Elsevier

Systems & Control Letters

Volume 6, Issue 3, August 1985, Pages 173-180
Systems & Control Letters

K competing queues with geometric service requirements and linear costs: The μc-rule is always optimal

https://doi.org/10.1016/0167-6911(85)90037-4Get rights and content

Abstract

In this note, a discrete-time system of K competing queues with geometric service requirements and arbitrary arrival patterns is studied. When the cost per slot is linear in the queue sizes, it is shown that the μc-rule minimizes the expected discounted cost over the infinite horizon.

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This work was supported in part by the Department of Energy under Grant DOE-ACOl-78ET29244, A5 and the National Science Foundation under Grant ECS-82-04451.

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