【摘要】 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<θ1)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.更多还原

【Abstract】 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,we present some corresponding results and numerical examples under special cases.更多还原