| 摘要: |
| 本文研究了一类具有两种故障状态的M/M/1可修排队系统时间依赖解的渐进性质问题.利用概率母函数证明了0是该系统主算子及其共轭算子几何重数为1的特征值.基于一定的约束条件下,获得了系统的时间依赖解强收敛于该系统的稳态解.推广了该排队系统动态分析的有关结论. |
| 关键词: 具有两种故障状态的M/M/1可修排队系统 共轭算子 几何重数 特征值 |
| DOI： |
| 分类号:O177.7 |
| 基金项目:国家社会科学基金资助(24XTJ003). |
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| AN EIGENVALUE OF THE REPAIRABLE M/M/1 QUEUEING SYSTEM WITH TWO KINDS OF BREAKDOWN STATES AND ITS APPLICATION |
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ZHOU Xue-liang1,2, ZHANG Qing-hong2
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1.School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, China;2.Ministry of Public Infrastructure, Xinjiang Light Industry Vocational and Technical College, Urumqi 830021, China
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| Abstract: |
| The asymptotic property of the time-dependent solution corresponding to a repairable M/M/1 queueing system with two kinds of breakdown states has been studied. We prove that 0 is an eigenvalue of the main operator and its conjugate operator with geometric multiplicity one corresponding to the queueing system by using the probability generating function. Based on certain constraints, the time-dependent solution of the system strongly converges to the steady-state solution of the system is obtained. Some conclusions of the dynamic analysis of the queuing system are extended. |
| Key words: the repairable queueing system with two kinds of breakdown states adjoint operator geometric multiplicity eigenvalue |
