In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the time interval where the fault will occur: the @math -predictability does not only specify that the fault will be predicted before it occurs, but also that the predictor will be able to predict that its occurrence will occur in @math to @math observations from now. We also provide a quadratic algorithm that decides predictability of the system.
Predictability as presented in this paper was introduced by Genc and Lafortune @cite_13 . Their approach was however only Boolean: they addressed the question can the fault be predicted before it occurs?'' They presented an exponential space algorithm using a structure similar to our optimal predictor. They also announced the existence of a polytime algorithm, similar to the twin plant used for diagnosability and formally presented in an extension of their work @cite_3 .
@cite_13 @cite_3
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The exponential growth of computational power of the extreme scale machines over the past few decades has led to a corresponding decrease in reliability and a sharp increase of the frequency of hardware faults. Our research focuses on the mathematical challenges presented by the silent hardware faults; i.e., faults that can perturb the result of computations in an inconspicuous way. Using the approach of selective reliability, we present an analytic fault mode that can be used to study the resilience properties of a numerical algorithm. We apply our approach to the classical fixed point iteration and demonstrate that in the presence of hardware faults, the classical method fails to converge in expectation. We preset a modified resilient algorithm that detects and rejects faults resulting in error with large magnitude, while small faults are negated by the natural self-correcting properties of the algorithm. We show that our method is convergent (in first and second statistical moments) even in the presenc... To facilitate proactive fault management in large-scale systems such as IBM Blue Gene P, online failure prediction is of paramount importance. While many techniques have been presented for online failure prediction, questions arise regarding two commonly used approaches: period-based and event-driven. Which one has better accuracy? What is the best observation window (i.e., the time interval used to collect evidence before making a prediction)? How does the lead time (i.e., the time interval from the prediction to the failure occurrence) impact prediction arruracy? To answer these questions, we analyze and compare period-based and event-driven prediction approaches via a Bayesian prediction model. We evaluate these prediction approaches, under a variety of testing parameters, by means of RAS logs collected from a production supercomputer at Argonne National Laboratory. Experimental results show that the period-based Bayesian model and the event-driven Bayesian model can achieve up to 65.0 and 83.8 prediction accuracy, respectively. Furthermore, our sensitivity study indicates that the event-driven approach seems more suitable for proactive fault management in large-scale systems like Blue Gene P.