Energy-optimal speed control of a generic device

The dynamic voltage and frequency scaling technique in CPUs is an example of adjusting a device's control variable to trade off power consumption and performance. This idea of energy optimization through speed control has been subsequently applied to other components of electronic systems such as disk drives and wireless transceivers. In this paper, the energy-optimal speed profile (a function of time) of a generic device that has to execute a given task in a given time is obtained analytically. The proposed approach is applicable to devices with either discrete or continuous-speed sets. The main novelty of the approach is that for discrete-speed sets, the nature of the underlying continuous power-speed relationship does not need to be known. The discrete power-speed data points only need to satisfy a W-convex relation: a discrete analog of a convex function. Based on the observation that most devices have W-convex power-speed relations, it is shown that the optimal speed profile uses at most one speed (for continuous speeds) or two speeds (for discrete-speed sets). Furthermore, each device has an intrinsic speed (independent of the task) u _c at which it consumes the least energy per unit work done. It is shown that this speed can be calculated directly from measured values of power-speed data points (for discrete-speed sets) or by an experimental line search procedure where each step involves measuring a power-speed data point (for continuous-speed sets). In either case, no curve fit or knowledge of analytical power models is required. The optimum speed profile was shown to be either u _c or the minimum feasible speed(s) for the given task, with the choice depending on the energy overheads and task parameters.