The Scale Factor: A New Degree of Freedom in Phase Type Approximation

Andrea Bobbio, András Horváth, Miklós Telek


This paper introduces a unified approach to phase-type approximation in which the discrete and the continuous phase-type models form a common model set. The models of this common set are assigned with a non-negative real parameter, the scale factor. The case when the scale factor is strictly positive results in Discrete phase-type distributions and the scale factor represents the time elapsed in one step. If the scale factor is 0, the resulting class is the class of Continuous phase-type distributions. Applying the above view, it is shown that there is no qualitative difference between the discrete and the continuous phase-type models.

Based on this unified view of phase-type models one can choose the best phase-type approximation of a stochastic model by optimizing the scale factor.

Keywords: Discrete and Continuous Phase type distributions, Phase type expansion, approximate analysis.


[Publications of András Horváth]

András Horváth, 2008-06-25