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Dynamic Analysis of Software Systems with Aperiodic Impulse Rejuvenation

Author

Listed:
  • Huixia Huo

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Houbao Xu

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Zhuoqian Chen

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

This paper aims to obtain the dynamical solution and instantaneous availability of software systems with aperiodic impulse rejuvenation. Firstly, we formulate the generic system with a group of coupled impulsive differential equations and transform it into an abstract Cauchy problem. Then we adopt a difference scheme and establish the convergence of this scheme by applying the Trotter–Kato theorem to obtain the system’s dynamical solution. Moreover, the instantaneous availability as an important evaluation index for software systems is derived, and its range is also estimated. At last, numerical examples are shown to illustrate the validity of theoretical results.

Suggested Citation

  • Huixia Huo & Houbao Xu & Zhuoqian Chen, 2022. "Dynamic Analysis of Software Systems with Aperiodic Impulse Rejuvenation," Mathematics, MDPI, vol. 10(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:197-:d:720735
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    References listed on IDEAS

    as
    1. Houbao Xu, 2011. "Modelling and well-posed analysis for software system with rejuvenation," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(6), pages 583-600, May.
    2. Meng, Haining & Liu, Jianjun & Hei, Xinhong, 2015. "Modeling and optimizing periodically inspected software rejuvenation policy based on geometric sequences," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 184-191.
    Full references (including those not matched with items on IDEAS)

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