Approximationg non-Markovian Behavior by Markovian Models
PhD Dissertation

András Horváth

The material presented in the dissertation is about approximating non-Markovian behavior by Markovian models.

Introduction to various aspects of the field is provided in Part I consisting of three chapters. Chapter 1 provides the background for discrete-time Phase-type (DPH) distributions. A short introduction to Markovian modeling for traffic engineering is given in Chapter 2. Characteristics of random quantities and random processes of telecommunication networks with related statistical tests are introduced in Chapter 3.

Part II investigates DPH distributions. It is shown that the use of DPH distributions, which received much less attention than the use of continuous-time Phase-type (CPH) distributions, can be beneficial in numerous modeling situations. We show that the minimal coefficient of variation of the acyclic DPH (ADPH) class is lower than that of the CPH class. Also the structure of the ADPH distribution exhibiting minimal coefficient of variation is provided. We present a fitting procedure as well and make use of it to perform and analyze several fitting experiments.

Chapters of Part III present algorithms that result in Markovian models capturing phenomena whose existence in telecommunication networks was reported recently and, initially, it was agreed that Markovian models are not appropriate to model them. In Chapter 7 we concentrate on random durations with heavy tail and give a Phase-type fitting procedure that handles separately the fitting of the body and the tail of the distribution. In the last two chapters of the dissertation, a step further is taken by fitting point processes instead of distributions. In Chapter 8 a heuristic fitting method is presented that, by treating separately the short- and long-range behavior, captures important features of real traffic sources. In the subsequent chapter of the dissertation, we introduce a set of Markovian arrival processes with special structure that exhibit multifractal behavior (as demonstrated by multifractal analysis) and also a fitting procedure to capture the multifractal properties of data sets.


[Publications of András Horváth]

András Horváth, 2008-06-25