Asymptotic Expansions for the Conditional Sojourn Time Distribution in the $M/M/1$-PS Queue

Details Asymptotic Expansions for the Conditional Sojourn Time Distribution in the $M/M/1$-PS Queue Asymptotic Expansions for the Conditional Sojourn Time Distribution in the $M/M/1$-PS Queue

2009-07-16

arxiv.org/abs/0907.2910v1

Queueing Syst 57 (2007) 157-168

Mathematics

Classical Analysis and ODEs

30 pages, 3 figures and 1 table

Scientific paper

10.1007/s11134-007-9054-5

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 \cite{MO} and Flatto \cite{FL}.

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