Statistical Simulation of Size Behavior for TCP Windows

The methods for statistical simulation of Poisson and Wiener random processes are studied in the paper. The algorithms for simulation of a Wiener process are based on its spectral representation. There are constructed models with given reliability and accuracy. The algorithm for simulation of a Poisson process relies on the distribution of the intervals between jump times of the process. Stochastic models of data transmission and network traffic are widely used in the design and operation of data networks. These models allow us to estimate traffic losses and identify ways to improve service quality. Different approaches and methods for managing network overload, including Random Early Detection algorithms, are used in data networks. The Random Early Detection algorithm allows controlling the loading of the router's queue and, under determining the overload, carrying out the dropping of packets with some probability. The reset of a package is based on probability calculation. The algorithm is oriented towards working with Transmission Control Protocol, so dropping packets allows the load source to reduce the size of the window and, thus, to reduce the load. The model of a network behavior is described by stochastic differential equations. In the paper, there are constructed solutions for such equations. For simulation of realizations of stochastic differential equations, their representation in the form of difference equation and statistical models of Poisson and Wiener random processes are used. The simulation results are used to control the size of Transmission Control Protocol windows.