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Law of Large Number Limits of Limited Processor-Sharing Queues

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, and Centrum voor Wiskunde en Informatica, 1098SJ, Amsterdam, The Netherlands
jrz{at}gatech.edu
dai{at}gatech.edu
bertzwart{at}gatech.edu

Motivated by applications in computer and communication systems, we consider a processor-sharing queue where the number of jobs served is not larger than K. We propose a measure-valued fluid model for this limited processor-sharing queue and show that there exists a unique associated fluid model solution. In addition, we show that this fluid model arises as the limit of a sequence of appropriately scaled processor-sharing queues.

Key Words: limited processor sharing; measure-valued process; fluid model; invariant manifold; convolution equation
History: Received: December 4, 2007; revision received: May 21, 2009;