Energy Efficiency Analysis for the Single Frequency Approximation (SFA) Scheme

Abstract

Energy-efficient designs are important issues in computing systems. This article studies the energy efficiency of a simple and linear-time strategy, called the Single Frequency Approximation (SFA) scheme, for periodic real-time tasks on multicore 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 incurred 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 incurred 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 unicore dynamic power management technique for reducing the energy consumption for idling can be easily incorporated individually on each core in the voltage island. This article also provides an analysis of energy consumption for SFA combined with procrastination for Dynamic Power Management (DPM), resulting in an increment of 1 from the previous results for task execution. Furthermore, we also extend our analysis for deriving the approximation factor of SFA for a multicore system with multiple voltage islands.