Energy efficiency analysis for the Single Frequency Approximation (SFA) scheme

Energy-efficient designs are important issues in computing systems. This paper studies the energy efficiency of a simple and linear-time strategy, called Single Frequency Approximation (SFA) scheme, for periodic real-time tasks on multi-core systems with a shared supply voltage in a voltage island. The strategy executes all the cores at a single frequency to just meet the timing constraints. SFA has been adopted in the literature after task partitioning, but the worst-case performance of SFA, in terms of energy consumption, is an open problem. We provide comprehensive analysis for SFA to derive the cycle utilization distribution for its worst-case behaviour for energy minimization. Our analysis shows that the energy consumption by using SFA for task execution is at most 1.53 (1.74, 2.10, 2.69, respectively), compared to the energy consumption of the optimal voltage/frequency scaling, when the dynamic power consumption is a cubic function of the frequency and the voltage island has up to 4 (8, 16, 32, respectively) cores. The analysis shows that SFA is indeed an effective scheme under practical settings, even though it is not optimal. Furthermore, since all the cores run at a single frequency and no frequency alignment for Dynamic Voltage and Frequency Scaling (DVFS) between cores is needed, any uni-core dynamic power management technique for reducing the energy consumption for idling can be easily incorporated individually on each core in the voltage island. This paper also provides the analysis of energy consumption for SFA, combined with the procrastination for Dynamic Power Management (DPM). Furthermore, we also extend our analysis for deriving the approximation factor of SFA for a multi-core system with multiple voltage islands.