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.
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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.
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Atar, R., Shaki, Y.Y. & Shwartz, A. A blind policy for equalizing cumulative idleness. Queueing Syst 67, 275–293 (2011). https://doi.org/10.1007/s11134-011-9212-7
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DOI: https://doi.org/10.1007/s11134-011-9212-7