A two-level method of fast re-routing with load balancing in a software-defined network (SDN) is proposed. The novelty of the method consists, firstly, in the introduction of a two-level hierarchy of calculating the routing variables responsible for the formation of the primary and backup paths, and secondly, in ensuring a balanced load of the communication links of the network, which meets the requirements of the traffic engineering concept. The method provides implementation of link, node, path, and bandwidth protection schemes for fast re-routing in SDN. The separation in accordance with the interaction prediction principle along two hierarchical levels of the calculation functions of the primary (lower level) and backup (upper level) routes allowed to abandon the initial sufficiently large and nonlinear optimization problem by transiting to the iterative solution of linear optimization problems of half the dimension. The analysis of the proposed method confirmed its efficiency and effectiveness in terms of obtaining optimal solutions for ensuring balanced load of communication links and implementing the required network element protection schemes for fast re-routing in SDN.

A tensor data-flow model of multipath routing with guarantee of quality by several indices is presented. The novelty of the model consists in transfer to the updated version of the flow storage conditions taking into account packets possible losses caused by overflow of the buffer queue on the network routers. Due to the tensor formalization of the network model it was possible to receive in the analytical form the conditions of imparting quality to simultaneous service by multiple various indices, namely, the transmission rate, mean delay and packages loss probability. The results of the research have shown the advantages of the offered method; they have made themselves evident in the improvements in the end-to end multipath delay, increase in the transmission rate, packets jitter minimization resulted from realization of the routing multipath strategy, increase in the probability of meeting the QoS-requirements and decrease in service abandonments caused by nonfulfillment of the specified quality level.

The dynamics analysis of multipath QoS-routing tensor model with support of different flows classes is presented. The novelty of the tensor model is a representation of its covariant and contravariant components and metric of the introduced geometrical space as a function of time. The QoS-routing guarantees for different flows classes with different metrics such as average packet rate and average end-to-end delay were proposed. The research results demonstrated that it is especially important to take into account the dynamics of network state changes in the conditions of high utilization of its interfaces, when the average packet end-to-end delay along the network paths behaves nonstationary, changing quite widely during the router update timer.

An optimization model of MPLS Traffic Engineering Fast ReRoute is proposed. The novelty of the model is that the optimization problem of load balancing at Fast ReRoute with bandwidth protection is presented in the linear form. Such a solution, in practice, reduces the computational complexity of the calculation the routing variables responsible for the formation of the primary and backup paths and ensuring a balanced load of the network links, which meets the requirements of the Traffic Engineering concept. The model provides the implementation of the link, node, and bandwidth protection schemes for MPLS Traffic Engineering Fast ReRoute. The analysis of the proposed model confirmed its functionality and efficiency from the point of view of obtaining optimal solutions for ensuring balanced load of network links and implementing the required network elements (link, node) and bandwidth protection schemes.

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.

In this paper, the consistent solution for default gateway protection within fault-tolerant routing in an IP network is presented, and it is based on development of the appropriate flow-based mathematical model. Within the framework of the proposed model, a fault-tolerant routing problem has been reduced to the solution of the optimization problem of nonlinear programming. Fault-tolerance functions are implemented by introducing additional routing variables responsible for the calculation of a backup default gateway and the corresponding path (multipath) in the transport network. Several examples have demonstrated features of the application of the proposed model in solving default gateway protection within fault-tolerant routing for the case of realization of single path and multipath routing. The results have confirmed the efficiency of the proposed model and adequacy of the calculation results obtained