Properties of fractal traffic on the output of a queuing system

The article presents the results of a study of the event flow properties, which is a model of network traffic with fractal (self-similar) properties after processing in a queuing system. The base model of the traffic uses fractal shot-noise driven poisson process (fsndp). Definitions and the most common statistical properties of common fractal (self-similar) processes and fsndp model are described in terms of measurable network traffic characteristics. Previously the authors proved matching the most important statistical characteristics of real traffic in distributed information systems to this model process. Through simulation it is determined that the output stream also shows the properties of self-similarity, and the degree of self-similar properties increases with increasing system utilization rate. It is also confirmed that the dependences identified are common to the input stream with different degree of self-similar properties, and degree of self-similarity of the input stream to the output stream properties is leveled for high-load queuing systems, while systems with low load rate demonstrate insignificant rise of fractal properties such as hurst factor comparing to input event stream. Rising of fractal properties with increasing load is explained basing on application phenomenon of peak values cut-off in times of maximum load. Numerical parameters of the model simulated are based on previously performed statistical analysis of dumped network traffic of real client-server data processing application in a telecom operator wan network. The results have been suggested as the basis for the development of tensor models of queuing networks with fractal load, and future study of analytical expressions for queuing networks fed by fractal load streams.