Current results and open questions on PH and MAP characterization

Levente Bodrog · Armin Heindl · Gábor Horväth · Miklós Telek · András Horváth

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Advanced Queuing Theory Analysis Probability and Statistical Research Petri Nets in System Modeling

Abstract

Stochastic processes with matrix exponential kernels have a wide range of applications due to the availability of efficient matrix analytic methods. The characterization of these processes is in progress in recent years. Basic questions like the flexibility, the degree of freedom, the most efficient (canonical) representation of these models are under study. The presentation collects a set of available results and related open questions.

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2007A minimal representation of Markov arrival processes and a moments matching method 2007A Markovian canonical form of second-order matrix-exponential processes 2006Spectral Polynomial Algorithms for Computing Bi-Diagonal Representations for Phase Type Distributions and Matrix-Exponential Distributions 2007Matching More Than Three Moments with Acyclic Phase Type Distributions 2007Moment characterization of matrix exponential and Markovian arrival processes 2005A Note on Unicyclic Representations of Phase Type Distributions 2007A Canonical Representation of Order 3 Phase Type Distributions

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