Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman
| Autor: | Tursunjan Keyim, Abdukerim Haji |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Resolvent set
Semigroup 010102 general mathematics Mathematical analysis Zero (complex analysis) 01 natural sciences 010305 fluids & plasmas Operator (computer programming) Exponential stability 0103 physical sciences Irreducibility 0101 mathematics C0-semigroup Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Applied Mathematics and Physics. :185-193 |
| ISSN: | 2327-4379 2327-4352 |
| DOI: | 10.4236/jamp.2017.51018 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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