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Queueing Syst (2011) 67: 275293 DOI 10.1007/s11134-011-9212-7

Summary: Queueing Syst (2011) 67: 275­293
DOI 10.1007/s11134-011-9212-7
A blind policy for equalizing cumulative idleness
Rami Atar · Yair Y. Shaki · Adam Shwartz
Received: 1 May 2010 / Revised: 12 December 2010 / Published online: 9 February 2011
© Springer Science+Business Media, LLC 2011
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.
Keywords Blind control · Diffusion limits · Halfin­Whitt regime · Fairness ·
Many-server systems
Mathematics Subject Classification (2000) 68M20 · 60F17 · 93E99
1 Introduction


Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology


Collections: Engineering