Transformation of acyclic phase type distributions for correlation fitting

Abstract

In this paper similarity transformations for Acyclic Phase Type Distributions (APHs) are considered, and representations maximizing the first joint moment that can be reached when the distribution is expanded into a Markovian Arrival Process (MAP) are investigated. For the acyclic case the optimal representation corresponds to a hyperexponential representation, which is optimal among all possible representations that can be reached by similarity transformations. The parameterization aspect for the possible transformation of APHs into a hyperexponential form is revealed, together with corresponding transformation rules. For the case when APHs cannot be transformed into a hyperexponential representation a heuristic optimization method is presented to obtain good representations, while transformation methods to increase the first joint moment by adding additional phases are derived. © 2013 Springer-Verlag.