本文關(guān)鍵詞：帶伯努利反饋的批量到達的單服務(wù)臺排隊系統(tǒng)的泛函重對數(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： 泛函重對數(shù)律 重對數(shù)律 強逼近 批量到達排隊 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的單服務(wù)臺排隊系統(tǒng)(GIB/GI/1)的強逼近,然后在強逼近結(jié)果基礎(chǔ)之上研究該排隊系統(tǒng)的泛函重對數(shù)律和相應(yīng)的重對數(shù)律. 強逼近是隨機過程中一種重要的近似方式,其思想是將隨機過程近似逼近到一個布朗運動網(wǎng)絡(luò).關(guān)于帶伯努利反饋的批量到達的單服務(wù)臺排隊系統(tǒng)的強逼近研究中,不需限定排隊系統(tǒng)的服務(wù)強度,利用到達過程、服務(wù)過程等過程的極限理論得到了排隊系統(tǒng)的隊長過程、負荷過程、閑期過程、忙期過程和離去過程五個指標(biāo)過程的強逼近結(jié)果,為下一步得到排隊模型的泛函重對數(shù)律提供了必要的準(zhǔn)備. 泛函重對數(shù)律和重對數(shù)律是用來描述隨機過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,通過隨機過程偏離其流體極限的大小程度來度量其漸近隨機波動的情況.關(guān)于帶伯努利反饋的批量到達的單服務(wù)臺排隊系統(tǒng)的泛函重對數(shù)律的研究中,分別在三種系統(tǒng)服務(wù)強度下即負載(ρ1)、臨界負載(ρ＝1)和超載(p1)的情形下,建立排隊模型五個度量指標(biāo)即隊長過程、負荷過程、閑期過程、忙期過程和離去過程的泛函重對數(shù)律.采用的方式是先將排隊系統(tǒng)指標(biāo)過程的泛函重對數(shù)律轉(zhuǎn)化為相應(yīng)強逼近的泛函重對數(shù)律,通過分析強逼近給出的布朗運動及布朗運動的泛函重對數(shù)律得到目標(biāo)結(jié)果.而重對數(shù)律可以看做是泛函重對數(shù)律的一種精細化結(jié)果,可以由泛函重對數(shù)律連續(xù)函數(shù)集的一致上下確界得到.本文對結(jié)果做了一些直觀上的分析,同時給出了關(guān)于重對數(shù)律數(shù)值實例,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)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O226

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本文編號：1413769