基于马尔可夫骨架过程理论的最小队长排队系统

【作者】 李明；

【导师】 侯振挺；

【作者基本信息】 中南大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 最小队长排队系统是排队论中一类重要的排队模型,此模型已经应用到信息通讯中的码分多址(CDMA)蜂窝系统.本论文应用由侯振挺等人所创立的马尔可夫骨架过程这一新的理论工具研究了此类排队模型,此论文的内容和主要结果如下:第一章概述了排队论研究的历史和现状,同时列出了论文的结构及主要结果.第二章介绍了马尔可夫骨架过程理论,包括马尔可夫骨架过程的概念、向后和向前方程、极限分布等.第三章研究了M/(G/1)~2型最小队长排队系统,得到此类排队模型队长的瞬时分布和极限分布,并证明了它的瞬时分布是一个向后方程的最小非负解.第四章分析了GI/(M/1)~2型最小队长排队系统,得到此类排队模型队长的瞬时分布和极限分布,同时证明了它的瞬时分布是一个向后方程的最小非负解.第五章研究了GI/(G/1)~2型最小队长排队系统,得到此类排队模型队长的瞬时分布和极限分布,并证明了它的瞬时分布是一个向后方程的最小非负解.更多还原

【Abstract】 The shortest queueing system is one of the important class models in queueing theory, this model has been applied to information and communication in Code Division Multiple Access (CDMA) cellular systems.In this thesis ,apply with the theory of Markov skeleton process ,which is a new theory tools establised by Hou Zhenting etal,to study the shortest queueing system.The content and main result of the thesis as follows:In chapter 1, the queuing theory research history and the present situation are outlined ,simultaneously has listed the thesis structure and the main result.In chapter 2,the preliminary knowledge of Markov skeleton process are introduced, including the concept of Markov skeleton process, backward and forward equation, limit distribution, and other important elements.In chapter 3,study the M/(G/1)~2 type shortest queueing system and the transient distribution and the limit distribution of the queue length of the types queueing model are obtained and prove that the transient distribution is the minimal nonnegative solution of the backward equation.In chapter 4,analysis the GI/(M/1)~2 type shortest queueing system and the transient distribution and the limit distribution of the queue length of the types queueing model are obtained and prove that the transient distribution is the minimal nonnegative solution of the backward equation.In chapter 5,study the GI/(G/1)~2 type shortest queueing system, the transient distribution and the limit distribution of the queue length of the types queueing model are obtained and prove that the transient distribution is the minimal nonnegative solution of the backward equation.更多还原