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

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Listed:
  • Xing Qiao
  • Dan Ma
  • Fu Zheng
  • Guangtian Zhu

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 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.

Suggested Citation

  • Xing Qiao & Dan Ma & Fu Zheng & Guangtian Zhu, 2013. "The Well‐Posedness and Stability Analysis of a Computer Series System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:131076
    DOI: 10.1155/2013/131076
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    References listed on IDEAS

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    1. Zhang, Yuan Lin & Wang, Guan Jun, 2007. "A deteriorating cold standby repairable system with priority in use," European Journal of Operational Research, Elsevier, vol. 183(1), pages 278-295, November.
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