Dynamic Analysis of Software Systems with Aperiodic Impulse Rejuvenation

Huixia Huo, Houbao Xu and Zhuoqian Chen
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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

Mathematics, 2022, vol. 10, issue 2, 1-13

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.

Keywords: software systems; dynamical solution; instantaneous availability; Trotter–Kato theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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