Modelling and dynamic behaviour analysis of the software rejuvenation system with periodic impulse

Software rejuvenation is a policy to counter the phenomenon of software ageing. However, how to implement software rejuvenation is still an important issue. In this paper, periodic impulse control is proposed as an effective tool to perform software rejuvenation and improve the availability of software system. First, we formulate the software rejuvenation system with periodic impulse by a group of coupled differential equations with impulsive action. Then the well-posedness of the system is demonstrated by using operator semigroup theory. At the end of the paper, numerical examples are shown to illustrate the dynamic behaviour of the system and the relationship between the system instantaneous availability and the impulsive indexes, including impulse interval and impulse strength, which yields that the system availability can be improved by adjusting the impulsive indexes.