A blind policy for equalizing cumulative idleness

Rami Atar; Yair Y. Shaki; Adam Shwartz

doi:10.1007/s11134-011-9212-7

A blind policy for equalizing cumulative idleness

Rami Atar, Yair Y. Shaki, Adam Shwartz

Technion-Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We consider a system with a single queue and multiple server pools of heterogeneous exponential servers. The system operates under a policy that always routes a job to the pool with longest cumulative idleness among pools with available servers, in an attempt to achieve fairness toward servers. It is easy to find examples of a system with a fixed number of servers, for which fairness is not achieved by this policy in any reasonable sense. Our main result shows that in the many-server regime of Halfin and Whitt, the policy does attain equalization of cumulative idleness, and that the equalization time, defined within any given precision level, remains bounded in the limit. An important feature of this policy is that it acts 'blindly', in that it requires no information on the service or arrival rates.

Original language	English
Pages (from-to)	275-293
Number of pages	19
Journal	Queueing Systems
Volume	67
Issue number	4
DOIs	https://doi.org/10.1007/s11134-011-9212-7
State	Published - Apr 2011
Externally published	Yes

Bibliographical note

Funding Information:
Research supported in part by BSF (Grant 2008466), ISF (Grant 1349/08) and the fund for promotion of research at the Technion. Research supported in part by BSF (Grant 2008466), ISF (Grant 1349/08) and the Viterbi Postdoctoral Fellowship. The Julius M. and Bernice Neiman Chair in Engineering. Research supported in part by BSF (Grant 2008466) and the fund for promotion of research at the Technion.

Funding

Research supported in part by BSF (Grant 2008466), ISF (Grant 1349/08) and the fund for promotion of research at the Technion. Research supported in part by BSF (Grant 2008466), ISF (Grant 1349/08) and the Viterbi Postdoctoral Fellowship. The Julius M. and Bernice Neiman Chair in Engineering. Research supported in part by BSF (Grant 2008466) and the fund for promotion of research at the Technion.

Funders	Funder number
United States-Israel Binational Science Foundation	2008466
Israel Science Foundation	1349/08
Technion-Israel Institute of Technology

Keywords

Blind control
Diffusion limits
Fairness
Halfin-Whitt regime
Many-server systems

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10.1007/s11134-011-9212-7

Cite this

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N2 - We consider a system with a single queue and multiple server pools of heterogeneous exponential servers. The system operates under a policy that always routes a job to the pool with longest cumulative idleness among pools with available servers, in an attempt to achieve fairness toward servers. It is easy to find examples of a system with a fixed number of servers, for which fairness is not achieved by this policy in any reasonable sense. Our main result shows that in the many-server regime of Halfin and Whitt, the policy does attain equalization of cumulative idleness, and that the equalization time, defined within any given precision level, remains bounded in the limit. An important feature of this policy is that it acts 'blindly', in that it requires no information on the service or arrival rates.

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A blind policy for equalizing cumulative idleness

Abstract

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Keywords

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