| Abstract [eng] |
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. |
