%0 Journal Article
%T On Sojourn Times in the Finite Capacity $M/M/1$ Queue with Processor Sharing
%A Qiang Zhen
%A Charles Knessl
%J Mathematics
%D 2009
%I arXiv
%R 10.1016/j.orl.2009.09.007
%X We consider a processor shared $M/M/1$ queue that can accommodate at most a finite number $K$ of customers. We give an exact expression for the sojourn time distribution in the finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit $K\to\infty$, by locating the dominant singularity of the Laplace transform.
%U http://arxiv.org/abs/0907.2908v1