Journal of Applied Mathematics

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

Xing Qiao, Dan Ma, Fu Zheng, and Guangtian Zhu

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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 c0 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.

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J. Appl. Math., Volume 2013 (2013), Article ID 131076, 9 pages.

First available in Project Euclid: 14 March 2014

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Qiao, Xing; Ma, Dan; Zheng, Fu; Zhu, Guangtian. The Well-Posedness and Stability Analysis of a Computer Series System. J. Appl. Math. 2013 (2013), Article ID 131076, 9 pages. doi:10.1155/2013/131076.

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