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Fluid Limits for Processor-Sharing Queues with Impatience

Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903, USA
INRIA-Rocquencourt, RAP Project, Domaine de Voluceau, BP 105, 78153 Le Chesnay, France
Georgia Institute of Technology, Stewart School of ISyE, 765 Ferst Drive, Atlanta, Georgia 30332, USA
gromoll{at}virginia.edu, http://www.faculty.virginia.edu/gromoll/
Philippe.Robert{at}inria.fr, http://www-rocq.inria.fr/robert
bertzwart{at}gatech.edu

We investigate a processor-sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue or renege before completing service. The random time representing a job's patience has a general distribution and may be dependent on its initial service time requirement. A scaling procedure that gives rise to a fluid model with nontrivial yet tractable steady state behavior is presented. This fluid model captures many essential features of the underlying stochastic model, and it is used to analyze the impact of impatience in processor-sharing queues.

Key Words: processor sharing; queues with impatience; measure-valued process; fluid limits; delay-differential equations; empirical processes
History: Received: April 5, 2006; revision received: August 30, 2007;

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