The Well-Posedness and Stability Analysis of a Computer Series System
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 nonn...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/131076 |
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| _version_ | 1832564181507768320 |
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| author | Xing Qiao Dan Ma Fu Zheng Guangtian Zhu |
| author_facet | Xing Qiao Dan Ma Fu Zheng Guangtian Zhu |
| author_sort | Xing Qiao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2e2c567262154d61b6626f460cfabe30 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2e2c567262154d61b6626f460cfabe302025-02-03T01:11:34ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/131076131076The Well-Posedness and Stability Analysis of a Computer Series SystemXing Qiao0Dan Ma1Fu Zheng2Guangtian Zhu3School of Mathematical Science, Daqing Normal University, Daqing 163712, ChinaSchool of Mathematical Science, Daqing Normal University, Daqing 163712, ChinaDepartment of Mathematics, Bohai University, Jinzhou 121013, ChinaAcademy of Mathematics and System Sciences C.A.S., Beijing 100080, ChinaA 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.http://dx.doi.org/10.1155/2013/131076 |
| spellingShingle | Xing Qiao Dan Ma Fu Zheng Guangtian Zhu The Well-Posedness and Stability Analysis of a Computer Series System Journal of Applied Mathematics |
| title | The Well-Posedness and Stability Analysis of a Computer Series System |
| title_full | The Well-Posedness and Stability Analysis of a Computer Series System |
| title_fullStr | The Well-Posedness and Stability Analysis of a Computer Series System |
| title_full_unstemmed | The Well-Posedness and Stability Analysis of a Computer Series System |
| title_short | The Well-Posedness and Stability Analysis of a Computer Series System |
| title_sort | well posedness and stability analysis of a computer series system |
| url | http://dx.doi.org/10.1155/2013/131076 |
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