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| 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. 从而在一定约束条件下, 推出该排队系统的时间依赖解强收敛于该系统的稳态解. |
| 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 liang
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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. Thus, under a certain constraints, we obtain that the time-dependent solution of this model converges strongly to its steady-state solution. |
| Key words: the repairable queueing system with two kinds of breakdown states adjoint operator geometric multiplicity eigenvalue |
