IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v240y2023ics0951832023004982.html
   My bibliography  Save this article

A network reliability algorithm for a stochastic flow network with non-conservation flow

Author

Listed:
  • Huang, Ding-Hsiang

Abstract

Network reliability is defined as the probability that at least demand d can be sent successfully through a system with multistate arcs. Some existing algorithms based on minimal paths (MPs) have been developed to extract all d-MPs for network reliability evaluation under the assumption of the conservation flow law. All the d-MPs are necessary capacity vectors for d. However, non-conservation flow cases, including decrease and increase flows, exist in real systems. Thus, an algorithm for generating all the d-MPs in non-conservation flow cases is required for network reliability evaluation. Such the d-MPs are renamed d-MPncs as follows. In this study, the change rates of all the arcs are defined to represent the changes in the flow. A recursive algorithm is developed to generate all feasible flow vectors satisfying at least d with the integer-type flow to represent undivided demands. Consumed-capacity vectors with respect to all the MPs are formulated to calculate the exact consumed capacity for all arcs and to obtain capacity vectors as d-MPnc candidates. Finally, a cyclic check and comparison approach are performed to search for all the d-MPncs. A numerical example, time complexity, and efficiency investigation are presented to demonstrate the feasibility of the proposed algorithm.

Suggested Citation

  • Huang, Ding-Hsiang, 2023. "A network reliability algorithm for a stochastic flow network with non-conservation flow," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    • Handle: RePEc:eee:reensy:v:240:y:2023:i:c:s0951832023004982
    DOI: 10.1016/j.ress.2023.109584
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832023004982
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2023.109584?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. George-Williams, Hindolo & Patelli, Edoardo, 2016. "A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 351-367.
    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. Yi-Kuei Lin & Cheng-Ta Yeh & Cheng-Fu Huang, 2017. "Reliability assessment of a multistate freight network for perishable merchandise with multiple suppliers and buyers," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(1), pages 74-83, January.
    5. Yeh, Cheng-Ta, 2020. "A hybrid approach to solve a bi-objective optimization problem of a capacitated-flow network with a time factor," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. 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).
    7. Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-An & Fang, Yining, 2021. "An improved bounding algorithm for approximating multistate network reliability based on state-space decomposition method," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    8. Yeh, Wei-Chang & Bae, Changseok & Huang, Chia-Ling, 2015. "A new cut-based algorithm for the multi-state flow network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 1-7.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kozyra, Paweł Marcin, 2024. "A parallel algorithm for reliability assessment of multi-state flow networks based on simultaneous finding of all multi-state minimal paths and performing state space decomposition," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    2. Huang, Ding-Hsiang, 2024. "An algorithm to generate all d-lower boundary points for a stochastic flow network using dynamic flow constraints," Reliability Engineering and System Safety, Elsevier, vol. 249(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Yi-Feng Niu & Meng-Meng Yuan & Xiu-Zhen Xu, 2025. "Optimal carrier selection to improve logistics network reliability with delivery spoilage," Annals of Operations Research, Springer, vol. 346(3), pages 2195-2223, March.
    3. Niu, Yi-Feng & Xiang, Hai-Yan & Xu, Xiu-Zhen, 2024. "Expected performance evaluation and optimization of a multi-distribution multi-state logistics network based on network reliability," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    4. Huang, Ding-Hsiang, 2024. "An algorithm to generate all d-lower boundary points for a stochastic flow network using dynamic flow constraints," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    5. Huang, Cheng-Fu & Huang, Ding-Hsiang & Lin, Yi-Kuei, 2022. "Network reliability evaluation for multi-state computing networks considering demand as the non-integer type," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    6. 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).
    7. Lin, Shuai & Jia, Limin & Zhang, Hengrun & Zhang, Pengzhu, 2022. "Reliability of high-speed electric multiple units in terms of the expanded multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    8. Chang, Ping-Chen, 2022. "MC-based simulation approach for two-terminal multi-state network reliability evaluation without knowing d-MCs," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    9. Niu, Yi-Feng & Zhou, Run-Hui & Xu, Xiu-Zhen & Xiang, Hai-Yan, 2024. "A reliability index to measure multi-state flow network considering capacity restoration level and maintenance cost," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    10. Zhou, Yifan & Liu, Libo & Li, Hao, 2022. "Reliability estimation and optimisation of multistate flow networks using a conditional Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    11. Xu, Bei & Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-an & Fang, Yining, 2022. "A multistate network approach for reliability evaluation of unmanned swarms by considering information exchange capacity," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    12. 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).
    13. 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).
    14. Li, Xianxiong & Lan, Xinbo & Mirzaei, A & Aghdam Bonab, Mohammad Jalilvand, 2022. "Reliability and robust resource allocation for Cache-enabled HetNets: QoS-aware mobile edge computing," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    15. Kozyra, Paweł Marcin, 2024. "A parallel algorithm for reliability assessment of multi-state flow networks based on simultaneous finding of all multi-state minimal paths and performing state space decomposition," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    16. Huang, Ding-Hsiang, 2024. "Network reliability of a stochastic flow network by wrapping linear programming models into a Monte-Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    17. 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).
    18. Niu, Yi-Feng & Wang, Jun-Feng & Xu, Xiu-Zhen & Xu, Qian-Xin, 2025. "Reliability evaluation for a multi-commodity multi-state distribution network under transportation emission consideration," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    19. 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).
    20. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:240:y:2023:i:c:s0951832023004982. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.