Markov arrival processes (MAPs) are used extensively in traffic modeling.
Consequently a wide variety of fitting procedures have been developed.
Most of these however are computationally demanding or not general enough.
To resolve this problem, a specific type two-step procedure have been made,
in which a phase-type distribution (PH) is fitted to static parameters
(to distribution or moments of arrival intervals) in the first step, then,
in the second step a MAP is generated from this PH, with fitting to dynamic parameters (autocorrelation, joint moments).
A general problem of these methods is that it may severely restrict the attainable range of dynamic parameters.
In this thesis I present an optimization method, that aims at providing a favorable starting point for the second step,
by using equivalent transformations of the PH that was produced by the first step.
During the transformations, the method maximizes a chosen goal function.
In this work I examine a couple of goal functions, comparing them with an other PH transformation method developed before.
I evaluate the results and mention a few possible directions of improvement.