空竭服务多级适应性休假Geom^X/G/1排队系统分析

Analysis of Geom^X/G/1 queueing system with exhaustive service discipline and adptive multi-stage vacations

在空竭服务多级适应性休假Geom/G/1型排队系统的基础上,讨论空竭服务多级适应性休假GeomX /G/1型排队系统的稳态队长.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,结果表明系统队长存在随机分解,而且附加队长有明确的概率意义.

Based on the Geom/G/1 queueing system with exhaustive service discipline and adptive multistage vacations, the queue length of the Geom^X/G/1 queueing system with exhaustive service discipline and adptive multi-stage vacations is discussed. By means of imbedded Markov chains, the PGF of the system size in steady state is obtained. It shows that the system size can be decomposed into two random variables and the addition queue length has definite probability singnificance.