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

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

arXiv comment30 pages, 3 figures and 1 table

Cited by in corpus (3)

• On a Processor Sharing Queue That Models Balking
• On Sojourn Times in the $M/M/1$-PS Model, Conditioned on the Number of Other Users
• Asymptotic Expansions for the Sojourn Time Distribution in the $M/G/1$-PS Queue