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

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  • 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
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    References listed on IDEAS

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    1. 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.
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    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).

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