Matching Three Moments with Minimal Acyclic Phase Type Distributions

Andrea Bobbio · András Horváth · Miklós Telek

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

A number of approximate analysis techniques are based on matching moments of continuous time phase type (PH) distributions. This paper presents an explicit method to compose minimal order continuous time acyclic phase type (APH) distributions with a given first three moments. To this end we also evaluate the bounds for the first three moments of order n APH distributions (APH(n)). The investigations of these properties are based on a basic transformation, which extends the APH(n − 1) class with an additional phase in order to describe the APH(n) class.

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1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1987The least variable phase type distribution is erlang

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