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PROPERTIES OF THE GITTINS INDEX WITH APPLICATION TO OPTIMAL SCHEDULING

Published online by Cambridge University Press:  17 May 2011

Samuli Aalto ,
Urtzi Ayesta  and
Rhonda Righter
Samuli Aalto
Affiliation:
Aalto University, Espoo, Finland E-mail: samuli.aalto@tkk.fi
Urtzi Ayesta
Affiliation:
Basque Center for Applied Mathematics, Derio, Spain, and Basque Foundation for Science, Derio, Spain E-mail: ayesta@bcamath.org
Rhonda Righter
Affiliation:
University of California at Berkeley, Berkeley, CA E-mail: rrighter@ieor.berkeley.edu
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Abstract

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We consider the optimal scheduling problem for a single-server queue without arrivals. We allow preemptions, and our purpose is to minimize the expected flow time. The optimal nonanticipating discipline is known to be the Gittins index policy, which, however, is defined in an implicit way. Until now, its general behavior in this specific problem has been characterized only in a few special cases. In this article, we give as complete a characterization as possible. It turns out that the optimal policy always belongs to the family of multilevel processor sharing disciplines.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 3 , July 2011 , pp. 269 - 288
Copyright
Copyright © Cambridge University Press 2011

References

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