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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 809460, 9 pages
http://dx.doi.org/10.1155/2013/809460
Research Article

Several Types of Convergence Rates of the M/G/1 Queueing System

1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
2School of Science, North China University of Technology, Beijing 100144, China

Received 25 October 2012; Accepted 31 December 2012

Academic Editor: Xiaochen Sun

Copyright © 2013 Xiaohua Li and Jungang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the workload process of the M/G/1 queueing system. Firstly, we give the explicit criteria for the geometric rate of convergence and the geometric decay of stationary tail. And the parameters and for the geometric rate of convergence and the geometric decay of the stationary tail are obtained, respectively. Then, we give the explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases. And we give the parameters and of the rate of convergence and the decay of the stationary tail, respectively, for the subgeometric rate , , .