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Heavy traffic asymptotics of the queue length in the GI/M/l – K queue

Published online by Cambridge University Press:  26 September 2008

Yongzhi Yang  and
Charles Knessl
Yongzhi Yang
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (M/C 249), 851 South Morgan Street, Chicago, IL 60607-7045, USA
Charles Knessl*
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (M/C 249), 851 South Morgan Street, Chicago, IL 60607-7045, USA
*
* For Correspondence.
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Abstract

We consider the GI/M/1 – K queue which has a capacity of K customers. Using singular perturbation methods, we construct asymptotic approximations to the stationary queue length distribution. We assume that K is large and treat several different parameter regimes. Extensive numerical comparisons are used to show the quality of the proposed approximations.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 5 , October 1996 , pp. 519 - 543
Copyright
Copyright © Cambridge University Press 1996

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