In [1], Jejurikar and Gupta investigated energy savings due to optimal slowdown of periodic tasks in real-time task systems, where tasks have varying power characteristics and task deadlines are less than the periods. The authors presented a bisection method for computing near-optimal constant slowdown factors, when all the tasks are assigned the same slowdown factor. For the case when tasks have different slowdown factors, they presented a method for computing near-optimal slowdown factors as a solution to a convex optimization problem, using the ellipsoid method. In this note, we show a method to cast the problem of finding near-optimal slowdown factors that minimize the total energy consumption as a geometric program (GP), which can be efficiently solved using modern interior-point methods. More importantly, we show that the problem of finding nearoptimal constant slowdown factors has an analytic solution. We demonstrate the GP approach by solving several numerical instances using a...
Ravindra Jejurikar, Rajesh K. Gupta