Nonclairvoyant Speed Scaling for Flow and Energy

We give three results related to online nonclairvoyant speed scaling to minimize total flow time plus energy. We give a nonclairvoyant algorithm LAPS, and show that for every power function of the form P(s)=s ^α , LAPS is O(1)-competitive; more precisely, the competitive ratio is 8 for α=2, 13 for α=3, and frac2a²lnafrac{2alpha^{2}}{lnalpha} for α>3. We then show that there is no constant c, and no deterministic nonclairvoyant algorithm A, such that A is c-competitive for every power function of the form P(s)=s ^α . So necessarily the achievable competitive ratio increases as the steepness of the power function increases. Finally we show that there is a fixed, very steep, power function for which no nonclairvoyant algorithm can be O(1)-competitive.