Computationally efficient and numerically stable reliability bounds for repairable fault-tolerant systems

Carrasco, Juan A.

doi:10.1109/12.990125

Cited by 20 publications

(15 citation statements)

References 18 publications

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“…Regenerative randomization (RR) (Carrasco, 2003) is another variant targeted at a class of CTMC models, class C , including both exact and bounding failure/repair CTMC models of fault-tolerant systems with exponential failure and repair time distributions, repair in every state with failed components, and failure rates much smaller than repair rates, computing E[r X(t) ] with reward rates ≥ 0 with bounded from above absolute truncation error, and having, for class C models, a computational cost in terms of CPU time that can be smaller than that of SR. Based on RR, bounding regenerative randomization (Carrasco, 2002) is targeted at a class of CTMC models, class C , slightly less general than class C , but also including both exact and bounding failure/repair CTMC models of faulttolerant systems with exponential failure and repair time distributions, repair in every state with failed components, and failure rates much smaller than repair rates, and computing seemingly tight bounds at a computational cost in terms of CPU time that should be small relative to the model size when that model size is large. Downloaded by [Mary Ann Muller] at 07:08 21 January 2014…”

Section: Introductionmentioning

confidence: 99%

Reliability Bounds for Fault-Tolerant Systems with Deferred Repair using Bounding Split Regenerative Randomization

Temsamani¹,

Carrasco

2013

Communications in Statistics - Simulation and Computation

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Section: Introductionmentioning

confidence: 99%

Reliability Bounds for Fault-Tolerant Systems with Deferred Repair using Bounding Split Regenerative Randomization

Temsamani¹,

Carrasco

2013

Communications in Statistics - Simulation and Computation

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“…Since the term with s j = 0 (simultaneous failure of all of the PUs) corresponds to failure in task execution, it can be removed from U(z) before performing the operator (19).…”

Section: Total Task Execution Time Distributionmentioning

confidence: 99%

“…Many research works have been devoted to the study of fault-tolerant system's reliability [4][5][6][7][8][12][13][14][15][16][17][18][19][20]. The fault tolerance usually requires additional resources and results in performance penalties (particularly with regard to computation time), which constitutes a tradeoff between software performance and reliability.…”

Section: Introductionmentioning

confidence: 99%

Reliability of fault-tolerant systems with parallel task processing

Levitin

Xie

Zhang

2007

European Journal of Operational Research

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The paper considers performance and reliability of fault-tolerant software running on a hardware system that consists of multiple processing units. The software consists of functionally equivalent but independently developed versions that start execution simultaneously. The computational complexity and reliability of different versions are different. The system completes the task execution when the outputs of a pre-specified number of versions coincide. The processing units are characterized by different availability and processing speed. It is assumed that they are able to share the computational burden perfectly and that execution of each version can be fully parallelized. The algorithm based on the universal generating function technique is used for determining the distribution of system task execution time. This algorithm allows analysts to evaluate complex hardware-software reliability and performance indices such as expected task execution time and probability that the task is completed within a given time. Illustrative examples are also presented. The algorithm based on the universal generating function technique is used for determining the distribution of system task execution time. This algorithm allows analysts to evaluate complex hardware-software reliability and performance indices such as expected task execution time and probability that the task is completed within a given time. Illustrative examples are presented.

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“…The high computational cost of the standard randomization method for stiff models has motivated the development in the last years of several variants which can outperform the standard randomization method: selective randomization [11,12], multistepping [3, Section 3.1.2], adaptive uniformization [13], adaptive/standard uniformization [14], uniformization with steady-state detection [1,15] and regenerative randomization [16,17]. Randomization-based methods computing bounds which can be much more efficient than "exact" methods have also been proposed [18].…”

Section: Introductionmentioning

confidence: 99%

Transient Analysis of Rewarded Continuous Time Markov Models by Regenerative Randomization with Laplace Transform Inversion

Carrasco

2003

The Computer Journal

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In this paper we develop a variant, regenerative randomization with Laplace transform inversion, of a previously proposed method (the regenerative randomization method) for the transient analysis of rewarded continuous time Markov models. Those models find applications in dependability and performability analysis of computer and telecommunication systems. The variant differs from regenerative randomization in that the truncated transformed model obtained in that method is solved using a Laplace transform inversion algorithm instead of standard randomization. As regenerative randomization, the variant requires the selection of a regenerative state on which the performance of the method depends. For a class of models, class C', including typical failure/repair models, a natural selection for the regenerative state exists and, with that selection, theoretical results are available assessing the performance of the method in terms of "visible" characteristics. Using dependability class C' models of moderate size of a RAID 5 architecture we compare the performance of the variant with those of regenerative randomization and randomization with steady-state detection for irreducible models, and with those of regenerative randomization and standard randomization for models with absorbing states. For irreducible models, the new variant seems to be about as fast as randomization with steady-state detection for models which are not too small when the initial probability distribution is concentrated in the regenerative state, and significantly faster than regenerative randomization when the model is stiff and not very large. For stiff models with absorbing states, the new variant is much faster than standard randomization and significantly faster than regenerative randomization when the model is not very large. In addition, the variant seems to be able to achieve stringent accuracy levels safely.

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Computationally efficient and numerically stable reliability bounds for repairable fault-tolerant systems

Cited by 20 publications

References 18 publications

Reliability Bounds for Fault-Tolerant Systems with Deferred Repair using Bounding Split Regenerative Randomization

Reliability Bounds for Fault-Tolerant Systems with Deferred Repair using Bounding Split Regenerative Randomization

Reliability of fault-tolerant systems with parallel task processing

Transient Analysis of Rewarded Continuous Time Markov Models by Regenerative Randomization with Laplace Transform Inversion

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