Towards Optimal Multi-Level Checkpointing

We provide a framework to analyze multi-level checkpointing protocols, by formally defining a <inline-formula> <tex-math notation="LaTeX">k</tex-math> <inline-graphic xlink:href="benoit-ieq1-2643660.gif"/> </inline-formula>-level checkpointing patter...

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Veröffentlicht in:IEEE transactions on computers Jg. 66; H. 7; S. 1212 - 1226
Hauptverfasser: Benoit, Anne, Cavelan, Aurelien, Le Fevre, Valentin, Robert, Yves, Sun, Hongyang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.07.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Schlagworte:
Algorithms
Checkpointing
Computer Science
Computer simulation
Distributed, Parallel, and Cluster Computing
Dynamic programming
Error analysis
fail-stop errors
Heuristic algorithms
multi-level checkpointing
optimal pattern
Optimization
Optimized production technology
Protocols
Resilience
Shape
Optimal pattern
Fail-stop errors
Multi-level checkpointing
Resilience
ISSN:0018-9340, 1557-9956
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Zusammenfassung:We provide a framework to analyze multi-level checkpointing protocols, by formally defining a <inline-formula> <tex-math notation="LaTeX">k</tex-math> <inline-graphic xlink:href="benoit-ieq1-2643660.gif"/> </inline-formula>-level checkpointing pattern. We provide a first-order approximation to the optimal checkpointing period, and show that the corresponding overhead is in the order of <inline-formula> <tex-math notation="LaTeX">\sum _{\ell =1}^{k}\sqrt{2\lambda _\ell C_\ell}</tex-math> <inline-graphic xlink:href="benoit-ieq2-2643660.gif"/> </inline-formula>, where <inline-formula> <tex-math notation="LaTeX">\lambda _\ell</tex-math> <inline-graphic xlink:href="benoit-ieq3-2643660.gif"/> </inline-formula> is the error rate at level  <inline-formula><tex-math notation="LaTeX">\ell</tex-math> <inline-graphic xlink:href="benoit-ieq4-2643660.gif"/> </inline-formula>, and <inline-formula> <tex-math notation="LaTeX">C_\ell</tex-math> <inline-graphic xlink:href="benoit-ieq5-2643660.gif"/> </inline-formula> the checkpointing cost at level <inline-formula><tex-math notation="LaTeX">\ell </tex-math> <inline-graphic xlink:href="benoit-ieq6-2643660.gif"/> </inline-formula>. This nicely extends the classical Young/Daly formula on single-level checkpointing. Furthermore, we are able to fully characterize the shape of the optimal pattern (number and positions of checkpoints), and we provide a dynamic programming algorithm to determine the optimal subset of levels to be used. Finally, we perform simulations to check the accuracy of the theoretical study and to confirm the optimality of the subset of levels returned by the dynamic programming algorithm. The results nicely corroborate the theoretical study, and demonstrate the usefulness of multi-level checkpointing with the optimal subset of levels.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2016.2643660