Using the EM-algorithm to Approximate the Distribution of a Mixture by Hyperexponents

Modern infocommunication networks are developing very intensively, the structure of networks and the nature of applications are changing, which leads to the need for new approaches to research the parameters of their functioning. The paper proposes the solution to the problem of approximating an arbitrary probability density in the G/G/1 system using hyperexponential distributions. Moreover, to determine the parameters of the probability density of the hyperexponential distribution, it is proposed to use the EM algorithm. An example of approximation by a system of type H2/D2/1 of a real implementation of IP network traffic is given.