摘要在某些排队系统里，有的“顾客”类必须优先获得服务，这就是带有优先权的排队模型。人们已经对这种带优先权的模型进行了深入的研究并将其应用到实际生活中，例如临保期食品的销售，计算机的数据传输，通信协议等等。就目前而言，大多数对排队论的研究都是基于单服务台模型，然而我们在现实生活中见到的更多的则是多服务台模型，因此通过研究排队系统，将其方法平行推广到排队系统有着极其重要的意义。86486

本文研究了带有强占优先权的受控排队系统，首先，文章的开头阐述了排队论的研究现状、研究什么、为什么要研究以及优先权的发展背景；其次，第二部分介绍了排队论中常见的模型，例如有（无）限源的排队系统、带有强占优先权的排队系统、带有负顾客的排队系统和带有反馈优先权的排队系统，并给出了常用的分析方法，如嵌入马尔可夫链、生灭过程以及其衍生出来的拟生灭过程法。最后一部分针对具体的带有强占优先权的受控排队系统，借助矩阵分析法完成对两类信元的求解，接着通过合理假设参数的数值，用一个具体的例子证明了算法的有效性，并合理推断出该方法可平行推广到排队系统中。

毕业论文关键词：排队；强占优先权；流量控制；拟生灭过程；稳态分布

Abstract In some systems, some of the "customers" must get priority service, which is a preemptive priority queue。 People has studied this model a lot and applied it into real life, such as sales of food that is nearly bad, transmission of computer datas, communication protocols and so on。 And now, most studies of queuing theory is based on single-desk model, but in real life, multi-server model is often seen, so by studying the M / M / 2 queuing system, we can parallel the method to M / M / c queuing system, which is of very important significance。

     In this paper, we study a controlled M / M / 2 queuing system with preemptive priority。 First of all, the first part describes the research status of queuing theory, the content and purpose of queuing theory and the development of priority research; secondly, the second part introduces some common models in queuing theory。 For example, there are limited (unlimited) source queuing systems, queuing systems with preemptive priority or negative customers or feedback。 In addition, the common analytical methods are given, such as embedded Markov chains, birth-and-death process and the QBD law。 The last part of the paper studies a controlled M / M / 2 queue with preemptive priority, an algorithm for calculating the steady-state distribution of the two kinds of cells is designed by using the matrix analytic method。 The numerical example is given to show the validity of the arithmetic expressions, and this method can be generalized similarly to M / M / c queuing model。

Keywords: queue; preemptive priority; flow control; quasi-birth-and-death process; steady distribution

目录

第一章 绪论 1

1。1 排队论研究现状 1

1。2 排队论研究的内容和目的 1

1。2。1 性态研究 2

1。2。2 统计推断 2

1。2。3 最优化问题 2

1。3 优先权排队的发展背景 3

第二章 排队论常见模型及分析方法 5

2。1几类常见的排队系统 5

2。1。1有（无）限源的简单排队系统