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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 924712, 9 pages
http://dx.doi.org/10.1155/2014/924712
Research Article

On the Steady-State System Size Distribution for a Discrete-Time Geo/G/1 Repairable Queue

School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 28 September 2013; Accepted 10 February 2014; Published 19 March 2014

Academic Editor: Carlo Piccardi

Copyright © 2014 Renbin Liu and Zhaohui Deng. 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

This paper studies a discrete-time N-policy Geo/G/1 queueing system with feedback and repairable server. With a probabilistic analysis method and renewal process theory, the steady-state system size distribution is derived. Further, the steady-state system size distribution derived in this work is extremely suitable for numerical calculations. Numerical example illustrates the important application of steady-state system size distribution in system capacity design for a network access proxy system.