On sojourn times in the finite capacity M/M/1 queue with processor sharing

Authors:
Qiang Zhen;Charles Knessl
Affiliations:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S Morgan St(M/C 249), Chicago, IL 60607, USA;Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S Morgan St(M/C 249), Chicago, IL 60607, USA
Venue:
Operations Research Letters
Year:
2009

Citing 4
Cited 0

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On the sojourn time distribution in a finite capacity processor shared queue

Journal of the ACM (JACM)
Waiting Time Distributions for Processor-Sharing Systems

Journal of the ACM (JACM)
The equivalence between processor sharing and service in random order

Operations Research Letters

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Abstract

We consider a processor shared M/M/1 queue that can accommodate at most a finite number K of customers. We give an exact expression for the sojourn time distribution in this finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit K-~.