离散时间多重休假的Geom^x/G/1排队系统的队长分布  

Queue-Length Distribution for Discrete Time Geom/G/1 Queue with Multiple Vacatioms and Bulk Arrival

作　　者：唐应辉[1] 黄蜀娟[2] 云曦[2] 

机构地区：[1]四川师范大学数学与软件科学学院 [2]电子科技大学应用数学学院

出　　处：《电子学报》2009年第7期1407-1411,共5页Acta Electronica Sinica

基　　金：国家自然科学基金(No.70871084);教育部高校博士点专项基金(No.200806360001)

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.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.

关 键 词：离散时间排队 成批到达 Geom/G/1 瞬态分布 稳态分布 递推表达式 

分 类 号：O226[理学—运筹学与控制论]