%0 Journal Article
%T Asymptotic Expansions for the Conditional Sojourn Time Distribution in the $M/M/1$-PS Queue
%A Qiang Zhen
%A Charles Knessl
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s11134-007-9054-5
%X 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}.
%U http://arxiv.org/abs/0907.2910v1