Scalable k-out-of-n models for dependability analysis with Bayesian networks

Abstract

Availability analysis is indispensable in evaluating the dependability of safety and business-critical systems, for which fault tree analysis (FTA) has proven very useful throughout research and industry. Fault trees (FT) can be analyzed by means of a rich set of mathematical models. One particular model are Bayesian networks (BNs) which have gained considerable popularity recently due to their powerful inference abilities. However, large-scale systems, as found in modern data centers for cloud computing, pose modeling challenges that require scalable availability models. An equivalent BN of a FT has no scalable representation for the k-out-of-n (k/n) voting gate because the conditional probability table that constitutes the k/n voting gate grows exponentially in n. Thus, the memory becomes the limiting factor.We propose a scalable k/n voting gate representation for BNs, based on the temporal noisy adder. The resulting model reduces the initial exponential to polynomial memory growth without a custom inference algorithm. Previous BN implementations of the k/n voting gate could only handle around 30 input events until memory limits make inference infeasible. However, our evaluation shows that our scalable model can handle more than 700 input events per gate, making it possible to evaluate large scale systems.

Availability analysis of redundant and replicated cloud services with Bayesian networks

“…For approximate inference, we use the forward sampling method, and for exact inference, we used the Lauritzen-Spiegelhalter Algorithm method 31 from the gRain 1.3.2 package. 32,33 Furthermore, we used in all experiments the scalable Bayesian network representations for AND/OR and voting gates by Heckerman 25 and Bibartiu et al 24 The implementation of the algorithms and evaluation methods for the presented Bayesian network model are available as open source 1 . Moreover, all experiments will consider two different data center infrastructures.…”

“…However, this problem can be mitigated for the AND/OR, and k-out-of-n model. Heckerman [25] provides an equivalent AND/OR model that reduces the space complexity to linear, while Bibartiu et al [24] provide an equivalent (scalable) k-out-of-n model with polynomial complexity. Having these scalable models, we can substitute the existing AND/OR, and k-out-of-n models in the Bayesian network model with their scalable counterparts.…”

“…However, this problem can be mitigated for the AND/OR, and k‐out‐of‐n model. Heckerman 25 provides an equivalent AND/OR model that reduces the space complexity to linear, while Bibartiu et al 24 . provide an equivalent (scalable) k‐out‐of‐n model with polynomial complexity.…”

“…[21][22][23] They support a rich set of efficient inference algorithms suitable for fault diagnostic 15 and availability prediction. Moreover, with the introduction of scalable Bayesian network structures, 24,25 we argue that Bayesian networks are a good fit to assess large-scale redundant and replicated cloud services.…”

Reliability Evaluation of Linear or Circular Consecutive k-out-of-n: F System Using Dynamic Bayesian Network

“…Madhumitha and Vijayalakshmi [23] calculated the mean time to failure and confidence interval using Bayesian methods for the Cons.k/n:F systems. Bibartiu, Durr and Grau [24] defined the memory growth for the k/n voting gate was lowered from exponential to polynomial in the range of input events due to a scalable Bayesian network model. Nashwan [25] provided formula to calculate the precise reliability and failure likelihood functions for the linear and circular r-gap successive k-out-of-m-from-n:F systems.…”