Solovska I. Tensor methods of traffic modeling in telecommunication networks

Aim: the development of tensor methods for traffic modeling providing more efficient problems solving in telecommunications to improve quality characteristics of telecommunication networks (TCN) performance. Object: the process of traffic modeling in TCN. Subject: tensor methods of traffic modeling in TCN. Scientific novelty and practical application of obtained results: For the first time the node tensor method has been developed for TCN traffic modeling by the tensor representation of a set of network nodes and tracks of their connection. This allowed: to solve the problem of multipath traffic routing and efficient use of network buffer resources with guaranteed time of package delivery providing more thorough consideration of network traffic characteristics and the processes of service; to solve the problem of multiservice traffic quality of service (QoS) characteristic estimation, considering the parameters diversity of network traffic according to k-classes serviced in a single multiservice flow (node tensor method with k-classes of traffic); for a complex structure like allocated NGN network, to obtain the solution for the network on the base of decomposion method, which, in its turn, allows to simplify the process of estimating traffic servicing characteristics, and significantly reduce the number of computational operations (node tensor method on the base of decomposion). For the first time has been developed the contour tensor method, providing tensor consideration of TCN structure not only from the point of view of traffic transmission between certain network nodes, but taking into account the possibility of traffic circulation in network contours. It allowed: to solve the problem of finding the probability-time characteristics of the queuing network (QN) consisting of queuing systems (QS) to obtain estimations of the quality characteristics of various types of QN; to solve the problem of configuring mode of the network objects connections for complex topology and architecture based on the decomposition method, which provides a QoS characteristics for the network as a whole on the basis of the results from a separate subnets (the contour tensor method based on decomposition). For the first time, the tensor method of contours and nodal pairs is proposed for traffic modeling, which, unlike the previously proposed methods, provides the tensor consideration of the TCN as a set of network nodes and the paths of their interaction and as traffic circulating within the network circuits at the same time that solved the problem of traffic modeling with the QoS characteristics assessment simultaneously in several parameters by a single method. For the first time, it is proposed the method of tensor splines, which allows to obtain the invariant to dimensions and system of coordinates solutions, combining structural and functional properties of TCN in modeling: it is proposed the linearization method by passing to the Riemannian space, using the covariant differentiation by tensor splines, which provided non-linear state characteristics of network objects; it is obtained the method of solving nonlinear problems on the set of tensor splines using tensor linearization of nonlinear discrete neighboring systems by which it is simplified the study of the functional properties of the TCN; it is developed the method for solving nonlinear optimal control problems by tensor splines, which allows to find the solution of systems of linear inhomogeneous differential equations for the different classes of control functions. These methods are used in the justification of design solutions at the design stage and the further operation of next generation networks (NGN) and mobile networks, as it is confirmed by the relevant acts of implementation.