Approximating heavy tailed behaviour with
Phase type distributions

András Horváth, Miklós Telek


In this paper two main problems are investigated. The first one is the effect of the goal function of the applied fitting method on the goodness of Phase type fitting. We discuss a numerical method based on a simple numerical optimization procedure that allows us to fit any non-negative distribution with a Phase type (PH) distribution according to any arbitrary distance measure. By comparing the fitting results obtained by minimizing different distance measures, conclusions are drawn regarding the role of the optimization criteria.

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.


[Publications of András Horváth]

András Horváth, 2008-06-25