• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.687-705
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• 2006

In this paper we consider GPH distribution that is defined as a distribution for sum of random number of random variables following exponential distribution. We establish approximation process of general distributions to GPH distributions and offer numerical results for various cases to show the accuracy of the approximation. We also propose analysis method of delay distribution of queueing systems using approximation to GPH distributions and offer numerical results for various queueing systems to show applicability of GPH approximation.

• Journal of the military operations research society of Korea
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• v.22 no.1
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• pp.114-128
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• 1996

In this paper, a life distribution fitting method based on generalized phase-type distributions(GPH) is presented. By fitting the life distribution to a GPH, we can utilize various useful properties of the GPH. Two different approaches are used according to the properties of the given failure time data. One is an approximation to a GPH through the piecewise Weibull failure rate(PWF) model and the other is a direct approximation to a GPH using the empirical distribution function. Two numerical examples are also presented. In the first example, both of the two approaches are utilized and compared for an incomplete data set. And in the second example, the direct approximation method from an empirical distribution is utilized for the analysis of a complete data set. In both cases, we could confirm the validity of the proposed method.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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• pp.85-98
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• 1994

The distribution of random sum of i. i. d. exponential random variables is called GHP (Generalized Phase-Type) distribution. The class of GPH distributions is large enough to include PH (Phase-Type) distributions and has several properties which can be applied conveniently for computational purposes. In this paper, we show that any distribution difined on R$^{+}$ can be app-roximated by the GPH distribution and demonstrate the accuracy of the approximation through various numerical examples. Also, we introduce an efficient way to compute the delay and waiting various numerical examples. Also, we introduce an efficient way to compute the delay and waiting time distributions of the GPH/GPH/1 queueing system which can be used as an approximation model for the GI/G/1 system, and validate its accuracy through numerical examples. The theoretical and experimental results of this paper help us accept the usefulness of the approximations based on GPH distribution.n.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.359-364
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• 2001

In this study, we try to improve the accuracy of QN-GPH by the help of simulation approach. We first establish an estimation method for GPH distributions with sufficient accuracy based on empirical distribution, and then perform a brief trial run to find appropriate empirical distributions. After getting GPH form of distributions, we continue the QN-GPH analytic steps and compute necessary performance measures. We apply the method to find sojourn time distributions in a 8-node queueing system and compare the results with the whole simulation and the original two-parametric approximation.