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

Xing Qiao | Zendy; Dan Ma | Zendy; Fu Zheng | Zendy; Guangtian Zhu | Zendy

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

Author(s) -

Xing Qiao,

Dan Ma,

Fu Zheng,

Guangtian Zhu

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/131076

Subject(s) - eigenvalues and eigenvectors , stability (learning theory) , operator (biology) , series (stratigraphy) , computer science , algorithm , reliability (semiconductor) , mathematics , software , semigroup , discrete mathematics , machine learning , thermodynamics , chemistry , physics , paleontology , biochemistry , power (physics) , repressor , quantum mechanics , biology , transcription factor , gene , programming language

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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