Approximation in preemptive stochastic online scheduling

Authors:
Nicole Megow;Tjark Vredeveld
Affiliations:
Technische Universität Berlin, Institut für Mathematik, Berlin, Germany;Maastricht University, Department of Quantitative Economics, MD Maastricht, The Netherlands
Venue:
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Year:
2006

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Abstract

We present a first constant performance guarantee for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive a policy with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policy applies to the recently introduced stochastic online scheduling model in which jobs arrive online over time. In contrast to the previously considered nonpreemptive setting, our preemptive policy extensively utilizes information on processing time distributions other than the first (and second) moments. In order to derive our result we introduce a new nontrivial lower bound on the expected value of an unknown optimal policy that we derive from an optimal policy for the basic problem on a single machine without release dates. This problem is known to be solved optimally by a Gittins index priority rule. This priority index also inspires the design of our policy.