空竭服务多级适应性休假Geom^X/G(Geom/G)/1可修排队系统分析

Analysis of the Geom^X/G(Geom/G)/1 Repairable Queue with Exhaustive Service Discipline and Adaptive Multistage Vacations

本文先将空竭服务多级适应性休假GeomX/G(Geom/G)/1可修排队系统转化为一个等价的GeomX/ G/1排队系统,再利用嵌入马尔可夫链方法,得到了稳态状态下顾客离去时刻系统队长的母函数。此外,对系统的一个忙循环进行分析,使用Wald定理和离散时间更新报酬定理得到系统的稳态可用度。

In this paper, first we transform the Geom^X/G(Geom/G)/1 repairable queue with exhaustive service discipline and adaptive multistage vacations into the Geom^X//1 queue.By means of imbedded Markov chains, in the steady state, we obtain the PGF of the system size. In addition, the stable availability of the systemy is also provided.