Анализ очереди в системе G/G/1 на основе гиперэкспоненциальных распределений

Abstract

For real-time applications, the change in packet delay, which is usually called delay jitter, is one of the most important parameters of quality of service in modern infocommunication networks when processing multimedia streams, along with the delay and the probability of packet loss. This article discusses approaches to assessing jitter in modern infocommunication networks when processing non-Poissonian traffic in the G/G/1 system. To approximate the system of an arbitrary queue G/G/1, a model based on hyperexponential distributions of the type H2/H2/1 was used. As a processed stream, the implementation of IP network traffic with the absence of mutual correlations between the time intervals between packets and the times of packet processing is used. An important task in this case is to determine the parameters of hyperexponential distributions for the time intervals between packets and packet processing times. The paper presents two methods for determining the parameters of hyperexponential distributions: using the method of moments and using the EM-algorithm. The paper analyzes the influence of the network load factor on the jitter value when using two models for determining the parameters of hyperexponential distributions. This analysis showed a slight increase in jitter with increasing network load both in the case of using the method of moments and in the case of the EM algorithm. It has been determined that the estimates of the jitter values in the case of applying the method of moments and the EM algorithm are quite close in value. The main result of the work is to obtain simple calculation formulas for the analysis of jitter in the G/G/1 system using hyperexponential distributions.