软件再生系统解的渐近稳定性分析

The Asymptotic Stability of the Solution of Software Rejuvenation System

用补充变量的方法建立了各状态之间转移概率服从一般分布的软件再生系统的数学模型 .并用泛函分析中的 C0 半群理论对系统算子的谱点分布情况作了研究 ,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除 0点外均为系统算子的正则点 ,作为线性算子半群稳定性的一个直接结果 。

With the well known method of supplementary variables, this paper establishes the mathematical model of the rejuvenation software systems which ″life time″ of each state follows general distribution, and then studies the asymptotic behavior of such systems. By the positive C 0semigroup which is generated by the the operator A determined by the rejuvenation software system, we show that the steady nonnegative solution of the system which is just the normalized eigenvector of A corresponding to eigenvalue 0. By spectral analysis of A, we prove that all spectrum of A lie in the left half plane and there is no spectrum on the imaginary axis except 0. As a result of the stability of semigroup theory of linear operators, we get the asymptotic stability of rejuvenation software systems.