【作者】 殷允乐；

【导师】 王金亭；

【作者基本信息】 北京交通大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 离散时间重试排队理论是排队论中的一个重要分支.近年来,由于离散时间排队系统在数字通讯系统和网络等一些相关领域的应用越来越为广泛,更多的学者致力于离散时间排队系统的研究.许多计算机网络和互联网的运作都是以离散时间为基准的,它们内部的所有行为都是发生在一些规则的时间点上.其实研究离散时间排队理论的重要原因之一是在模拟计算机网络和通讯系统时,离散时间排队系统比其对应的连续时间排队系统更为合适,也更贴近于真实的情况.在现实生活中,离散时间排队系统已经广泛应用于模拟计算机和通信网络.在本文中我们一共分析了两个不同的离散时间重试排队系统模型.第一个模型是有不成功启动、成批到达、可控制进入的离散时间重试排队系统.第二个模型是有不成功启动、成批到达和反馈的离散时间重试排队系统.在每个模型中,我们讨论了在这个离散时间重试排队系统中的马尔可夫链以及它的遍历条件,并计算出了该系统在稳态条件下的一些参数,并说明了一些参数对重试空间平均队长的影响.另外,在一些模型中,本文还给出了两个随机分解法则,并用定理对随机分解法则做了进一步的解释.更多还原

【Abstract】 Discrete-time queueing systems with repeated customers are important branch of Queueing Theory. Recently, There is a growing interest in the analysis of discrete-time queues due to their applications in communication systems and other related areas. Many computer and communication systems operate on a discrete time basis where events can only happen at regularly spaced epochs. One of the main reasons for analysing discrete-time queues is that these systems are more appropriate than their continuous-time counterparts for modelling computer and telecommunication systems. Now discrete-time queueing systems with repeated customers has been widely used in view of their applicability in the study of many computer and communication systems in which time is slotted.In this paper, we study two queueing systems, that is, A Discrete-Time Retrial Queue with Starting Failures, Batch Arrive, Admission Control. A Discrete-Time Retrial Queue with Starting Failures, Batch Arrive and Feedback. In each model, we analyse the Markov Chain underlying the regarded queueing system and its ergodicity condition. Then, we present some performance measures of the system in steady-state. Finally, some numerical examples show the influence of the parameters on several performance characteristics. In some models, we give two stochastic decomposition laws and give the two stochastic decomposition for further explaination.更多还原