Law of Large Number Limits of Limited Processor-Sharing Queues

Authors:
Jiheng Zhang;J. G. Dai;Bert Zwart
Affiliations:
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, 1098 SJ Amsterdam, The Netherland ...
Venue:
Mathematics of Operations Research
Year:
2009

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Abstract

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.