导　　师： 刘再明

学科专业： 070103

授予学位： 博士

作　　者： ;

机构地区： 中南大学

摘　　要： 本篇博士学位论文研究了几类复杂的排队系统.这些排队系统主要包括G-排队系统、重试排队系统、休假排队系统、可修排队系统、离散时间排队系统、马尔可夫到达排队系统及其混合.全文由如下七部分组成. 第一章是绪论,简要地介绍了排队论的历史背景、研究内容、发展现状以及本文所做的主要工作和主要的创新点. 第二章分析了一个具有非空竭服务随机休假策略的M／G／1重试可修G-排队系统.正、负顾客的到达服从两个独立的泊松过程.其中负顾客的到达不仅移除一个正在服务的顾客,而且致使服务台损坏.服务台采取随机休假策略,即服务台的工作时间服从指数分布.休假时间和修理时间均服从任意分布.我们发展了一个新方法,即通过构造一个具有吸收态的马尔可夫链且利用经典M／G／1排队系统的稳态条件求得了该系统稳态存在的充分必要条件.利用补充变量方法建立了系统的稳态方程组,然后利用取母函数得到了系统状态和重试组中顾客数联合分布的概率母函数,进而求得了系统在稳态下的一系列重要的排队性能指标.而后,我们对系统进行可靠性分析.通过将服务台发生故障视为马尔可夫链的吸收状态,构造了一个新的排队系统,由此得到了一些重要的可靠性指标.此外,我们还分析了系统的忙期和一些有趣的特例.最后,我们还给出了几个数值实例来说明某些参数对系统性能指标的影响. 第三章研究了一个具有不耐烦顾客、灾难、N策略休假和反馈机制的MX／G／1重试可修G-排队系统.利用Foster准则和Kaplan条件得到了系统稳态存在的充分必要条件.利用补充变量法,建立了系统稳态时的平衡方程组.通过求解这些方程,得到了系统状态和重试组中顾客数联合分布的概率母函数.进而求得了系统在稳态下的一系列重要的排队性能指标.而后,我们� In this Ph.D. thesis, we investigate several classes of complex queueing systems which include G-queueing systems, retrial queueing systems, vacation queueing systems, discrete-time queueing systems, Markov arrival queueing systems and their mixture. This Ph.D. thesis is organized as follows. Chapter 1 is preface. The historical background, the subject, the recent develop-ment of queueing theory and the main results and innovative contributions of this thesis are introduced. In Chapter 2, we analyze an M//G//1 retrial queue with negative customers and non-exhaustive vacations subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. A breakdown at the busy server is represented by the arrival of a negative customer which causes the the customer being in service to be lost. The server takes a vacation of random length after an exponential time when the server is up. It is assumed that the server has arbitrary repair time and vacation time distributions. We develop a new method to discuss the stable condition by finding absorb distribution and using the stable condition of classical M//G//1 queue. By applying the supplementary variables method, we obtain the system of equilibrium equations. By taking generating functions of these equations, we derived the solutions for queueing measures. Furthermore, we analyze the system reliability by regarding a new queueing system where the failure states of the server are assumed to be absorbent states. We also analyze the busy period of the system. Some special cases of interest are discussed and some known results have been derived. The effects of various parameters on the system performance are analyzed numerically. In Chapter 3, we discuss an MX//G//1 retrial queue with impatient customers and feedback under N-policy vacation schedule subject to disastrous failures at which times all customers in the system are lost. The necessary and sufficient condition for the stability

关 键 词： 排队论 可靠性理论 随机运筹学 马尔可夫过程 性能评估

领　　域： [理学] [理学]