Probabilistic approximations based on GPH distributions

The distribution of the random sum of i.i.d. exponential random variables is called a GPH (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, the authors show that any distribution defined on R’+ can be approximated by the GPH distribution and demonstrate the accuracy of the approximation through various numerical examples. Also, the authors 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 experimenal results of this paper help us accept the usefulness of the approximations based on GPH distributions. [In Korean.]