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STOCHASTIC OPTIMAL DYNAMIC CONTROL OF GIm/GIm/1n QUEUES WITH TIME-VARYING WORKLOADS

Published online by Cambridge University Press:  19 May 2016

Yingdong Lu ,
Mayank Sharma ,
Mark S. Squillante  and
Bo Zhang
Yingdong Lu
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Mayank Sharma
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Mark S. Squillante
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Bo Zhang
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
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Abstract

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Motivated by applications in areas such as cloud computing and information technology services, we consider GI/GI/1 queueing systems under workloads (arrival and service processes) that vary according to one discrete time scale and under controls (server capacity) that vary according to another discrete time scale. We take a stochastic optimal control approach and formulate the corresponding optimal dynamic control problem as a stochastic dynamic program. Under general assumptions for the queueing system, we derive structural properties for the optimal dynamic control policy, establishing that the optimal policy can be obtained through a sequence of convex programs. We also derive fluid and diffusion approximations for the problem and propose analytical and computational approaches in these settings. Computational experiments demonstrate the benefits of our theoretical results over standard heuristics.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 3: Erol Gelenbe's 70th Birthday , July 2016 , pp. 470 - 491
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

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