Development of the Dynamic Tensor Model for Traffic Management in a Telecommunication Network with the Support of Different Classes of Service

A model of traffic management, based on the tensor generalization of nonlinear differential equations of network state was proposed. This made it possible to obtain coordinated solution of the problems of routing and link resource allocation between the flows of different classes. The solution makes it possible to provide for the Quality of Service by the parameters of the average packet transmission rate and the packet delay, including the nonstationary operating mode of the network routers interfaces. The coordinate system of interpolar paths and internal node pairs was used in the tensor geometrization of the network structure. This made it possible to provide for the solution, in which the QoS requirements were satisfied not only along the basic paths, but also on the entire set of calculated routes. The problem of traffic management in the telecommunication network was set as the problem of optimization. In this case, it was necessary to calculate many sets of control variables of two types, responsible for flow routing and for determining the order of the link resource allocation in the network in the course of minimization of the quadratic criterion of optimality. The selection of the criterion of quadratic form was determined by the fact that its use contributes to obtaining solutions of the balanced use of available network resources. On the other hand, the consideration of the state dynamics of network interfaces over time made it possible to provide meeting the requirements on the packets transmission rate and the average delay not in a specific moment of time, but throughout the entire routing table update timer