Abstract
The characterization and the canonical representation of order n phase type distributions (PH(n)) is an open research problem.
This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper we summarize the related results for n = 3. Starting from these results we recommend a canonical representation of the PH(3) class and present a transformation procedure to obtain the canonical representation based on any (not only Markovian) vector-matrix representation of the distribution.
Using this canonical transformation method we evaluate the moment bounds of the PH(3) distribution set and present the results of our numerical investigations.
This work is partially supported by the Italian-Hungarian R&D project 9/2003 and by the OTKA K61709 grant.
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Horváth, G., Telek, M. (2007). A Canonical Representation of Order 3 Phase Type Distributions. In: Wolter, K. (eds) Formal Methods and Stochastic Models for Performance Evaluation. EPEW 2007. Lecture Notes in Computer Science, vol 4748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75211-0_5
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DOI: https://doi.org/10.1007/978-3-540-75211-0_5
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