Estimating Markov-Modulated Compound Poisson Processes

Hiroyuki Okamura; Yuya Kamahara; Tadashi Dohi

2nd International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Estimating Markov-Modulated Compound Poisson Processes

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@INPROCEEDINGS{10.4108/valuetools.2007.1935,
    author={Hiroyuki Okamura and Yuya Kamahara and Tadashi Dohi},
    title={Estimating Markov-Modulated Compound Poisson Processes},
    proceedings={2nd International ICST Conference on Performance Evaluation Methodologies and Tools},
    proceedings_a={VALUETOOLS},
    year={2010},
    month={5},
    keywords={Markov-modulated compound Poisson process compound Markovian arrival process maximum likelihood estimation EM algorithm uniformization},
    doi={10.4108/valuetools.2007.1935}
}

Hiroyuki Okamura
Yuya Kamahara
Tadashi Dohi
Year: 2010
Estimating Markov-Modulated Compound Poisson Processes
VALUETOOLS
ICST
DOI: 10.4108/valuetools.2007.1935

Hiroyuki Okamura¹^,*, Yuya Kamahara¹^,*, Tadashi Dohi¹^,*

1: Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

*Contact email: okamu@rel.hiroshimau._ac.jp, kahamara@rel.hiroshimau._ac.jp, dohi@rel.hiroshima-u.ac.jp

Abstract

This paper addresses a parameter estimation problem for Markov-modulated compound Poisson process (MMCPP) and compound Markovian arrival process (CMAP). MMCPP and CMAP are extended from Markov-modulated Poisson process (MMPP) and Markovian arrival process (MAP) by combining compound Poisson process (CPP). The EM (expectation-maximization) algorithm is well known as an effective method in order to perform the statistical estimation for the family of MAPs. In this paper, we develop the EM algorithm for MMCPP and CMAP by using the similar technique to the forward-backward algorithm of hidden Markov model (HMM). In particular, we derive concrete estimation algorithms for MMCPP and CMAP whose outputs are given by exponential distributions or multivariate normal distributions.

Keywords: Markov-modulated compound Poisson process compound Markovian arrival process maximum likelihood estimation EM algorithm uniformization

Published: 2010-05-16
Modified: 2011-09-14

: http://dx.doi.org/10.4108/valuetools.2007.1935