No abstract

The Young/Daly formula for periodic checkpointing is known to hold for a divisible load application where one can checkpoint at any time-step. In an nutshell, the optimal period is P YD = 2µ f C where µ f is the Mean Time Between Failures (MTBF) and C is the checkpoint time. This paper assesses the accuracy of the formula for applications decomposed into computational iterations where: (i) the duration of an iteration is stochastic, i.e., obeys a probability distribution law D of mean µ D ; and (ii) one can checkpoint only at the end of an iteration. We first consider static strategies where checkpoints are taken after a given number of iterations k and provide a closed-form, asymptotically optimal, formula for k, valid for any distribution D. We then show that using the Young/Daly formula to compute k (as k•µ D = P YD ) is a first order approximation of 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 W th , and otherwise proceed to the next iteration. Similarly, we provide a closed-form formula for this threshold and show that P YD is a first-order approximation of W th . 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 a first-order approximation). Hence we establish that the relevance of the formula goes well beyond its original framework.

This work provides an optimal checkpointing strategy to protect iterative applications from fail-stop errors. We consider a very general framework, where the application repeats the same execution pattern by executing consecutive iterations, and where each iteration is composed of several tasks. These tasks have different execution lengths and different checkpoint costs. Assume that there are n tasks and that task a i , where 0 ≤ i < n, has execution time t i and checkpoint cost C i . A naive strategy would checkpoint after each task. A strategy inspired by the Young/Daly formula would select the task a min with smallest checkpoint cost C min and would checkpoint after every p th instance of that task, leading to a checkpointing period P Y D = pT where T = n−1 i=0 a i is the time per iteration. One would choose the period so that P Y D = pT ≈ √ 2µC min to obey the Young/Daly formula, where µ is the application MTBF. Both the naive and Young/Daly strategies are suboptimal. Our main contribution is to show that the optimal checkpoint strategy is globally periodic, and to design a dynamic programming algorithm that computes the optimal checkpointing pattern. This pattern may well checkpoint many different tasks, and this across many different iterations. We show through simulations, both from synthetic and real-life application scenarios, that the optimal strategy significantly outperforms the naive and Young/Daly strategies.