本文關(guān)鍵詞：帶伯努利反饋的批量到達(dá)的單服務(wù)臺(tái)排隊(duì)系統(tǒng)的泛函重對(duì)數(shù)律　出處：《北京郵電大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 泛函重對(duì)數(shù)律 重對(duì)數(shù)律 強(qiáng)逼近 批量到達(dá)排隊(duì) 伯努利反饋

【摘要】：本文首先研究了帶伯努利反饋的批量到達(dá)的單服務(wù)臺(tái)排隊(duì)系統(tǒng)(GIB/GI/1)的強(qiáng)逼近,然后在強(qiáng)逼近結(jié)果基礎(chǔ)之上研究該排隊(duì)系統(tǒng)的泛函重對(duì)數(shù)律和相應(yīng)的重對(duì)數(shù)律. 強(qiáng)逼近是隨機(jī)過(guò)程中一種重要的近似方式,其思想是將隨機(jī)過(guò)程近似逼近到一個(gè)布朗運(yùn)動(dòng)網(wǎng)絡(luò).關(guān)于帶伯努利反饋的批量到達(dá)的單服務(wù)臺(tái)排隊(duì)系統(tǒng)的強(qiáng)逼近研究中,不需限定排隊(duì)系統(tǒng)的服務(wù)強(qiáng)度,利用到達(dá)過(guò)程、服務(wù)過(guò)程等過(guò)程的極限理論得到了排隊(duì)系統(tǒng)的隊(duì)長(zhǎng)過(guò)程、負(fù)荷過(guò)程、閑期過(guò)程、忙期過(guò)程和離去過(guò)程五個(gè)指標(biāo)過(guò)程的強(qiáng)逼近結(jié)果,為下一步得到排隊(duì)模型的泛函重對(duì)數(shù)律提供了必要的準(zhǔn)備. 泛函重對(duì)數(shù)律和重對(duì)數(shù)律是用來(lái)描述隨機(jī)過(guò)程漸近行為的兩種重要方式,它們分別從函數(shù)集的角度和數(shù)值角度,通過(guò)隨機(jī)過(guò)程偏離其流體極限的大小程度來(lái)度量其漸近隨機(jī)波動(dòng)的情況.關(guān)于帶伯努利反饋的批量到達(dá)的單服務(wù)臺(tái)排隊(duì)系統(tǒng)的泛函重對(duì)數(shù)律的研究中,分別在三種系統(tǒng)服務(wù)強(qiáng)度下即負(fù)載(ρ1)、臨界負(fù)載(ρ＝1)和超載(p1)的情形下,建立排隊(duì)模型五個(gè)度量指標(biāo)即隊(duì)長(zhǎng)過(guò)程、負(fù)荷過(guò)程、閑期過(guò)程、忙期過(guò)程和離去過(guò)程的泛函重對(duì)數(shù)律.采用的方式是先將排隊(duì)系統(tǒng)指標(biāo)過(guò)程的泛函重對(duì)數(shù)律轉(zhuǎn)化為相應(yīng)強(qiáng)逼近的泛函重對(duì)數(shù)律,通過(guò)分析強(qiáng)逼近給出的布朗運(yùn)動(dòng)及布朗運(yùn)動(dòng)的泛函重對(duì)數(shù)律得到目標(biāo)結(jié)果.而重對(duì)數(shù)律可以看做是泛函重對(duì)數(shù)律的一種精細(xì)化結(jié)果,可以由泛函重對(duì)數(shù)律連續(xù)函數(shù)集的一致上下確界得到.本文對(duì)結(jié)果做了一些直觀上的分析,同時(shí)給出了關(guān)于重對(duì)數(shù)律數(shù)值實(shí)例,并畫出了相應(yīng)的圖形.
[Abstract]:In this paper, we first study the strong approximation of the batch arrival queueing system with Bernoulli feedback (GIB / GI / 1). Then the functional logarithm law and the corresponding iterated logarithm law of the queueing system are studied on the basis of strong approximation results. Strong approximation is an important approximation method in stochastic processes. The idea is to approximate the stochastic process to a Brownian motion network. In the study of the strong approximation of a batch arrival queueing system with Bernoulli feedback, there is no need to limit the service strength of the queueing system. By using the limit theory of arrival process, service process and so on, the strong approximation results of five index processes of queue system, such as queue length process, load process, idle period process, busy period process and departure process, are obtained. It provides the necessary preparation for the next step to obtain the functional logarithm law of queueing model. The law of functional iterated logarithm and the law of iterated logarithm are two important ways to describe the asymptotic behavior of stochastic processes from the angle of function set and numerical value respectively. The asymptotic stochastic fluctuations of stochastic processes are measured by deviating from their fluid limit. In the study of functional iterated logarithm law for batch arrival single service station queueing systems with Bernoulli feedback. In the case of three kinds of system service strength, namely, the load (蟻 1), the critical load (蟻 1) and the overload (p 1), five metrics of queue model are established, that is, the queue length process, the load process, and the idle period process. The law of functional iterated logarithm of the busy period process and the departure process is first transformed from the functional logarithm law of the index process of the queuing system to the corresponding strong approximation law of the functional iterated logarithm. The results are obtained by analyzing the functional law of iterated logarithm of Brownian motion and Brownian motion given by strong approximation, and the law of iterated logarithm can be regarded as a refined result of the law of iterated logarithm of functional. It can be obtained from the uniform upper and lower bounds of the set of functional iterated logarithmic law continuous functions. In this paper, some intuitionistic analysis of the result is given, and a numerical example of the law of iterated logarithm is given, and the corresponding figure is drawn.
【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)：1413769