Statistical models of network traffic

The article considers the issues of statistical modeling of traffic in telecommunication networks with packet switching. The simulation results are used in the development of network technical condition management systems, in particular, diagnostics, troubleshooting and network configuration management. The peculiarities of congestion control of separate network segments are emphasized. With improper analysis the overload condition can be mistaken for equipment failure. Therefore, control and elimination of congestion is a statistical task. The concept of end-to-end network diagnostics is considered. This concept provides for effective assessment of the quality of functioning of all network components taking into account their interrelationships. The main issues are the interaction of equipment, inefficient configuration, improper network organization and user operation. Methods of traffic statistical control characteristics based on perforated and marker bucket algorithms are analyzed. A feature of these algorithms is the formation of a strict output stream at a rate that does not depend on the non-uniformity of the input stream. The possibility of improving the token bucket algorithm by adapting to changes in the statistical characteristics of traffic is shown. To solve this problem, statistical mathematical models of network traffic are built. Data traffic circulating in telecommunication networks by packet switching has self-similar (fractal) properties. The self-similar process retains its properties when considered at different time scales (invariance to scale changes). The degree of statistical stability of the process with multiple scaling is determined by the Hirst parameter (the self-similarity parameter). Graphs of statistical characteristics of low-speed and high-speed data traffic are obtained. Their comparative analysis is carried out.