Asymptotic stability of software systems with rejuvenation policy

Asymptotic stability of software systems with rejuvenation policy is studied. Both partial restart and reboot from crash are considered in gradually deteriorating software systems. An integral-differential mathematical model of software systems is constructed. We show that the system operator generates a positive C-0-semigroup of contractions in the state Banach space. Moreover, 0 is an eigenvalue with algebraical multiplicity 1 and it is also a unique spectral point on the imaginary axis. As a result, the asymptotic stability of software systems is then obtained and the steady-state space of the system is spanned by the eigenfunction of eigenvalue 0.