Speed scaling with a solar cell

We consider the speed scaling problem of scheduling a collection of tasks with release times, deadlines, and sizes so as to minimize the energy recharge rate. This is the first theoretical investigation of speed scaling for devices with a regenerative energy source. We show that the problem can be expressed as a polynomial sized convex program. We that using the KKT conditions, one can obtain an efficient algorithm to verify the optimality of a schedule. We show that the energy optimal YDS schedule, is 2-approximate with respect to the recharge rate. We show that the online algorithm BKP is O(1)-competitive with respect to recharge rate.