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Approximately optimal scheduling of an M/G/1 queue with heavy tails

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Abstract

Distributions with a heavy tail are difficult to estimate. If the design of an optimal scheduling policy is sensitive to the details of heavy tail distributions of the service times, an approximately optimal solution is difficult to obtain. This paper shows that the mean optimal scheduling of an M/G/1 queue with heavy tailed service times does not present this difficulty and that an approximately optimal strategy can be derived by truncating the distributions.

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Notes

  1. If \(X\) denotes the service time, then the distribution satisfies NBUE if \(E(X)>E[X-s\mid X>s]\) for any \(s>0\).

  2. An analogous index-based optimal policy was derived for the more general case of a multi-class M/G/1 queue, but considering only non-preemptive policies, in the seminal work by Klimov; see [9] and [10].

  3. Recently, [4] gave a remarkable characterization of the Gittins index policy for the queue with no arrivals, where they showed that the optimal policy belongs to the class of multi-level processor sharing disciplines; see [1].

  4. Using arguments similar to those in [5] it is easy to show that this result would not hold for non-preemptive policies (where preemption is only allowed when a high-priority job arrives).

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Acknowledgments

This work is supported by MURI Grant BAA 07-036.18

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  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, 94720, USA

    Vijay Kamble & Jean Walrand

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  1. Vijay Kamble
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  2. Jean Walrand
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Correspondence to Vijay Kamble.

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Kamble, V., Walrand, J. Approximately optimal scheduling of an M/G/1 queue with heavy tails. Queueing Syst 80, 261–271 (2015). https://doi.org/10.1007/s11134-015-9435-0

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  • DOI: https://doi.org/10.1007/s11134-015-9435-0

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