An Algorithm to Compute the All-terminal Reliability Measure

Cancela, Héctor; Rubino, Gerardo; Urquhart, María E.

doi:10.1007/bf03398660

Cited by 3 publications

(4 citation statements)

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“…Each convolutional layer was followed by batch normalization and ReLU layers, considering that such a structure generated successful results in a previous image classification study with CNN. 55 In addition to these initial values, different multiplier (mul) values of 1, 4, and 8 were applied to the number of filters, i.e., combinations of number of filters (8,16,32,32), (32,64,128,128), and (64,128,256,256) were investigated for selection of the best number of filters.…”

Section: Hyperparametersmentioning

confidence: 99%

“…On the other hand, if the successful operation is defined as all nodes being able to communicate, that is, a node s must be able to communicate with all the other n − 1 nodes, then the all-terminal problem is appropriate. All-terminal reliability is an important measure for broadcasting in telecommunication networks, 15,16 local area and industrial networks, 17 wireless networks. 18,19 A more general concept is k -terminal reliability.…”

Section: Introductionmentioning

confidence: 99%

“…23,24 Advanced network reliability techniques have been oriented to the k-terminal and all-terminal reliability. 17,25–28 This paper focuses on the all-terminal reliability, as it has practical applications especially in communications networks, 15–19 and because it requires all the nodes to be connected to each other, which provides a holistic reliability measure for the network. Moreover, all-terminal reliability provides a more general starting point for comparison with previous and/or future studies because it does not require the additional parameter k .…”

Section: Introductionmentioning

confidence: 99%

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All-terminal network reliability estimation using convolutional neural networks

Davila-Frias

Yadav

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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Estimating the all-terminal network reliability by using artificial neural networks (ANNs) has emerged as a promissory alternative to classical exact NP-hard algorithms. Approaches based on traditional ANNs have usually considered the network reliability upper bound as part of the inputs, which implies additional time-consuming calculations during both training and testing phases. This paper proposes the use of Convolutional Neural Networks (CNNs), without the reliability upper-bound as an input, to address the all-terminal network reliability estimation problem. The present study introduces a multidimensional matrix format to embed the topological and link reliability information of networks. The unique contribution of this article is the method to capture the topology of a network in terms of its adjacency matrix, link reliability, and topological attributes providing a novel use of CNN beyond image classification. Since CNNs have been successful for image classification, appropriate modifications are needed and introduced to use them in the estimation of network reliability. A regression output layer is proposed, preceded by a sigmoid layer to achieve predictions within the range of reliability characteristic, a feature that some previous ANN-based works lack. Several training parameters together with a filter multiplier (CNN architecture parameter) were investigated. The actual values and the ones predicted with the best trained CNN were compared in the light of RMSE (0.04406) and p-value (0.3) showing non-significant difference. This study provides evidence supporting the hypothesis that the network reliability can be estimated by CNNs from its topology and link reliability information, embedded as an image-like multidimensional matrix. Another important result of the proposed approach is the significant reduction in computational time. An average of 1.18 ms/network was achieved by the CNN, whereas backtracking exact algorithm took around 500 s/network.

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Section: Hyperparametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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All-terminal network reliability estimation using convolutional neural networks

Davila-Frias

Yadav

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…We performed some experiments in order to compare these two approaches. We chose an exact com-binatorics method (adapting the algorithm proposed in (Cancela, Rubino, and Urquhart 2001) to the 2-terminal case). This algorithm is an improved version of the method proposed in (Ahmad 1982), having the property of using a bounded amount of memory which is known before running.…”

Section: Motivation For Sensitivity Analysismentioning

confidence: 99%

Sensitivity analysis for robust parameter design experiments

Litko¹

2005

Proceedings of the Winter Simulation Conference, 2005.

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We analyze the computation of sensitivities in network reliability analysis. The associated models are graphs whose components are weighted by probabilities (their reliabilities) and they are widely used, for instance, in the design of communication networks. The paper deals with the sensitivities of usual reliability network metrics, with respect to the reliabilities of the components. The importance of sensitivities in this context is discussed and it is shown how to efficiently estmate the vector of sensitivities using Monte Carlo procedures. A first result allows to evaluate sensitivities using the standard Monte Carlo approach. A second method is then presented to deal efficiently with the rare event case. The ideas presented here can be applied to other classes of reliability problems and/or methods. INTRODUCTION The ModelStochastic graphs are widely used models for representing complex multi-component systems subject to component failures. They consist of graphs whose elements (nodes and arcs or edges) are weighted by probabilities. The output usually obtained from this type of structure is the probability of events representing a desired behavior of the system modeled. In this paper we consider the problem of the computation of reliability measures and we focus on a fundamental family of metrics, called K-terminal reliability, in the following version: the input is a stochastic undirected graph G = (V, E) where V is the set of vertices and E is the set of edges. We denote by E the number of edges: E = |E|. The graph may represent, for instance, a communication network. In this case, the vertices correspond to nodes sending and receiving information and the edges model communication lines. This application is used as a reference in the paper. For instance, the terms vertex and node are used as synonymous, and the same with edge or line or link. At a fixed time τ , each line is in one of two states: either working (operational) or completely down (unoperational, behaving as if it did not exist in the network). To simplify the presentation, we assume that nodes are perfect and that only lines can fail, but this is not critical since we are using Monte Carlo techniques. The graph is also assumed to be undirected, that is, the lines of the modeled communication network are bi-directional (messages can pass in both directions.) Finally, we assume that the graph is connected and without loops.The state of line or edge e at time τ is a binary random variable X e with value 1 if the line is working or 0 if it does not work. A basic assumption now is that (X e , e ∈ E) is a family of independent random variables. The K-terminal problem is the following: Given the probability r e of the event {X e = 1} for each line e of the network and a subset K of the set of vertices V, compute the probability R that, at time τ , the nodes can communicate with each other. In other words, if the first graph G = (V, E) is fixed, the set E of operational lines at time τ defines a subgraph G = (V, E ) of the previous one.The number R...

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A deep neural network and Bayesian method based framework for all-terminal network reliability estimation considering degradation

Davila-Frias

Yodo

et al. 2023

Reliability Engineering & System Safety

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An Algorithm to Compute the All-terminal Reliability Measure

Cited by 3 publications

References 5 publications

All-terminal network reliability estimation using convolutional neural networks

All-terminal network reliability estimation using convolutional neural networks

Sensitivity analysis for robust parameter design experiments

A deep neural network and Bayesian method based framework for all-terminal network reliability estimation considering degradation

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