Journal of Applied Mathematics and Physics

Volume 5, Issue 1 (January 2017)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.63  Citations  

Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

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DOI: 10.4236/jamp.2017.51018    915 Downloads   1,222 Views  

ABSTRACT

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.

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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.

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