一类随机排队网络的稳定性及其模拟
发布时间：2018-07-23 08:33
【摘要】：重入型排队网络(Re-entrant line)是一种实际中广泛存在的随机排队网络模型。它可以用来模拟复杂的半导体生产制造系统,如晶片制造,薄膜生产等。由于排队网络的性能分析基本都假设系统在平稳环境下运行,于是一个人们普遍关心的问题是重入型排队网络在什么条件下是稳定的,即平稳分布存在。这里平稳分布的存在性指的是描述排队网络动态行为的马氏过程的平稳分布的存在性。与传统研究随机排队网络稳定性的方法不同,本文采用流体模型的方法,研究了在GMHLPPS服务规则下,重入型排队网络的稳定性。具体讲,我们以流体模型为工具,通过构造Lyapunov函数,证明了流模型是稳定的,从而得到上述平稳分布的存在性。本文主要分为三章。 第一章是导论,主要介绍了排队论的历史发展和排队论的基础知识、排队网络模型、排队网络稳定性理论等内容,简要概括了从利用马氏过程来研究排队网络的经典排队理论到现代利用流体模型来研究排队网络的发展。最后介绍了本文所用的GMHLPPS服务规则,这是一种进程共享(PS)的服务规则,是对MHLPPS服务规则引入权重向量得到的。 第二章利用马氏过程研究了单服务台排队的平稳分布：一个是M/M/1模型,另一个是单服务台两类顾客的Re-entrant line在GMHLPPS服务规则下的模型。对M/M/1模型做了一些模拟,得到了与理论相一致的结果。由于模型比较简单,当系统稳定时,运用生灭过程就可以求出这两个模型的平稳分布。 第三章利用流体模型研究了GMHLPPS服务规则下一般re-entrant line的稳定性。通过构造一种特殊类型的Lyapunov函数,即熵函数,证明了：如果Re-entrant line满足通常的服务强度条件,则GMHLPPS服务规则下的Re-entrant line是稳定的,即描述排队网络动态行为的马氏过程的平稳分布是存在的。
[Abstract]:Re-entrant line is a widely used stochastic queuing network model in practice. It can be used to simulate complex semiconductor manufacturing systems, such as wafer manufacturing, thin film production and so on. Since the performance analysis of queueing networks assumes that the system is running in a stationary environment, it is generally concerned about the conditions under which reentrant queuing networks are stable, that is, the existence of stationary distributions. The existence of stationary distribution refers to the existence of stationary distribution of Markov processes describing the dynamic behavior of queueing networks. Different from the traditional method to study the stability of stochastic queueing networks, the stability of reentrant queueing networks under GMHLPPS service rules is studied by using the fluid model method. Specifically, we use the fluid model as a tool, by constructing Lyapunov function, we prove that the flow model is stable and obtain the existence of the above stationary distribution. This paper is divided into three chapters. The first chapter is an introduction, which mainly introduces the historical development of queuing theory and the basic knowledge of queuing theory, queuing network model, queuing network stability theory and so on. This paper briefly summarizes the development of queueing network from classical queuing theory using Markov process to modern queuing network by using fluid model. Finally, this paper introduces the GMHLPPS service rule, which is a process sharing (PS) service rule, which is obtained by introducing the weight vector to the MHLPPS service rule. In chapter 2, we use Markov process to study the stationary distribution of single server queuing: one is the M / M / 1 model, the other is the re-entrant line model of two types of customers under GML PPS service rules. The M / M / 1 model is simulated and the results are consistent with the theory. Because the model is relatively simple, when the system is stable, the stationary distribution of the two models can be obtained by using the birth and death process. In chapter 3, the stability of general re-entrant line under GML PPS service rules is studied by using fluid model. By constructing a special type of Lyapunov function, namely entropy function, it is proved that if Re-entrant line satisfies the usual service strength condition, then Re-entrant line under GML PPS service rule is stable. That is, the stationary distribution of Markov processes describing the dynamic behavior of queueing networks exists.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O226
本文编号：2138819
[Abstract]:Re-entrant line is a widely used stochastic queuing network model in practice. It can be used to simulate complex semiconductor manufacturing systems, such as wafer manufacturing, thin film production and so on. Since the performance analysis of queueing networks assumes that the system is running in a stationary environment, it is generally concerned about the conditions under which reentrant queuing networks are stable, that is, the existence of stationary distributions. The existence of stationary distribution refers to the existence of stationary distribution of Markov processes describing the dynamic behavior of queueing networks. Different from the traditional method to study the stability of stochastic queueing networks, the stability of reentrant queueing networks under GMHLPPS service rules is studied by using the fluid model method. Specifically, we use the fluid model as a tool, by constructing Lyapunov function, we prove that the flow model is stable and obtain the existence of the above stationary distribution. This paper is divided into three chapters. The first chapter is an introduction, which mainly introduces the historical development of queuing theory and the basic knowledge of queuing theory, queuing network model, queuing network stability theory and so on. This paper briefly summarizes the development of queueing network from classical queuing theory using Markov process to modern queuing network by using fluid model. Finally, this paper introduces the GMHLPPS service rule, which is a process sharing (PS) service rule, which is obtained by introducing the weight vector to the MHLPPS service rule. In chapter 2, we use Markov process to study the stationary distribution of single server queuing: one is the M / M / 1 model, the other is the re-entrant line model of two types of customers under GML PPS service rules. The M / M / 1 model is simulated and the results are consistent with the theory. Because the model is relatively simple, when the system is stable, the stationary distribution of the two models can be obtained by using the birth and death process. In chapter 3, the stability of general re-entrant line under GML PPS service rules is studied by using fluid model. By constructing a special type of Lyapunov function, namely entropy function, it is proved that if Re-entrant line satisfies the usual service strength condition, then Re-entrant line under GML PPS service rule is stable. That is, the stationary distribution of Markov processes describing the dynamic behavior of queueing networks exists.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O226
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