Journal of Applied Mathematics
Volume 2013 (2013), Article ID 131076, 9 pages
http://dx.doi.org/10.1155/2013/131076
Research Article

The Well-Posedness and Stability Analysis of a Computer Series System

Xing Qiao,1 Dan Ma,1 Fu Zheng,2 and Guangtian Zhu3

1School of Mathematical Science, Daqing Normal University, Daqing 163712, China
2Department of Mathematics, Bohai University, Jinzhou 121013, China
3Academy of Mathematics and System Sciences C.A.S., Beijing 100080, China

Received 13 August 2012; Accepted 2 April 2013

Academic Editor: Vu Phat

Copyright © 2013 Xing Qiao et al. 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

A repairable computer system model which consists of hardware and software in series is established in this paper. This study is devoted to discussing the unique existence of the solution and the stability of the studied system. In view of semigroup theory, we prove the existence of a unique nonnegative solution of the system. Then by analyzing the spectra distribution of the system operator, we deduce that the transient solution of the system strongly converges to the nonnegative steady-state solution which is the eigenvector corresponding to eigenvalue 0 of the system operator. Finally, some reliability indices of the system are provided at the end of the paper with a new method.