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Sojourn time distribution in some processor-shared queues

Published online by Cambridge University Press:  26 September 2008

Xiaoming Tan  and
Charles Knessl
Xiaoming Tan
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (M/C 249), PO Box 4348, Chicago, IL 60680, USA
Charles Knessl
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (M/C 249), PO Box 4348, Chicago, IL 60680, USA
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Abstract

We develop a technique for obtaining asymptotic properties of the sojourn time distribution in processor-sharing queues. We treat the standard M/M/1-PS queue and its finite capacity version, the M/M/1/K-PS queue. Using perturbation methods, we construct asymptotic expansions for the distribution of a tagged customer's sojourn time, conditioned on that customer's total required service. The asymptotic limit assumes that (i) the traffic intensity is close to one for the infinite capacity model, and (ii) that the system's capacity is large for the finite capacity queue.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 4 , December 1993 , pp. 437 - 448
Copyright
Copyright © Cambridge University Press 1993

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