Author, Institution: Mindaugas Bražėnas, Kaunas University of Technology
Science area, field of science: Natural Sciences, Informatics P009
Scientific Supervisor: Prof. Dr. Habil. Eimutis Valakevičius (Kaunas University of Technology, Natural Sciences, Informatics, N009).
Dissertation Defence Board of Informatics Science Field:
Prof. habil. dr. Rimantas Barauskas (Kaunas University of Technology, Natural Sciences, Informatics, N009) – chairman,
Prof. Dr. Habil. Raimondas Čiegis (Vilnius Gediminas Technical University, Natural Sciences, Informatics, N009),
Prof. Dr. Gintaras Palubeckis (Kaunas University of Technology, Natural Sciences, Informatics, N009),
Prof. Dr. Habil. Minvydas Kazys Ragulskis (Kaunas University of Technology, Natural Sciences, Informatics, N009),
Assoc. Prof. Dr. Zsolt Saffer (Vienna University of Technology, Austria, Natural Sciences, Informatics, N009).
The doctoral dissertation is available at the libraries of Kaunas University of Technology (Donelaičio 20, Kaunas), Vytautas Magnus University (K. Donelaičio g. 52, Kaunas) and Vilnius Gediminas Technical University (Saulėtekio al. 14, Vilnius).
In this doctoral thesis the problem of parameter search of Phase-type distributions and Markovian arrival processes are investigated.
The hypothesis of sufficient number (i.e., 2n-1) of transitions in Phase-type (PH) distribution matrix form representation of order n is validated empirically, for the case of PH(4). The generated structure sets have been used to search for Phase-type distribution parameters while fitting (by expectation maximization method, EM) nine benchmark distributions. Based on results, the hypothesis statement, that it is sufficient to have 7 transitions to represent almost any PH(4) distribution, is validated. In addition, Phase-type fitting using randomly generated structures has been investigated. A finite request queue model has been implemented for comparing dense and sparse Phase-type distribution application, also.
The algorithms for parallel parameter search of Markovian arrival process of ER-CHMM matrix form representation structure have been developed. The classic forward-backward EM method algorithm has been reformulated for parallel execution at the cost of increased computational complexity. Two algorithm variations have been obtained by adapting the Baum-Welch algorithm principles and the third variation developed. The properties of algorithms have been investigated and recommendations on choosing a suitable algorithm have been given.
Finally, the EM method algorithm has been derived for transient Markovian arrival process fitting.