Dynamic Analysis of the Software Rejuvenation System with Degradation Levels

A preemptive rollback policy called software rejuvenation, as an effective tool to improve the performance of the software system, has been widely discussed on the premise that all states of the system follow the exponential distribution. However, the research on the software rejuvenation system with nonexponential repair time is very limited. This paper aims to study the dynamic behavior and evaluation index of the software rejuvenation system with general repair time. Firstly, we establish a software rejuvenation system by assigning a performance capacity level in each of the possible states, and formulate the system with an abstract Cauchy problem. Then the well-posedness of the system is proved by using cofinal theory and analyzing the spectral distribution of the system operators, and the expression of the system overall performance capacity as an important evaluation index is also given. In addition, an approximate system is constructed and the dynamical solution of the software rejuvenation system is obtained as the limit of the approximate system dynamical solution. At last, numerical examples are presented to illustrate dynamic behavior of the system and the influence of the the evaluation index on the rejuvenation strategy.