Partial Detectors Versus Replication To Cope With Silent Errors
Comparaison de la détection partielle et de la réplication pour les erreurs silencieuses
Résumé
This work considers an iterative algorithm that executes on an error-prone platform. Silent errors strike at each iteration with some probability. A detector is applied as a verification mechanism before taking a checkpoint. However, this mechanism is likely not perfect, and fails to detect some errors. More precisely, an error striking at iteration I will be detected only after iteration (I -1)+X, where X is a random variable obeying a probability distribution with bounded support [1, D] such as a truncated geometric distribution. Intuitively, the error silently amplifies during some iterations before it can be detected at distance X or higher. As a consequence, when taking a verification before a checkpoint, there is the risk of missing an error that has struck recently but cannot be detected yet. The simplest solution is to keep two checkpoints in memory, and to use two segments of D -1 iterations, each followed by a verification and a checkpoint: in steady state, perform D -1 iterations after the last checkpoint and take a verification; (i) if successful, we can safely erase the oldest checkpoint, because the most recent checkpoint is necessarily verified. We take a new checkpoint to replace the old one, which is not verified yet; (ii) otherwise, we need to rollback to the oldest checkpoint, not to the last one which may not be verified. Can this simple scheme perform better than replication? What is the optimal number of segments (hence of checkpoints) to keep in memory, and what is the length of these segments? This work answers these questions, both theoretically and through Monte Carlo simulations.
Ce travail s’intéresse aux algorithmes itératifs qui s’exécutent sur des plates-formes soumises à des erreurs silencieuses et compare la réplication avec l’utilisation de détecteurs partiels (capables de détecter une partie des erreurs, mais pas toutes les erreurs).
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