带伯努利反馈的批量到达的单服务台排队系统的泛函重对数律

发布时间：2018-01-12 10:05

本文关键词：带伯努利反馈的批量到达的单服务台排队系统的泛函重对数律　出处：《北京邮电大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文首先研究了带伯努利反馈的批量到达的单服务台排队系统(GIB/GI/1)的强逼近,然后在强逼近结果基础之上研究该排队系统的泛函重对数律和相应的重对数律. 强逼近是随机过程中一种重要的近似方式,其思想是将随机过程近似逼近到一个布朗运动网络.关于带伯努利反馈的批量到达的单服务台排队系统的强逼近研究中,不需限定排队系统的服务强度,利用到达过程、服务过程等过程的极限理论得到了排队系统的队长过程、负荷过程、闲期过程、忙期过程和离去过程五个指标过程的强逼近结果,为下一步得到排队模型的泛函重对数律提供了必要的准备. 泛函重对数律和重对数律是用来描述随机过程渐近行为的两种重要方式,它们分别从函数集的角度和数值角度,通过随机过程偏离其流体极限的大小程度来度量其渐近随机波动的情况.关于带伯努利反馈的批量到达的单服务台排队系统的泛函重对数律的研究中,分别在三种系统服务强度下即负载(ρ1)、临界负载(ρ＝1)和超载(p1)的情形下,建立排队模型五个度量指标即队长过程、负荷过程、闲期过程、忙期过程和离去过程的泛函重对数律.采用的方式是先将排队系统指标过程的泛函重对数律转化为相应强逼近的泛函重对数律,通过分析强逼近给出的布朗运动及布朗运动的泛函重对数律得到目标结果.而重对数律可以看做是泛函重对数律的一种精细化结果,可以由泛函重对数律连续函数集的一致上下确界得到.本文对结果做了一些直观上的分析,同时给出了关于重对数律数值实例,并画出了相应的图形.
[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.
【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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