On Sojourn Times in the Finite Capacity $M/M/1$ Queue with Processor Sharing

Abstract

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.

10 pages

Cited by in corpus (2)

• On Sojourn Times in the $M/M/1$-PS Model, Conditioned on the Number of Other Users
• Asymptotic Analysis of Spectral Properties of Finite Capacity Processor Shared Queues