Is Tail-Optimal Scheduling Possible?
This paper focuses on the competitive analysis of scheduling disciplines in a large deviations setting. Although there are policies that are known to optimize the sojourn time tail under a large class of heavy-tailed job sizes (e.g., processor sharing and shortest remaining processing time) and there are policies known to optimize the sojourn time tail in the case of light-tailed job sizes (e.g., first come first served), no policies are known that can optimize the sojourn time tail across both light- and heavy-tailed job size distributions. We prove that no such work-conserving, nonanticipatory, nonlearning policy exists, and thus that a policy must learn (or know) the job size distribution in order to optimize the sojourn time tail.
© 2012 INFORMS. Received August 2009; revisions received April 2011, February 2012; accepted April 2012. Published online in Articles in Advance October 9, 2012. Adam Wierman's research is partly supported by the National Science Foundation Computing and Communication Foundations [Grant 0830511], Microsoft Research, and the Okawa Foundation. Bert Zwart's research is partly supported by the National Science Foundation [Grants 0727400 and 0805979], an IBM faculty award, and a VIDI grant from the Netherlands Organisation for Scientific Research.
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