带休假延迟和休假可中止的Geom/Geom/1排队

本文研究了一个带有休假延迟和休假可中止的Geom/Geom/1排队系统。当服务台结束对一个顾客服务而使系统变空时并不是立即开始工作休假，而是进入一个为休假做准备的空闲期，称之为延迟休假期。如果在这个延迟休假期内没有顾客到达，服务台才进入工作休假。在这个模型中，工作休假是可中止的。利用拟生灭过程和矩阵几何解方法，我们给出了稳态下队长的分布和队长的概率母函数。此外，我们也得到了队长和逗留时间的随机分解结构及附加队长和附加延迟的分布。

The Geom/Geom/1 Queue with Delayed Vacation and Vacation Interruptions

In this paper, we study a Geom/Geom/1 queue with delayed vacation and vacation interruptions. Even if the server has completed all customers, it does not immediately enter working vacation. Only when there are no customers during the delayed vacation, the server begins a working vacation. We also introduce vacation interruption policy during the working vacation. Using quasi-birth-and-death process and matrix-geometric solution method, we give the steady-state distributions for queue length and the probability generating function. Then we gain the stochastic decomposition structure of queue length and sojourn time in the stationary state and obtain the distributions for additional queue length and additional delay time.