A New Technique for Generating Minimal Cut Sets in Nontrivial Network

Rebaiaia, Mohamed-Larbi; Aït‐Kadi, Daoud

doi:10.1016/j.aasri.2013.10.060

Cited by 14 publications

(7 citation statements)

References 7 publications

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“…Younes and Girgis 46 formed a two-fold methodology; first find the minimal path set; and then compute the reliability based on probabilistic association of the links in the minimal path to calculate network reliability of a computer network. Rebaiaia and Ait-Kadi 47 proposed an algorithm that could produce results for cut-sets in linear time. Yeh 48 proposed a method to calculate minimal cuts for the networks, which evolve by addition of new nodes to facilitate expansion of existing system.…”

Section: Minimal Cut Methodsmentioning

confidence: 99%

A literature review on network reliability analysis and its engineering applications

Gaur

Yadav

Soni

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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The applications of networks can be observed in numerous engineering realms mainly computers and communication, transportation, electric transmission and oil and gas distribution. Estimating the reliability of such networks is a critical task for the well-being of society as well as a nation. The paradigm of network reliability has evolved considerably over the past few decades. The purpose of this article is to present the developments in network reliability domain in a laconic manner. This paper discusses the various metrics used to evaluate network connectivity along with their mathematical backgrounds. The various algorithms namely State Enumeration, Sum of disjoint product, Minimal Cut Set, Factoring theorem, Cellular Automata, Subset Simulation, Percolation theory, Binary Decision Diagrams, and Universal Generating Functions are enumerated in this review study. The application part of algorithms with their advantages, limitations and scope are presented. Finally, the methodologies used for assessment of network reliability are discussed. This article aims at providing a holistic view of the network reliability practices, which may prove to be helpful for researchers across the globe.

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Section: Minimal Cut Methodsmentioning

confidence: 99%

A literature review on network reliability analysis and its engineering applications

Gaur

Yadav

Soni

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…Each node and each link have an associative probability of success and failure. Usually, n-type approaches are used by various authors to achieve maximum reliability goals like Monte Carlo Simulation, Particle Swarm optimization, Upper and Lower bounds of reliability, and simulation-based reliability estimation [15][16][17][18]. The reliability measurement is an important factor for optimal network design.…”

Section: Assume That ( ) ≥mentioning

confidence: 99%

Estimation of all-terminal network reliability using press forward GA with stochastic selection method

Anuradha¹

2021

TURCOMAT

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Network reliability is an important measure of how well the network meets its design aim and mathematically is the probability that a network will perform communication efficiently for at least a given period of time. The reliability analysis is used for determining the probability of correct functioning of a system in terrain conditions. Estimating the all-terminal network reliability is an NP-hard problem, the press forward Genetic Algorithm is also an alternative to solve the problem of all-terminal network reliability. This paper presents a reliability evaluation method by using a feed-forward genetic algorithm with a random selection of nodes and links i.e., estimate the network reliability such that the flow is not less than a given threshold. To verify the efficiency of an algorithm, various sets of runs are applied to identify the most reliable network and the algorithm is tested on the network size of 2,4,6,8, --------256 nodes with link N(N-1)/2. The results of the algorithm are obtained for all-terminal reliability problem based on close analysis of the complexity of the network. Our assumption for reliability evaluation of node 1 to node N, with link reliability of 50%. Another result of the proposed GA approach is the significant reduction in computational time.

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“…A prominent problem of reliability engineering is the problem of obtaining the minimal sum for a switching function (Two-valued Boolean function) whenever the minimal sum for its complement is given, or equivalently, deriving the prime implicants (PIs) of a function in terms of those of its complement. This problem is usually referred to as the inversion problem, and in reliability context it deals with the derivation of minimal cutsets (PIs of system failure) in terms of minimal paths (PIs of system success) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Solution of this problem is necessary when minimal paths are known, while the failure modes or cutsets of the system are needed [4].…”

Section: Introductionmentioning

confidence: 99%

Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

Rushdi

Amashah

2021

JERR

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This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.

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A New Technique for Generating Minimal Cut Sets in Nontrivial Network

Cited by 14 publications

References 7 publications

A literature review on network reliability analysis and its engineering applications

A literature review on network reliability analysis and its engineering applications

Estimation of all-terminal network reliability using press forward GA with stochastic selection method

Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

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