Abstract
Matrix-geometric distributions (MG) and discrete (time) rational arrival processes (DRAP) are natural extensions of discrete phase-type distributions (DPH) and discrete Markov arrival processes (DMAP) respectively. However, the exact relation of the Markovian classes and their non-Markovian counterparts and the boundaries of these classes are not known yet. It has been shown that for the order two case the MG and DPH classes are equivalent. In this paper we prove that the equivalence holds for the order two DMAPs and DRAPs as well. We prove this equivalence by introducing a Markovian canonical form for order two DRAPs and by showing, that this canonical form can indeed be used to describe the whole order two DRAP class.
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Mészáros, A., Telek, M. (2013). Canonical Representation of Discrete Order 2 MAP and RAP. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds) Computer Performance Engineering. EPEW 2013. Lecture Notes in Computer Science, vol 8168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40725-3_8
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DOI: https://doi.org/10.1007/978-3-642-40725-3_8
Publisher Name: Springer, Berlin, Heidelberg
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