Марківська гаусівська модель процесу зміни довжини черги маршрутизатора

Abstract

This work presents a statistical analysis of experimental data aimed at confirming the Markov properties of the modeled process based on its correlation characteristics. A Markov Gaussian model describing the dynamics of router queue length is proposed, and its parameters are justified using the least squares method. Simulation experiments were conducted, demonstrating the adequacy of the chosen mathematical model. This is supported by the small error variances of the correlation function and spectral density, as well as the close agreement between the mean values of the real process and the model (m = 39.2926 and mx = 39.2876). The practical significance of the results lies in their applicability to congestion control problems, particularly for estimating the queue length in router buffer management.