A survey of efficient reliability computation using disjoint products approach

Rai, Suresh; Veeraraghavan, Malathi; Trivedi, Kishor S.

doi:10.1002/net.3230250308

Cited by 89 publications

(27 citation statements)

References 25 publications

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“…This explains the high number of papers published for computing, bounding or estimating them, plus many other ones dedicated to related issues (topological network design, model transformation, among others). For instance, in some basic approaches are discussed, and a powerful method (called Factorization) is also described. We focus on the latter, but to understand the complexity of the problem, let us briefly consider some basic ways of representing and, in theory, computing these metrics.…”

Section: Exact Methodsmentioning

confidence: 99%

Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

2017

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In classical network reliability, the system under study is a network with perfect nodes and imperfect links that fail randomly and independently. The probability that a given subset K of terminal nodes belongs to the same connected component is called classical or K ‐Terminal reliability. Although (and because) the classical reliability computation belongs to the class of N P‐Hard problems, the literature offers many methods for this purpose, given the importance of the models. This article deals with diameter‐constrained reliability, where terminal nodes are further required to be connected by d hops or fewer ( d is a given strictly positive parameter of the metric called its diameter). This metric was defined in 2001, inspired by delay‐sensitive applications in telecommunications. Factorization theory is fundamental for the classical network reliability evaluation, and today it is a mature area. However, its extension to the diameter‐constrained context requires at least the recognition of irrelevant links, which is an open problem. In this article, irrelevant links are efficiently determined in the most used case, where |K|=2, thus providing a first step toward a Factorization theory in diameter‐constrained reliability. We also analyze the metric in series‐parallel and composition graphs. The article closes with a Factoring algorithm and a discussion of trends for future work. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(4), 283–291 2017

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Section: Exact Methodsmentioning

confidence: 99%

Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

2017

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“…Rai et al . conducted several experiments on the preprocessing of path/cut terms in SDP . Another preprocessing strategy was mentioned by Balan and Traldi .…”

Section: Related Workmentioning

confidence: 99%

A Parallel Strategy for the Logical‐probabilistic Calculus‐based Method to Calculate Two‐terminal Reliability

Nguyen

2015

Quality & Reliability Eng

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The theory of network reliability has been applied to many complicated network structures, such as computer and communication networks, piping systems, electricity networks, and traffic networks. The theory is used to evaluate the operational performance of networks that can be modeled by probabilistic graphs. Although evaluating network reliability is an Non-deterministic Polynomial-time hard problem, numerous solutions have been proposed. However, most of them are based on sequential computing, which under-utilizes the benefits of multi-core processor architectures. This paper addresses this limitation by proposing an efficient strategy for calculating the two-terminal (terminal-pair) reliability of a binary-state network that uses parallel computing. Existing methods are analyzed. Then, an efficient method for calculating terminal-pair reliability based on logical-probabilistic calculus is proposed. Finally, a parallel version of the proposed algorithm is developed. This is the first study to implement an algorithm for estimating terminal-pair reliability in parallel on multicore processor architectures. The experimental results show that the proposed algorithm and its parallel version outperform an existing sequential algorithm in terms of execution time.

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“…The most commonly used algorithms include state enumeration [10], factoring [76], inclusion/exclusion [77], sum of disjoint products (SDP) [64], and binary decision diagrams (BDD) [11]. Compared to other methods, BDD-based algorithms are more powerful and efficient in dependability evaluation because of their concise representation of Boolean functions and the ease of BDD manipulations [89].…”

Section: Fault Treesmentioning

confidence: 99%

Uncertainty Propagation through Software Dependability Models

Mishra

Trivedi

2011

2011 IEEE 22nd International Symposium on Software Reliability Engineering

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Systems in critical applications employ various hardware and software fault-tolerance techniques to ensure high dependability. Stochastic models are often used to analyze the dependability of these systems and assess the effectiveness of the fault-tolerance techniques employed. Measures like performance and performability of systems are also analyzed using stochastic models. These models take into account randomness in various events in the system (known as aleatory uncertainty) and are solved at fixed parameter values to obtain the measures of interest. However, in real life, the parameters of the stochastic models themselves are uncertain as they are derived from a finite (limited) number of observations or are simply based on expert opinions.Solving the stochastic models at fixed values of the model input parameters result in estimates of model output metrics which do not take into account the uncertainty in model input parameters (known as epistemic uncertainty).In this research work, we address the computation of uncertainty in output metrics of stochastic models due to epistemic uncertainty in model input parameters, with a focus on dependability and performance models of current computer and communication systems. We develop an approach for propagation of epistemic uncertainty in input parameters through stochastic dependability and performance models of varying complexity, to compute the uncertainty in the model output measures. and provides more robust estimates of uncertainty in the model output metrics than previous sampling based methods.We demonstrate the applicability of the uncertainty propagation approach by applying it to analytic stochastic dependability and performance models of computer systems, ranging from simple non-state-space models with a few input parameters to large state-space models and even hierarchical models with more than fifty input parameters. We further apply the uncertainty propagation approach to stochastic models with not only analytic or analytic-numeric solutions but also those with simulative solutions. We also consider a wide range of model output metrics including reliability and availability of computer systems, response time of a web service, capacity oriented availability of a communication system, security (probability of successful attack) of a network routing session, expected number of jobs in a queueing system with breakdown and repair of servers and call handoff probability of a cellular wireless communication cell.

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A survey of efficient reliability computation using disjoint products approach

Cited by 89 publications

References 25 publications

Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

A Parallel Strategy for the Logical‐probabilistic Calculus‐based Method to Calculate Two‐terminal Reliability

Uncertainty Propagation through Software Dependability Models

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