András Horváth, Miklós Telek
The second considered problem is the tail behaviour of Phase type distributions obtained via different fitting methods. To limit the numerical complexity of fitting methods (basically the evaluation of distance measures) the computations (numerical integration) are truncated at some point. Hence the information on the tail behaviour of the distribution is not considered beyond this point.
To approximate distributions with heavy tail we propose a complex method that uses different techniques to fit the main part and the tail of the distribution. The proposed method combines the advantages of fitting techniques and this way it overcomes some of their limitations.
The goodness of the discussed fitting methods are compared in queuing behaviour as well. The behaviour of the M/G/1 queue is compared with the one of the approximating M/PH/1 queue.