本文考虑多重休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率θ(0＜θ≤1)进入系统.通过引入"服务员忙期"和使用全概率分解技术,讨论了队长的瞬时性质,得到了队长瞬时分布的z-变换的递推式,以及队长平稳分布的递推式,并且证明了稳态队长的随机分解性质.最后,给出了在特殊情形下相应的一些结果和数值计算实例.%This paper considers a discrete-time Geo/G/1 queue with exhaustive service policy and multiple vacations in which the customers enter the system with probability θ (0 ＜ θ ≤ 1) during server vacations. By introducing the “server busy period” and using the total probability decomposition technique, the transient property of the queue length is discussed. Also, we obtain the recursion formulae of the z-transform of the transient distribution and the stationary distribution for the queue length. The stochastic decomposition property of the steady-state queue length is proved. Finally, wepresent some corresponding results and numerical examples under special cases.
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