【摘要】：重入型排隊(duì)網(wǎng)絡(luò)(Re-entrant line)是一種實(shí)際中廣泛存在的隨機(jī)排隊(duì)網(wǎng)絡(luò)模型。它可以用來模擬復(fù)雜的半導(dǎo)體生產(chǎn)制造系統(tǒng),如晶片制造,薄膜生產(chǎn)等。由于排隊(duì)網(wǎng)絡(luò)的性能分析基本都假設(shè)系統(tǒng)在平穩(wěn)環(huán)境下運(yùn)行,于是一個(gè)人們普遍關(guān)心的問題是重入型排隊(duì)網(wǎng)絡(luò)在什么條件下是穩(wěn)定的,即平穩(wěn)分布存在。這里平穩(wěn)分布的存在性指的是描述排隊(duì)網(wǎng)絡(luò)動(dòng)態(tài)行為的馬氏過程的平穩(wěn)分布的存在性。與傳統(tǒng)研究隨機(jī)排隊(duì)網(wǎng)絡(luò)穩(wěn)定性的方法不同,本文采用流體模型的方法,研究了在GMHLPPS服務(wù)規(guī)則下,重入型排隊(duì)網(wǎng)絡(luò)的穩(wěn)定性。具體講,我們以流體模型為工具,通過構(gòu)造Lyapunov函數(shù),證明了流模型是穩(wěn)定的,從而得到上述平穩(wěn)分布的存在性。本文主要分為三章。 第一章是導(dǎo)論,主要介紹了排隊(duì)論的歷史發(fā)展和排隊(duì)論的基礎(chǔ)知識(shí)、排隊(duì)網(wǎng)絡(luò)模型、排隊(duì)網(wǎng)絡(luò)穩(wěn)定性理論等內(nèi)容,簡(jiǎn)要概括了從利用馬氏過程來研究排隊(duì)網(wǎng)絡(luò)的經(jīng)典排隊(duì)理論到現(xiàn)代利用流體模型來研究排隊(duì)網(wǎng)絡(luò)的發(fā)展。最后介紹了本文所用的GMHLPPS服務(wù)規(guī)則,這是一種進(jìn)程共享(PS)的服務(wù)規(guī)則,是對(duì)MHLPPS服務(wù)規(guī)則引入權(quán)重向量得到的。 第二章利用馬氏過程研究了單服務(wù)臺(tái)排隊(duì)的平穩(wěn)分布：一個(gè)是M/M/1模型,另一個(gè)是單服務(wù)臺(tái)兩類顧客的Re-entrant line在GMHLPPS服務(wù)規(guī)則下的模型。對(duì)M/M/1模型做了一些模擬,得到了與理論相一致的結(jié)果。由于模型比較簡(jiǎn)單,當(dāng)系統(tǒng)穩(wěn)定時(shí),運(yùn)用生滅過程就可以求出這兩個(gè)模型的平穩(wěn)分布。 第三章利用流體模型研究了GMHLPPS服務(wù)規(guī)則下一般re-entrant line的穩(wěn)定性。通過構(gòu)造一種特殊類型的Lyapunov函數(shù),即熵函數(shù),證明了：如果Re-entrant line滿足通常的服務(wù)強(qiáng)度條件,則GMHLPPS服務(wù)規(guī)則下的Re-entrant line是穩(wěn)定的,即描述排隊(duì)網(wǎng)絡(luò)動(dòng)態(tài)行為的馬氏過程的平穩(wěn)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.
【學(xué)位授予單位】：北京郵電大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O226

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本文編號(hào)：2138819