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Universality of load balancing schemes on the diffusion scale

Part of: Operations research and management science Special processes Computer system organization

Published online by Cambridge University Press:  09 December 2016

Debankur Mukherjee ,
Sem C. Borst ,
Johan S. H. van Leeuwaarden  and
Philip A. Whiting
Debankur Mukherjee*
Affiliation:
Eindhoven University of Technology
Sem C. Borst*
Affiliation:
Eindhoven University of Technology and Nokia Bell Labs
Johan S. H. van Leeuwaarden*
Affiliation:
Eindhoven University of Technology
Philip A. Whiting*
Affiliation:
Macquarie University
*
* Postal address: Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, Netherlands.
* Postal address: Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, Netherlands.
* Postal address: Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, Netherlands.
*** Postal address: Department of Engineering, Macquarie University, North Ryde, NSW 2109, Australia.
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Abstract

We consider a system of N parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among d randomly selected servers otherwise (1≤d≤N). This load balancing scheme subsumes the so-called join-the-idle queue policy (d=1) and the celebrated join-the-shortest queue policy (d=N) as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin‒Whitt heavy-traffic regime, and establish that it does not depend on the value of d, implying that assigning tasks to idle servers is sufficient for diffusion level optimality.

Keywords

Join-the-idle-queue policyjoin-the-shortest-queue policyload balancingpower of tworouteingsample path comparisonstochastic couplingsupermarket model

MSC classification

Primary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B18: Communication networks 90B36: Scheduling theory, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1111 - 1124
Copyright
Copyright © Applied Probability Trust 2016 

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