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Application of deterministic annealing EM algorithm to MAP/PH parameter estimation

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Abstract

This paper proposes a variant of EM (expectation-maximization) algorithm for Markovian arrival process (MAP) and phase-type distribution (PH) parameter estimation. Especially, we derive the deterministic annealing EM (DAEM) algorithm for MAP/PH parameter estimation. The DAEM algorithm is one of the methods to overcome a local maxima problem associated with the conventional EM algorithm. This paper derives concrete E- and M-step formulas for MAP parameter estimation from inter-arrival time data and PH parameter estimation from point samples in the framework of DAEM algorithm. Numerical examples demonstrate the DAEM algorithm for Markov-modulated Poisson process (MMPP) and several classes of PH distribution.

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  1. The Internet traffic archive: http://ita.ee.lbl.gov/.

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Correspondence to Hiroyuki Okamura.

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This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), Grant No. 21510167 (2009–2011).

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Okamura, H., Kishikawa, H. & Dohi, T. Application of deterministic annealing EM algorithm to MAP/PH parameter estimation. Telecommun Syst 54, 79–90 (2013). https://doi.org/10.1007/s11235-013-9717-y

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