Server scheduling in the weighted ℓp norm

Abstract

We explain how the apparent goals of the Unix CPU scheduling policy can be formalized using the weighted ℓp norm of flows. We then show that the online algorithm, Highest Density First (HDF), and the nonclairvoyant algorithm, Weighted Shortest Elapsed Time First (WSETF), are almost fully scalable. That is, they are (1 + ∈)-speed O(1)-competitive. Even for unit weights, it was known that there is no O(1)-competitive algorithm. We also give a generic way to transform an algorithm A in an algorithm B in such a way that if A is O(1)-speed O(1)-competitive with respect to some ℓp norm of flow then B is O(1)-competitive with respect to the ℓp norm of completion times. Further, if A is online (nonclairvoyant) then B is online (nonclairvoyant). Combining these results gives an O(1)-competitive nonclairvoyant algorithm for ℓp norms of completion times. © Springer-Verlag 2004.