Server scheduling in the Lp norm: a rising tide lifts all boat

  • Authors:
  • Nikhil Bansal;Kirk Pruhs

  • Affiliations:
  • Carnegie Mellon University, Pittsburgh, PA;University of Pittsburgh, Pittsburgh, PA

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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Abstract

Often server systems do not implement the best known algorithms for optimizing average Quality of Service (QoS) out of concern of that these algorithms may be insufficiently fair to individual jobs. The standard method for balancing average QoS and fairness is optimize the Lp metric, 1 . Thus we consider server scheduling strategies to optimize the Lp norms of the standard QoS measures, flow and stretch. We first show that there is no no(1)-competitive online algorithm for the Lp norms of either flow or stretch. We then show that the standard clairvoyant algorithms for optimizing average QoS, SJF and SRPT, are O(1+ε)-speed O(1/ε)-competitive for the Lp norms of flow and stretch. And that the standard nonclairvoyant algorithm for optimizing average QoS, SETF, is O(1+ε)-speed O(1/ε(2+2/p))-competitive for the Lp norms of flow. These results argue that these standard algorithms will not starve jobs until the system is near peak capacity. In contrast, we show that the Round Robin, or Processor Sharing algorithm, which is sometimes adopted because of its seeming fairness properties, is not O(1+ε)-speed no(1)-competitive for sufficiently small ε.