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

doi:10.1016/j.ress.2023.109584

2023-12-01

PRE

Ding‐Hsiang Huang *

DOI：10.1016/j.ress.2023.109584

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摘要

En 中文

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. Consumedcapacity 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.

Keyword:

Stochastic non-conservation flow network

(SNFN)

Network reliability

Non-conservation flow

Time complexity

d-MP(d-MPnc)