BASIC PRINCIPLES OF CONVERGENCE OF TELECOMMUNICATION NETWORKS AND METHODS FOR THEIR MATHEMATICAL DESCRIPTION

Abstract

The principles of convergence of telecommunication networks are considered, the difference between modern transport and converged NGN networks, the advantages, disadvantages and opportunities for their further improvement are considered. the methods of building networks of the next and future generations, the outlined tasks of modernizing transport networks are analyzed, the features of routing in converged networks are indicated taking into account the increase in the throughput of DWDM transport technology and the formation of many virtual channels for each type of traffic. It is shown that convergence is mainly carried out between fixed radio networks, and the convergence of network technology services remains promising for subsequent studies. Brief modern mathematical approaches are presented for determining the quality assessment of telecommunication networks. The use of tensor analysis is justified, which allows one to evaluate the change in network parameters during the transition from one topology to another, to analyze the quality of service in networks with maximum load. Tensor analysis makes it possible to simplify the representation of complex structures and has a number of invariants. The functional invariant in tensor models is the equation, which preserves the recording form unchanged and independent of the coordinate system. A distinctive feature of traditional calculation methods, the tensor model simultaneously determines both the structure of networks (in implicit form using transformation matrices) and the processes that occur in them, that is, the transmission and distribution of flows. Existing flows in telecommunication networks are modeled, as a rule, by ON / OFF and armored fractal processes. The main indicators of fractal flows are the Hurst indicator and the severity of the tail. The possibility of predicting the traffic parameters of telecommunication networks using fractal processes is substantiated. total methodologically developed and applied is the theory of QS and graphs. The use of other mathematical devices is usually due to the inability to describe the modeling process in the framework of theories of graphs and QS. Tensor and fractal analysis is the most promising and can be effectively used to study the structural and functional properties of convergent telecommunication networks.