空竭服务多级适应性休假Geom^X/G(Geom/G)/1可修排队系统

Geom^X/G(Geom/G)/1 repairable queue with exhaustive service discipline and adaptive multistage vacations

在空竭服务多级适应性休假GeomX/G/1排队的基础上,讨论了空竭服务多级适应性休假GeomX/G(Geom/G)/1可修排队系统.利用嵌入马尔可夫链法,得到了稳态状态下顾客离去时刻系统队长的母函数,说明系统队长存在随机分解;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了系统的稳态可用度.

Based on the Geom^X/G/1 queueing system with exhaustive service discipline and adaptive multistage vacations, the Geom^X/G(Geom/G)/1 repairable queueing system with exhaustive service discipline and adaptive multistage vacations are considered. By means of imbedded Markov chains, in the steady state, the PGF of the system size is obtained. It shows that the system size can be decomposed into two random variables. The stable availability of the system is also provided.