On the theory of speculative checkpointing: time and energy considerations

Collective checkpoint/rollback is the most popular approach for dealing with fail-stop errors on high-performance computing platforms. Prior work has focused on choosing checkpoint intervals that minimize the total cost of checkpoint/rollback. This work introduces the notion of speculative checkpointing, where we probabilistically skip some checkpoints. The careful selection of checkpoints either to be taken or skipped has the potential to reduce the total checkpoint/rollback overhead. We mathematically formulate the overall checkpoint/rollback cost in the presence of speculation. We consider the choice of speculation as a fixed probability or a probability distribution. We formulate two criteria to be minimized: total execution time and approximate total energy. We derive the criteria for beneficial speculative checkpointing for exponential and arbitrary failure distributions. Furthermore, we analyze the joint optimization of energy and time to express the trade-offs mathematically. We validate the formulations and evaluate various scenarios using discrete-event simulation. Experimental evaluation validates the models and demonstrates that employing speculation and choosing to speculate by sampling a distribution derived from the failure distribution achieves the best performance.