A Computer Program for Approximating System Reliability

Nelson, A. C.; Batts, James R.; Beadles, Robert L.

doi:10.1109/tr.1970.5216391

Cited by 107 publications

(19 citation statements)

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“…For example, by eliminating the nodes of the graph in Figure 5 in the order 3, 1,9,8,7,2,6,5,11,4,10,12,13, the minimal cut sets between nodes 12 and 13 are obtained in 4.5 sec, instead of 2.6 sec required by the previous ordering.…”

Section: Expemmental Resultsmentioning

confidence: 99%

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A Gaussian Elimination Algorithm for the Enumeration of Cut Sets in a Graph

Martelli

1976

J. ACM

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By defining a suitable algebra for cut sets, it is possible to reduce the problem of enumerating the cut sets between all pairs of nodes in a graph to the problem of solving a system of linear equations An algorithm for solving thin system using Gausman elimination is presented in thin paper The efficiency of the algorithm depends on the implementation of sum and multiplication Therefore~ some properties of cut sets are investigated, which greatly slmphfy the implementation of these operations for the case of undirected graphs. The time required by the algorithm is shown to be hnear with the number of cut sets for complete graphs Some experimental results are given, proving that the efficiency of the algorithm increases by increasing the number of pairs of nodes for which the cut sets are computed.KEY WORDS AND PHRASES: graph theory, cut set enumeration, regular algebra, Gaussian elimination CR CATEGORIES, 5 20, 5 32 IntroductwnThe problem of enumerating all cut sets between all pairs of nodes in a graph is an, important combinatorial problem. For example, it can be the first step for the computation of the terminal rehabihty in a communication network [1,2,3].Several methods have been presented for enumerating all cut sets between two given nodes i and j, For instance, the method described in [2] first computes all simple paths and then finds all combinations of arcs cutting all paths. Another method [3] searches the given graph starting from node i and constructs a tree whose terminal nodes are the cut sets. Furthermore, the cut sets could be obtained by taking all hnear combinations of the cut sets belonging to a suitably constructed set [4].A regular algebra method was presented by the author in [5]. By giving a suitable algebra for cut sets, it is possible to reduce the problem of enumerating all cut sets to the problem of solving a system of linear equations in this algebra. Using this method, it is possible to compute simultaneously the cut sets between all pairs of nodes. A simalar approach has been used for enumerating all simple paths in a graph [6] or for finding shortest paths [7].]n Section 2 we present our method by giving the algebra for cut sets and by showing how our problem becomes one of solving a system of linear equations. Moreover, we give a Gaussian elimination algorithm for solving this system.A simple implementation of sum and multiplication m our algebra would make the Gaussian elimination algorithm very inefficient. Therefore, m Sections 3 and 4 we show how these operations can be implemented in an efficient way for undirected graphs by taking into account some properties of cut sets. Some aspects regarding the computa-

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Section: Expemmental Resultsmentioning

confidence: 99%

“…For example, it can be the first step for the computation of the terminal rehabihty in a communication network [1,2,3].…”

Section: Introductwnmentioning

confidence: 99%

A Gaussian Elimination Algorithm for the Enumeration of Cut Sets in a Graph

Martelli

1976

J. ACM

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“…7. In block 5 the following program actions take place: first, the program calls up the tie-set (cut-set) subroutine [12], which determines all tie sets between con-figuration input and output (the configuration cut sets are also available); and, secondly, it computes the availability and unavailability of all configuration tie sets, i.e. AT(I), UAT(I), I = 1, 2, ..., NT.…”

Section: Computer Programmentioning

confidence: 99%

General computational method for performing availability analysis of power-system configurations

Papadopoulos¹

1983

IEE Proc. C Gener. Transm. Distrib. UK

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The paper presents a general computational method and the relevant computer program which can be easily used to perform availability/unavailability analysis on power-system configurations. The mathematical availability formulation of the program is based primarily on: the tie sets (or cut sets) of the system configuration, the component failure rates and repair and maintenance times, some aspects of a Markov model of two states and the functional block concept. A real prerequisite for the successful utilisation of the program is the availability of realistic statistical data for the system components. For purposes of illustration, the computer program has been applied to evaluate the availability of two practical high-voltage/medium-voltage (HV/MV) substation configurations, from the standpoint of design, practical functionality and repair and maintenance procedures. The program is suitable in performing system availability/unavailability sensitivity analysis, based on value variations of system-component failure rates and repair and maintenance times.

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“…Nahman [3] suggested a method for determining the minimal cuts and paths of a general network with common-cause failures. The computation of the network reliability has been discussed by many researchers, such as Abraham [4], Aggarwal et al [5], Kim et al [6], Nelson et al [7], and Rai and Aggarwal [2]. This paper presents a simple algorithm for finding the minimal paths of a given network in terms of its links.…”

Section: Introductionmentioning

confidence: 99%

A tool for computing computer network reliability

Younes

Girgis

2005

International Journal of Computer Mathematics

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The computation of the reliability of a computer network is one of the important tasks of evaluating its performance. The idea of minimal paths can be used to determine the network reliability. This paper presents an algorithm for finding the minimal paths of a given network in terms of its links. Then, it presents an algorithm for calculating the reliability of the network in terms of the probabilities of success of the links of its minimal paths. The algorithm is based on a relation that uses the probabilities of the unions of the minimal paths of the network to obtain the network reliability. Also, the paper describes a tool that has been built for calculating the reliability of a given network. The tool has two main phases: the minimal paths generation phase, and the reliability computation phase. The first phase accepts the links of the network and their probabilities, then implements the first proposed algorithm to determine its minimal paths. The second phase implements the second proposed algorithm to calculate the network reliability. The results of using the tool to calculate the reliability of an example network are given.

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A Computer Program for Approximating System Reliability

Cited by 107 publications

References 1 publication

A Gaussian Elimination Algorithm for the Enumeration of Cut Sets in a Graph

A Gaussian Elimination Algorithm for the Enumeration of Cut Sets in a Graph

General computational method for performing availability analysis of power-system configurations

A tool for computing computer network reliability

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