Year: 2003
Type: preprint
Abstract: In this paper we study the maximum queue length $M$ (in terms of the number of customers present) in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy-tailed) service-time distributions the Foreground Background service discipline is optimal. This discipline gives service to the customer(s) that have received the least amount of service so far. It is shown that under this discipline $M$ has an exponentially decreasing tail. From the behaviour of $M$ we obtain asymptotics of the maximum queue length $M(t)$ over the interval $(0,t)$ for $t\to\infty$. These are applied to calculate the time to overflow of a buffer, both in stable and unstable queues.
Source: arXiv (Cornell University)
Author: Nuyens, Misja
Institution: University of Amsterdam
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W116424401