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Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks

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  • Jane, Chin-Chia
  • Laih, Yih-Wenn

Abstract

In this article, each arc in multi-state flow networks, in addition to multi-valued capacities and associated operation probabilities, is weighted with a transit time. As a result, the value of max-flow from source to sink within specified time horizon is multi-valued. Existing literature evaluates the transit time integrated reliability with a restriction that data is transmitted through k disjoint minimal paths. This article considers the same reliability problem. However, the transmission of data is extended from k disjoint minimal paths to a flow that includes all disjoint and non-disjoint minimal paths simultaneously. This paper presents an algorithm to evaluate the probability distribution of the values of dynamic max-flow. The expectation of dynamic max-flow as a representation of the distribution can be induced directly. The transit time integrated reliability Rd,T is then computed, which is the probability that at least d unit of data can be transmitted from source to sink within time horizon T. This study is the first that discusses transit time integrated reliability in terms of flow. Finally, computational experiments are conducted on a benchmark network to explore the properties of the proposed algorithms.

Suggested Citation

  • Jane, Chin-Chia & Laih, Yih-Wenn, 2017. "Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1045-1053.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:3:p:1045-1053
    DOI: 10.1016/j.ejor.2016.12.030
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    References listed on IDEAS

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    1. Jane, Chin-Chia & Yuan, John, 2001. "A sum of disjoint products algorithm for reliability evaluation of flow networks," European Journal of Operational Research, Elsevier, vol. 131(3), pages 664-675, June.
    2. Bruce Hoppe & Éva Tardos, 2000. "The Quickest Transshipment Problem," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 36-62, February.
    3. Jane, Chin-Chia, 2011. "Performance evaluation of logistics systems under cost and reliability considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(2), pages 130-137, March.
    4. Jane, Chin-Chia & Laih, Yih-Wenn, 2010. "A dynamic bounding algorithm for approximating multi-state two-terminal reliability," European Journal of Operational Research, Elsevier, vol. 205(3), pages 625-637, September.
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    Cited by:

    1. 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.
    2. Cheng-Ta Yeh & Lance Fiondella & Ping-Chen Chang, 2018. "Cost-oriented component redundancy allocation for a communication system subject to correlated failures and a transmission reliability threshold," Journal of Risk and Reliability, , vol. 232(3), pages 248-261, June.
    3. Chen, Yiming & Liu, Yu & Jiang, Tao, 2021. "Optimal maintenance strategy for multi-state systems with single maintenance capacity and arbitrarily distributed maintenance time," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    4. Wang, WuChang & Zhang, Yi & Li, YuXing & Hu, Qihui & Liu, Chengsong & Liu, Cuiwei, 2022. "Vulnerability analysis method based on risk assessment for gas transmission capabilities of natural gas pipeline networks," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    5. 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).
    6. 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).

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