Computer Network Reliability Research Articles

Assessing throughput and reliability in communication and computer networks

System performance and reliability are jointly assessed for highly reliable communication/computer networks. The model assumes that at most a small number of components can be down at a time and that the average repair/replacement time of a failed component is small when compared with the average failure times of network components. The system performance is measured in terms of network throughput at steady-state operation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bounding all‐terminal reliability in computer networks

AbstractMany bounds for the all‐terminal reliability of computer networks have been proposed. Of those computable in polynomial time, the Ball‐Provan bounds and the Lomonosov Polesskii bounds provide the tightest estimates. A strategy is developed here using linear programming to obtain bounds which are tighter than both the Lomonosov‐Polesskii and the Ball‐Provan bounds. Computational results on these new bounds are also reported.

On the determination of overall computer network reliability with m-level hierachical routing

In this paper the overall reliability of mch-level hierarchical computer networks is evaluated. This is an extension of an earlier work wherein two level hierarchical clustrering structures were examined [4]. The method presented first enumerates all the minimal cutsets and then very efficiently evaluates the overall network reliability. There are important savings in computation time and available memory, as the main idea behind the hierarchical design is to impose a decomposable structure which will result in a set of smaller subproblems. The developed technique is very useful in the overall reliability evaluation of large computer networks or many interconnected networks.

A Modified Technique for Computing Network Reliability

Ahmad (1982) has published a technique to compute the reliability of a network without resorting to paths or cutsets. However, the technique uses a random choice of next node connected to the previous node in the construction of a tree. This approach can lead to a large number of terms in the reliability expression. Our modified version of the Ahmad technique always produces a reliability expression with the same or fewer terms as the original technique.

Efficient algorithms for reliability analysis of planar networks - a survey

We survey some recent polynomial-time algorithms for the exact computation of network reliability. The algorithms apply to several classes of planar networks, which include series-parallel, inner-cycle-free, inner-four-cycle-free and planar cube-free. We describe these classes and discuss the related polynomial algorithms for computing their reliability.

Factoring Algorithms for Computing K-Terminal Network Reliability

Let GK denote a graph G whose edges can fail and with a set K ? V specified. Edge failures are independent and have known probabilities. The K-terminal reliability of GK, R(GK), is the probability that all vertices in K are connected by working edges. A factoring algorithm for computing network reliability recursively applies the formula R(GK) = piR(GK * ei) + qiR(GK - ei) where GK * ei is GK, with edge ei contracted, GK - ei is GK with ei deleted and pi ? 1 - qi is the reliability of edge ei. Various reliability-preserving reductions can be performed after each factoring operation in order to reduce computation. A unified framework is provided for complexity analysis and for determining optimal factoring strategies. Recent results are reviewed and extended within this framework.

Simplified Reliabilities for Consecutive-k-out-of-nSystems

Reliabilities for consecutive-k-out-of-n systems are typically given in the form of recursive equations. Some attempts have been made to use combinatorics to obtain closed-form solutions, but the solutions contain $k - 1$ summations. In this paper we obtain closed form solutions with one summation over $n/ k$ terms. For $k = 2$ we are able to eliminate all summations. We apply our result to compute the reliability of a k-loop computer network.

Computing terminal reliability of computer network

This paper discusses a technique for determination of the computer network reliability. The method utilizes the concepts of Boolean algebra and graph theory. It starts with the system success determinant obtained from the connection matrix and expands it using the simple rules defined in the text. The method does not require knowledge of either path set or cut set. It is recursive, straighforward and lacks computational complexity. An example illustrates the method.

Reliability Modeling and Analysis of Computer Networks

The reliability analysis of computer communication networks is generally based on Boolean algebra and probability theory. This paper discusses various reliability problems of computer networks including terminal-pair connectivity, tree connectivity, and multi-terminal connectivity. This paper also studies the dynamic computer network reliability by deriving time-dependent expressions for reliability measures assuming Markov behavior for failures and repairs. This allows computation of task and mission related measures such as mean time to first failure and mean time between failures. A detailed analysis of the bridge network is presented.

A factoring algorithm using polygon‐to‐chain reductions for computing K‐terminal network reliability

AbstractLet G = (V,E) be an undirected graph whose edges may fail, and let Gk denote G with a set k ⊆ V specified. Edge failures are assumed to be statistically independent and to have known probabilities. The k‐terminal reliability of Gk, denoted R(Gk), is the probability that all vertices in k are connected by working edges. Computing k‐terminal reliability is an NP‐hard problem not known to be in NP. A factoring algorithm for computing network reliability recursively applies the formula R(Gk) = PiR(Gk′*ei + qiR(Gk − ei)), where Gk′*ei is Gk with edge ei contracted, Gk − ei is Gk with ei deleted and pi = 1 − qi is the reliability of edge ei. Various reliability‐preserving reductions may be performed after each factoring operation in order to reduce computational complexity. The complexity of a slightly restricted factoring algorithm using standard reductions, along with newly developed polygon‐to‐chain reductions, will be bounded below by an invariant of G, the “minimum domination.” For 2 ≤ ∣K∣ ≤ 5 or ∣V∣ − 2 ≤ ∣K∣ ≤ ∣V∣, this bound is always achievable. The factoring algorithm with polygon‐to‐chain reductions will always perform as well as or better than an algorithm using only standard reductions, and for some networks, it will outperform the simpler algorithm by an exponential factor. This generalizes early results that were only valid for K = V. Removing the restriction on edge selection leaves results essentially unchanged in the upper range of ∣K∣, but minimum domination becomes only a tight upper bound for the lower range.

