The $G$-network as a stochastic data network model

The primary objective of this paper is the mathematical modelling of a data network consisting of terminal devices connected by routing devices and data links. A closed exponential $G$-network of single-server queueing nodes with positive requests and signals is used as a stochastic model. The model is studied in the asymptotic case of a large number of requests being processed. The mathematical approach used makes it possible to calculate the main statistical characteristics of a Markov process describing the model state, as well as to reconstruct analytically its normal probability density function based on the Gaussian approximation method. The results of the study allow us to analyse the data network performance in both transient and steady state. The areas of implementation of the research results are the pre-design of data networks and solving problems of their optimisation.