A practical implementation of the factoring theorem for network reliability

Page, Lavon B.; Perry, Jo Ellen

doi:10.1109/24.3752

Cited by 105 publications

(25 citation statements)

References 6 publications

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“…For undirected networks, factoring with network reductions provides the best possible time (see Ball et al 1995 andGaltier et al 2005 for a comprehensive discussion on the exact methods). The factoring code used in this paper to compute R X follows the procedure given by Page and Perry (1988). If a network is too large for exact calculation of reliability by factoring, simulation with network reductions is used.…”

Section: Evaluation Of Reliabilitymentioning

confidence: 99%

“…The upper bound is used to quickly eliminate unpromising solutions without further evaluating them. Using an algorithm based on the factoring theorem and network reductions (Page and Perry 1988), the exact reliability of networks much larger than previously reported is calculated. Finally, to complement the exact calculation, an efficient reduced variance simulation using network reductions is employed.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

Konak¹,

Smith

2011

INFORMS Journal on Computing

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T his paper presents a biobjective genetic algorithm (GA) to design reliable two-node connected telecommunication networks. Because the exact calculation of the reliability of a network is NP-hard, network designers have been reluctant to use network reliability as a design criterion; however, it is clearly an important aspect. Herein, three methods of reliability assessment are developed: an exact reliability calculation method using factoring, an efficient Monte Carlo estimation procedure using the sequential construction technique and network reductions, and an upper bound for the all-terminal reliability of networks with arbitrary arc reliabilities. These three methods of reliability assessment are used collectively in a biobjective GA with specialized mutation operators that perturb solutions without disturbing two-node connectivity. Computational experiments show that the proposed approach is tractable and significantly improves upon the results found by single-objective heuristics.

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Section: Evaluation Of Reliabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

Konak¹,

Smith

2011

INFORMS Journal on Computing

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“…The factoring algorithm was used for this purpose. The formula R N(K) is obtained by reduction of the graph representing the network [16,27]. The reduction process is based on a well-known principle of contracting and deleting of links which is recursively applied for all edges e i in graph G. Examples of reduction for specified sets K are shown in Figure 1 …”

Section: Determination Of Reliability Of a Network With Perfect Nodesmentioning

confidence: 99%

Reliability evaluation of networks with imperfect and repairable links and nodes

Pilch

2016

EiN

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Reliability evaluation of netwoRks with impeRfectand RepaiRable links and nodes niezawodność sieci z uszkadzającymi się i odnawianymi połączeniami oRaz węzłami* The paper presents the method for determining the reliability of a network whose elements (links and nodes) are imperfect (can fail) and repairable. The presented method uses the factoring algorithm, proposed π method and computer simulation. The factoring algorithm is used to obtain a formula for accurate computation of network reliability as a probability of connectedness among the specified set of nodes K (R N(K) W opracowaniu przedstawiono metodę wyznaczania niezawodności sieci, w których elementy (połączenia i węzły) mogą się uszkadzać i są odnawiane. Przedstawiona metoda wykorzystuje algorytm faktoryzacji, zaproponowaną metodę π oraz symulację komputerową. Na podstawie algorytmu faktoryzacji wyznaczany jest wzór do dokładnego obliczania niezawodności sieci jako prawdopodobieństwa połączenia między wybranym zbiorem K węzłów (R N(K)

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“…Another method is based on the factoring algorithm in which a component of the network is chosen, and then the network is decomposed into two sub-networks: the first assumes that the component has failed, and the second assumes it is functioning. In each case, we obtain the reliability of the network by considering the behavior of the chosen model; we refer the reader to Satyanarayana and Chang [38], Wood [42], Colbourn [9], and Page and Perry [34]. In the literature, Binary Decision Diagrams (BDD) are widely used as an efficient tool to evaluate the reliability of the networks.…”

mentioning

confidence: 99%

Network Reliability Modeling Under Stochastic Process of Component Failures

Zarezadeh

Asadi

2013

IEEE Trans. Rel.

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The concept of D-spectrum is a useful tool to investigate the reliability and stochastic properties of networks. In this paper, we consider a network consisting of components (links or nodes), and assume that the network has two states: up, and down. We study the D-spectrum-based reliability of the network under the assumption that the components are subject to failure according to a counting process. Mixture representation of the reliability of the network lifetime is given in terms of the reliability functions of arrival times. It is shown that, when the D-spectra of two networks are stochastically ordered, then under some conditions the lifetimes of two networks are also stochastically ordered. Under the special case when the process of the failure of the components is a nonhomogeneous Poisson process, we arrive at a mixture representation for the reliability function of the network lifetime, and explore several stochastic and aging properties of the network lifetime under different scenarios. The failure rate of the network lifetime and its asymptotic behavior is investigated. D-spectrum based representation theorems are also given on the basis of the stochastic precedence concept.Index Terms-D-spectrum, increasing failure rate, nonhomogeneous Poisson process, record values, stochastic ordering, stochastic precedence, system signature, two-state networks. ACRONYMSAND ABBREVIATIONS NHPP Nonhomogeneous Poisson process NBU New better than used NWU New worse than used MRL Mean residual lifetime m.v.f. Mean value function IFR Increasing failure rate DFR Decreasing failure rate NOTATIONS the node set of network the link set of network Manuscript

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A practical implementation of the factoring theorem for network reliability

Cited by 105 publications

References 6 publications

Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

Reliability evaluation of networks with imperfect and repairable links and nodes

Network Reliability Modeling Under Stochastic Process of Component Failures

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