Nonclairvoyant Speed Scaling for Flow and Energy

We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is $P(s)=s^alpha$. We give a nonclairvoyant algorithm that is shown to be $O(alpha^3)$-competitive. We then show an $Omega( alpha^{1/3-epsilon} )$ lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be $O(1)$-competitive