Asymptotic Stability of the Gnedenko System with Multiple Delay Vacations of a Repairman

Abstract

We investigate the Gnedenko system with multiple delay vacations of a repairman. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution of the system converges strongly to its steady state solution. Thus we prove asymptotic stability of the dynamic solution of the system.