Assessing the Reliability of Computer Software and Computer Networks: An Opportunity for Partnership with Computer Scientists

Abstract In this article we highlight three areas that are of importance in computer science and in which statisticians and applied probabilists can make valuable contributions. We outline these areas, survey the developments, and point out some of the unresolved problems.

A ring underlying probabilistic identities

In recent years, we have seen a renewed interest in the Inclusion-Exclusion Formula that is variously attributed to Poincare, Sylvester and several others. In part this interest is motivated by the need for efficient estimates of calculations with alternating sums such as arise, for example, in computing the reliability of large computer or communication networks. In part this interest has been motivated by the manifold algebraic structures that have been the outgrowth of computations with alternating sums, ranging all the way from spectral sequences in topology to the nitty-gritty of combinatorial enumeration. Recent papers along this line are those of Cerasoli [l] (where the classical inequalities of Frechet and others are derived from a single principle), D’Antona and Rota [2] (who introduce ring structures on sets) and the author [S]. The basic reference remains the classic work of Frechet [4], where, to be sure, more questions are raised than answered. In this paper we show that yet another algebraic structure can be associated with set theoretic enumeration. Specifically, in the following X will denote a discrete random variable (T.v.) assuming non-zero values in a finite number of positive integers. In other words we restrict ourselves to those discrete r.v. for which there exists an integer m such that P[X= k] = 0 whenever k d 0 or k > m. As usual M,, the moment of order s of X, is defined as the expected value of X” (s > 0). Thus it turns out that moments are expressed as polynomials of degree at most m:

Assessing the Reliability of Computer Software and Computer Networks: An Opportunity for Partnership with Computer Scientists

Assessing the Reliability of Computer Software and Computer Networks: An Opportunity for Partnership with Computer Scientists

The Wheatstone bridge reduction in network reliability computations : Rubin Johnson. IEEE Trans Reliab.R-32, 374 (October 1983)

The Wheatstone bridge reduction in network reliability computations : Rubin Johnson. IEEE Trans Reliab.R-32, 374 (October 1983)

Computing Network Reliability in Time Polynomial in the Number of Cuts

We present a new algorithm that computes the probability that there is an operating path from a node s to a node t in a stochastic network. The computation time of this algorithm is bounded by a polynomial in the number of (s, t)-cuts in the network. We also examine the complexity of other connectedness reliability problems with respect to the number of cutsets and pathsets in the network. These problems are distinguished as either having algorithms that are polynomial in the number of such sets, or having no such algorithms unless P = NP.

A Survey of Network Reliability and Domination Theory

We present a brief survey of the current state of the art in network reliability. We survey only exact methods and do not consider Monte Carlo methods. Most network reliability problems are, in the worst case, NP-hard and are, in a sense, more difficult than many standard combinatorial optimization problems. Nevertheless, there are, in fact, linear and polynomial time algorithms for network reliability problems of special structure. We review general methods for network reliability computation and discuss the central role played by domination theory in network reliability computational complexity. We also point out the connection with the more general problem of computing the reliability of coherent structures. The class of coherent structures contains both directed and undirected networks as well as logic (or fault) trees without not gates. This topic is a rich area for further research.

Mathematical theory of reliability: A historical perspective

The author reviews developments in mathematical reliability theory, especially those developments which have had or are likely to have impact on engineering reliability problems. The review to 1960 is based on a similar review which appeared in the 1965 book by R.E. Barlow and F. Proschan entitled Mathematical Theory of Reliability. It is pointed out that if the 1970s were the fault tree era, the 1980s may well turn out to be the era of network reliability, principally due to the importance of computer and computer network reliability.

The Wheatstone Bridge Reduction in Network Reliability Computations

The subgraph configuration known as the Wheatstone bridge of s-independent elements can be replaced by a single edge in a reliabilit-preserving network transformation. The formulas for calculating the good and bad probabilities of this edge are presented. This reduction technique reduces by more than half the complexity of some backtrack algorithms that solve network reliability problems. Computational experience indicates that the benefits are worth the extra efforts it takes to perform this reduction. For problems of moderate size, use of the Wheatstone bridge reduction typically led to computational savings of between 20% and 40%.

A simple technique for computing network reliability : S. Hasanuddin Ahmad. IEEE Trans. Reliab.R-31 (1), 41 (1982)

A simple technique for computing network reliability : S. Hasanuddin Ahmad. IEEE Trans. Reliab.R-31 (1), 41 (1982)

Performance statistics of a time-sharing computer network

User interaction with a computer is a very complex process and some of the complexity is inherent in the nature of computing. Many experiments in time-sharing and networking of computers have been very extensive and expensive. Nevertheless, a knowledge of the performance and reliability of computer networks is vital for efficient operations. One major problem in the evaluation of any time-sharing network seems to be the lack of quantitative understanding of the relationship for planning future network requirements as well as aiding the process of evaluating existing performance the workload at any computer center is often unique and not typical of a wide variety of commercial environment. This paper presents the following using data collected under actual operating conditions of the LSU time-sharing network. 1. a) statistical properties of the input traffic on the network, computer service time demands and selected performance measures. 2. b) A model relating to performance measures of the network. The model developed in this paper consists of two phases: Phase one consists of characterizing the workload performance of time-sharing network by the following model: f( κ) = α + βe λκ , where α, β and λ are constant coefficients and κ is a performance variable of the network. Phase two consists of developing a regression model of the performance variables of the network. The quality of the model is tested with some real observed data and the difference between predicted values and the observe values are very small. This is supported by the residual analysis of the data.