Author(s)

Tursunjan Keyim, Abdukerim Haji

College of Mathematics and System Sciences, Xinjiang University, Urumqi, China.

We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

Series-Parallel Repairable System, C₀-Semigroup, Irreducibility, Asymptotic Stability

Keyim, T. and Haji, A. (2017) Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman. Journal of Applied Mathematics and Physics, 5, 185-193. doi: 10.4236/jamp.2017.51018.