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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 890243, 16 pages
http://dx.doi.org/10.1155/2012/890243
Research Article

Further Research on the M/G/1 Retrial Queueing Model with Server Breakdowns

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Received 13 March 2012; Accepted 28 June 2012

Academic Editor: Song Cen

Copyright © 2012 Ehmet Kasim and Geni Gupur. 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 spectral properties of the operator which corresponds to the M/G/1 retrial queueing model with server breakdowns and obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator and 0 is not an eigenvalue of the operator. Our results show that the time-dependent solution of the model is probably strongly asymptotically stable.