Energy Efficient Task Partitioning Based on the Single Frequency Approximation Scheme

Energy-efficiency is a major concern in modern computing systems. For such systems, the presence of multiple voltage islands, where the voltage of each island can change independently and all cores in an island share the same supply voltage at any given time, is an expected compromise between global and per-core Dynamic Voltage and Frequency Scaling (DVFS). This paper focuses on energy minimization for a set of periodic tasks assigned on a voltage island. We present a simple and practical solution, that assigns the tasks onto cores in the island and then applies a DVFS schedule, particularly the Single Frequency Approximation (SFA) scheme. Furthermore, we provide thorough theoretical analysis of our solution, in terms of energy efficiency, against the optimal task partitioning and optimal DVFS schedule, especially for the state-of-the-art designs, that have a few number of cores per voltage island. The analysis shows that, our task partitioning scheme combined with SFA is a good and practical solution for energy efficiency. Particularly, when the number of cores in each voltage island is limited, the approximation factor is at most 2.01 (2.29, 2.55, 2.80, respectively) when the dynamic power consumption is a cubic function of the frequency and the islands have up to 4 (8, 16, 32, respectively) cores. Moreover, with non-negligible overhead for sleeping, further combination with any uni-core procrastination algorithm that consumes no more energy than keeping a core idle when it has no workload in its ready queue, increases the approximation factor by at most 1.