Stochastic online scheduling on parallel machines

Authors:
Nicole Megow;Marc Uetz;Tjark Vredeveld
Affiliations:
Institut für Mathematik, Technische Universität Berlin, Berlin, Germany;Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands;Department Optimization, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany
Venue:
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Year:
2004

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Abstract

We consider a non-preemptive, stochastic parallel machine scheduling model with the goal to minimize the weighted completion times of jobs. In contrast to the classical stochastic model where jobs with their processing time distributions are known beforehand, we assume that jobs appear one by one, and every job must be assigned to a machine online. We propose a simple online scheduling policy for that model, and prove a performance guarantee that matches the currently best known performance guarantee for stochastic parallel machine scheduling. For the more general model with job release dates we derive an analogous result, and for NBUE distributed processing times we even improve upon the previously best known performance guarantee for stochastic parallel machine scheduling. Moreover, we derive some lower bounds on approximation.