STOCHASTIC METHOD OF JITER ANALYSIS BASED ON CONVULATION OF HYPEREXPONENTIAL DISTRIBUTIONS FOR SELF-SIMPLE TRAFFIC

Abstract

This article presents a stochastic method for jitter analysis in queueing systems with self-similar traffic is proposed, which is based on the use of a convolution of hyperexponential distributions. The main attention is focused on the formalization of the variations in the delay time between consecutive packets in G/G/1 systems, where the traffic is characterized by long tails and fractal nature. The proposed approach allows us to estimate the average value of jitter through an integral model that takes into account independent distributions of arrival and service times, modeled as hyperexponential mixtures. The method is based on the calculation of the probability densities of delay times in the form of a convolution of the arrival and service density functions, which allows us to obtain a generalized expression for calculating jitter. The result of this approach is an analytical formula that reflects the dependence of jitter on the statistical characteristics of the incoming traffic, including self-similarity parameters. To improve the accuracy of the estimation, the influence of asymmetric structures in the distributions and service parameters with uneven weights was taken into account.

The study also conducted numerical simulations, which confirmed the influence of self-similarity on the increase in jitter even at fixed average delays. Experimental results showed that with an increase in the fractal intensity of the flow, traditional QoS metrics lose their informativeness, and only models taking into account jitter allow for an adequate assessment of the system load.

The proposed method is universal for a wide class of telecommunication systems with a self-similar nature of traffic. Its use can improve the accuracy of forecasting and resource planning in real-time networks, where even minor delay fluctuations can critically affect the quality of the transmitted content.