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中文摘要：
近几年来,由于在制造系统与电讯交换系统的设计和控制中和在计算机通信网络的模型刻画和分析中的广泛应用,使得离散时间排队系统受到越来越多的注意.本文考虑离散时间多重休假成批到达的Geom/G/1排队系统,从任意初始状态出发,使用全概率分解技术和u-变换,研究了队长的瞬态性质和稳态性质,首次导出了队长瞬态分布的u-变换形式的递推表达式和队长稳态分布的递推表达式,进一步也获得稳态队长的随机分解结果.特别地,通过本文可直接获得一系列特殊离散时间排队系统相应的结果.
英文摘要：
Recent years, discrete time queueing systems have been receiving attention due to their wide applications in design and control of manufacturing and teleconmunication systems, and in modeling and analyzing of computer communication networks. In this paper we consider the discrete time Geom/G/1 queue with multiple vacations and bulk arrival. By using the total probability decomposition technique and u-transform, we discuss the transient and equilibrium distributions of the queue length with the beginning of the any initial state,and obtain the recursion expressions of the u-transform for the transient queue length distribution and the steady queue length distribution. Furthermore, we also obtain the stochastic decomposition of the queue length at a random point in equilibrium. Especially we can obtain some correspooding results under some especial cases.
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