a multistate railway transportation network from the perspective of a travel agent," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    12. 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).
    13. Vartika Sharma & Rajesh Mishra, 2023. "Reliability analysis of complex networks based on irredundant subset cut group," Journal of Risk and Reliability, , vol. 237(4), pages 714-724, August.
    14. Yeh, Wei-Chang, 2023. "Novel recursive inclusion-exclusion technology based on BAT and MPs for heterogeneous-arc binary-state network reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    15. Huang, Ding-Hsiang & Huang, Cheng-Fu & Lin, Yi-Kuei, 2020. "A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1107-1114.
    16. Huang, Cheng-Hao & Huang, Ding-Hsiang & Lin, Yi-Kuei, 2023. "Network reliability prediction for random capacitated-flow networks via an artificial neural network," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    17. 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).
    18. Cheng-Fu Huang & Ding-Hsiang Huang & Yi-Kuei Lin, 2022. "System reliability analysis for a cloud-based network under edge server capacity and budget constraints," Annals of Operations Research, Springer, vol. 312(1), pages 217-234, May.
    19. Forghani-elahabad, Majid & Kagan, Nelson & Mahdavi-Amiri, Nezam, 2019. "An MP-based approximation algorithm on reliability evaluation of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    20. 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).
    21. 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).
    22. Yi-Kuei Lin & Shin-Guang Chen, 2022. "Reliability evaluation in terms of flow data mining for multistate networks," Annals of Operations Research, Springer, vol. 311(1), pages 225-237, April.

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