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Robustness of the Young/Daly formula for stochastic iterative applications

Abstract : The Young/Daly formula for periodic checkpointing is known to hold fora divisible load application where one can checkpoint at any time-step. In an nutshell, the optimal period isPYD=√2μfC where μf is the Mean Time Between Failures (MTBF) and C is the checkpoint time. This paper assesses the accuracy of the formulafor applications decomposed into computational iterations where: (i) the duration of aniteration is stochastic, i.e., obeys a probability distribution law D of mean μD ; and (ii) onecan checkpoint only at the end of an iteration. We first consider static strategies where checkpoints are taken after a given number of iterationskand provide a closed-form,asymptotically optimal, formula fork, valid for any distribution D. We then show that using the Young/Daly formula to compute k (ask·μD=PYD) is a first order approximationof this formula. We also consider dynamic strategies where one decides to checkpoint at the end of an iteration only if the total amount of work since the last checkpoint exceeds a threshold Wth, and otherwise proceed to the next iteration. Similarly, we provide aclosed-form formula for this threshold and show that PYD is a first-order approximation of Wth. Finally, we provide an extensive set of simulations where D is either Uniform,Gamma or truncated Normal, which shows the global accuracy of the Young/Daly formula,even when the distribution D had a large standard deviation (and when one cannot use afirst-order approximation). Hence we establish that the relevance of the formula goes well beyond its original framework
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Submitted on : Saturday, March 21, 2020 - 3:47:10 PM
Last modification on : Monday, May 16, 2022 - 4:46:02 PM


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Yishu Du, Loris Marchal, Guillaume Pallez, Yves Robert. Robustness of the Young/Daly formula for stochastic iterative applications. [Research Report] RR-9332, Inria Grenoble Rhône-Alpes. 2020. ⟨hal-02514107⟩



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