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Modeling of transient processes in Markov chains with an application to the Internet traffic description.

机译：马尔可夫链中瞬态过程的建模及其在Internet流量描述中的应用。

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摘要

This thesis is on Internet traffic modeling. This thesis examines and critiques long-range dependent characteristics of Internet traffic that are widely accepted in the literature. Based on the information presented in the key articles, this thesis concludes that there is not enough evidence to assume the long-range dependency of Internet traffic. This thesis suggests the more analytically tractable model of a nonstationary Markov process. The Markov assumption of the behavior of the system leads to a system of difference or differential equations. Under the nonstationary assumption, the most important question raised is the question of transient behavior of the system. This is especially true when the length of a period during which traffic can be considered stationary is of the same order as the length of the transient period of the system. An analytic solution for the transient period is not practical for large systems; therefore a numerical solution needs to be obtained. Traditional numerical methods use one of the available integration schemes. These schemes produce solution by numerically integrating system of equations with some integration step. One of the most prominent features of the system of equations considered in this thesis is that they are stiff or ill-defined. This makes their numerical solution using traditional methods unfeasible due to the limitations on the possible integration step. This thesis develops and uses a modified Pseudo Stationary Derivatives (PSD) method to obtain a numerical solution. The method modifies the original system of equations in a way that the solution of the modified system is close to the solution of the original, while the modified system allows a significant increase of the integration step. This thesis includes significant modifications to the PSD method, guaranteeing its applicability for Markov chain modeling. The original PSD method was designed for the solution of differential equations. In this thesis it is proved that this method can be applied for difference equations as well.
机译：本文是关于互联网流量建模的。本文研究并批评了文献中广泛接受的互联网流量的远程依赖性特征。根据关键文章中提供的信息，本文得出结论，没有足够的证据来假设Internet流量具有长期依赖性。本论文提出了一个非平稳马尔可夫过程的更易于分析的模型。系统行为的马尔可夫假设导致了一个差分或微分方程系统。在非平稳假设下，提出的最重要的问题是系统的瞬态行为问题。当可以将流量视为稳定的时间段的长度与系统的过渡时间段的长度处于相同数量级时，尤其如此。过渡期的解析解决方案对于大型系统不切实际。因此需要获得数值解。传统的数值方法使用一种可用的积分方案。这些方案通过对方程系统进行数值积分和一些积分步骤来产生解决方案。本文所考虑的方程组最突出的特点之一就是它们僵硬或定义不清。由于可能的积分步骤的限制，这使得使用传统方法进行数值求解变得不可行。本文开发并使用一种改进的伪平稳导数（PSD）方法获得数值解。该方法以使修改后的系统的解接近于原始解的方式修改原始方程组，而修改后的系统则允许大大增加积分步骤。本文对PSD方法进行了重大修改，保证了PSD方法在马尔可夫链建模中的适用性。最初的PSD方法是为微分方程的求解而设计的。本文证明了该方法也可以应用于差分方程。

著录项

  • 作者

    Roginsky, Michael.;

  • 作者单位

    University of California, Berkeley.;

  • 授予单位 University of California, Berkeley.;
  • 学科 Statistics.; Computer Science.
  • 学位 Ph.D.
  • 年度 2004
  • 页码 119 p.
  • 总页数 119
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;自动化技术、计算机技术;
  • 关键词

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