An optimal analytical solution for maximizing expected battery lifetime using the calculus of variations

摘要

The exponential growth in the semiconductor industry and hence the increase in chip complexity, has led to more power usage and power density in modem processors. On the other hand, most of today's embedded systems are battery-powered, so the power consumption is one of the most critical criteria in these systems. Dynamic Voltage and Frequency Scaling (DVFS) is known as one of the most effective energy-saving methods. In this paper, we propose the optimal DVFS profile to minimize the energy consumption of a battery-based system with uncertain task execution time under deadline constraints using the Calculus of Variations (CoV). The contribution of this work is to analytically calculate the lower bound of expected battery charge consumption for a given task with uncertain execution time. Most of the research in dynamic voltage and frequency scaling tends to discretize time and value factors. This is presumably because of the context of embedded systems which is mainly based on digital design and algorithms. However, important factors in power and energy, such as supply voltage, supply current, and operational frequency, are continuous functions of time. The CoV is a branch of mathematics, where system parameters are considered as continuous functions of time. So, for dealing with this kind of problems, which system parameters are continuous functions of time, we can use the CoV as a powerful way to solve continuous optimization problems. In this paper, we obtain the exact analytical solution for maximizing battery lifetime, which is applicable to any convex power model.