A different re-execution speed can help

We consider divisible load scientific applications executing on large-scale platforms subject to silent errors. While the goal is usually to complete the execution as fast as possible in expectation, another major concern is energy consumption. The use of dynamic voltage and frequency scaling (DVFS) can help save energy, but at the price of performance degradation. Consider the execution model where a set of K different speeds is given, and whenever a failure occurs, a different re-execution speed may be used. Can this help? We address the following bi-criteria problem: how to compute the optimal checkpointing period to minimize energy consumption while bounding the degradation in performance. We solve this bi-criteria problem by providing a closed-form solution for the checkpointing period, and demonstrate via a comprehensive set of simulations that a different re-execution speed can indeed help.