Flow-based model for traffic management in communication network were proposed, which provides a consistent solution of the following network tasks: multipath routing; traffic policing; and dynamic allocation of network throughput among the users flows. Obtained solutions provide the required values of the key indicators of Quality of Service such as packet rate, average delay and packet loss probability.
Lemeshko O.V., Garkusha S.V., Yeremenko O.S., Hailan A.M. Policy-based QoS management model for multiservice networks // International Siberian Conference on Control and Communications (SIBCON), 21-23 May 2015, Omsk, Russia. Publisher: IEEE. – PP. 1-4.

The main characteristics of QoS are estimated usually by methods of queuing theory. However, in the application to nets queuing theory considers processes for each of the systems (switches, routers, servers etc.) without taking into account the network topology. On the other hand, graph theory uses the topology for network analysis but cannot consider arrival and service processes in network systems. Tensor analysis of networks allows to provide an estimate of QoS characteristics with taking into account both the arrival and service processes and the network topology. This work presents the nodal tensor model as a tool for QoS analysis in the communications networks. In these models, the main systems of the communications network represented as single-line queuing systems (but and other types of queuing systems can be used). Models formed in accordance to the types of networks. The proposed models allow estimating the QoS characteristics for the individual routes and the entire network. Moreover, these models can be used to optimize the communications networks.
Ponomarev Dmitriy Yurievich The nodal tensor model for QoS estimation of communications networks // Проблеми телекомунікацій, Vol. 2013, Issue 2, 2013, pp. 27-32

Flow model for multipath routing with guaranteed the quality of service (QoS) is proposed. The model is based on the updated version of flow conservation law, which is taking into account the possible packet loss caused by buffer overflow at the network routers. The accounting such losses is related to revise conditions associated with the quality of service. By using tensor approach analytical boundary conditions were obtained. The conditions allow ensuring different parameters of the quality of service (rate, average delay and packet loss probability) at the same time. In addition, proposed model provides minimal value of average end-to-end packet delay where delays along all paths are same. As a result jitter caused by the multipath routing (difference between delays along different paths) is minimized. The developed conditions for QoS ensuring have invariant form which do not depend on the used at the interface. Changing the traffic models and/or packet servicing algorithm is related to a modification of the metric only within the same form of conditions.
Lemeshko O.V., Yevseyeva O.Yu., Garkusha S.V. A Tensor Model of Multipath Routing Based on Multiple QoS Metrics // 2013 International Siberian Conference on Control and Communications (SIBCON). Proceedings. – Krasnoyarsk: Siberian Federal University. Russia, Krasnoyarsk, September 12−13, 2013. IEEE Catalog Number: CFP13794-CDR. - P. 1-4.