The usefulness of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si466.svg" display="inline" id="d1e3994"><mml:mrow><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-MCs and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si466.svg" display="inline" id="d1e4008"><mml:mrow><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-MPs in network reliability

Kozyra, Paweł Marcin

doi:10.1016/j.ress.2023.109175

Cited by 8 publications

(4 citation statements)

References 51 publications

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“…Many algorithms in the literature have used the following results to search for all the d-MP s in an MFN [2,8,15,17,19,20,24,45,55].…”

Section: Preliminariesmentioning

confidence: 99%

“…In other words, not every X obtained by solving the system above is necessarily a d-MP. Therefore, the available algorithms in the literature first find all the solutions of this system and then check each solution for being a d-MP [2,8,15,17,19,20,24,45,53,55]. One of the most efficient techniques to check each solution of the system (2) to be a d-MP is the following lemma, which was presented in [19] and improved in [15].…”

Section: Preliminariesmentioning

confidence: 99%

“…To enhance the practicality of the problem, several researchers have explored the integration of cost (budget) constraints into the reliability assessment of MFNs [4,8,13,24,31,40]. Niu and Xu [40] contributed by proposing an enhanced algorithm for MFN reliability evaluation under cost constraints, incorporating a cycle-checking technique into their approach.…”

Section: Introductionmentioning

confidence: 99%

“…They presented an MPbased algorithm to assess the system's reliability while considering budget constraints. In [24], the author conducted a comprehensive review of MPand MC-based approaches in the literature for calculating reliability under budget and maintenance cost constraints. Moreover, some researchers have considered the time limitation on the flow transmission on a path resulting in the quickest path reliability problem and its extensions [34,41,42,43,44,45].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

1 Exact reliability evaluation of multistate flow networks

Forghani-elahabad¹

2021

Systems Reliability Engineering

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Evaluating the reliability of complex technical networks, such as those in energy distribution, logistics, and transportation systems, is of paramount importance. These networks are often represented as multistate flow networks (MFNs). While there has been considerable research on assessing MFN reliability, many studies still need to pay more attention to a critical factor: transmission distance constraints. These constraints are typical in real-world applications, such as Internet infrastructure, where controlling the distances between data centers, network nodes, and end-users is vital for ensuring low latency and efficient data transmission. This paper addresses the evaluation of MFN reliability under distance constraints. Specifically, it focuses on determining the probability that a minimum of d flow units can be transmitted successfully from a source node to a sink node, using only paths with lengths not exceeding a predefined distance limit of λ. We introduce an effective algorithm to tackle this challenge, provide a benchmark example to illustrate its application and analyze its computational complexity.

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“…Many algorithms in the literature have used the following results to search for all the d-MP s in an MFN [2,8,15,17,19,20,24,45,55].…”

Section: Preliminariesmentioning

confidence: 99%