TITLE:
Asymptotic Stability of Gaver’s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations
AUTHORS:
Abdukerim Haji
KEYWORDS:
Gaver’s Parallel Pystem, C0-Semigroup, Irreducibility, Asymptotic Stability
JOURNAL NAME:
World Journal of Engineering and Technology,
Vol.3 No.3C,
October
23,
2015
ABSTRACT:
We investigate Gaver’s parallel system
attended by a cold standby unit and a repairman with multiple vacations. 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 converges strongly to the steady state solution. Thus
we obtain asymptotic stability of the dynamic solution of the system.