Asymptotic expansions for the conditional sojourn time distribution in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/1-PS queue |
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Authors: | Qiang Zhen Charles Knessl |
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Institution: | (1) Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA |
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Abstract: | We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer’s service
requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where
the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results
of Morrison (SIAM J. Appl. Math. 45:152–167, 1985]) and Flatto (Ann. Appl. Probab. 7:382–409, 1997]).
This work was partly supported by NSF grant DMS 05-03745. |
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Keywords: | Processor sharing Asymptotics Sojourn time M/M/1 queue |
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