The analysis of influence of network architecture nonuniformity and traffic self-similarity properties to load balancing and average end-to-end delay is presented. Therefore, by non-uniformity of network architecture was implied that its structure could be represented by a separable graph or the one close to it. This means that the telecommunication network contained routers and links, which were simulated by articulation points and bridges, respectively. And, by non-uniformity may be implied the fact that the network could have a minimum cut, the rate of which was much less than the bandwidth of other cuts of the network. And for the analysis of influence of network architecture nonuniformity and traffic self-similarity properties to load balancing and average end-to-end delay the mathematical model of load balancing in the telecommunication network was used, within which not only the upper threshold of traffic load of the network links in general, but also certain coefficients of link utilization are minimized for maximally satisfaction of the requirements of the concept of Traffic Engineering. This made it possible to organize the load balancing process in the network more effectively and provide the best value of such an important quality of service indicator as the average end-to-end packet delay in the network.

In this paper, a flow-based decomposition model and a two-level hierarchical coordination method of inter-area routing in a backboneless network are proposed. In the framework of the proposed method of inter-area routing at the lower level there is a calculation of routes for individual areas, and the upper level task is the coordination of the lower-level solutions to provide connectivity of inter-area paths (multipath) both in its structure and in the nature of the users’ traffic balancing on it. The results of numerical calculations confirmed the adequacy of the proposed model and the convergence of the method of inter-area routing to optimal solutions for a finite number of iterations.

The balanced queue management scheme on the interfaces of routers of telecommunication networks has been developed. The novelty of the proposed scheme lies in the application of the two-level method of calculation. At the first level, the problem of allocation and optimal aggregation of packet flows by queues formed on the router interface is solved. At the second level, the problem of allocating and balancing the bandwidth of the interface, taking into account the classification of flows and queues, is solved.

The paper proposed a Fast ReRoute Model with VoIP Quality of Experience protection. Within the framework of the model, conditions for the implementation of multipath routing, modified flow conservation conditions were introduced taking into account possible packet loss at the nodes, protection conditions for network elements, and network bandwidth. The novelty of the model is the formalization of the QoE level protection conditions in terms of quality rating when transmitting VoIP traffic. These conditions were obtained during the tensor description of the network, which made it possible to calculate the probability of packet loss and the average end-to-end delay for the primary and backup routes. As a criterion for the optimality of the solutions obtained, the condition associated with maximizing the overall performance of the telecommunication network was chosen. The results of numerical studies have generally confirmed the adequacy and operability of the proposed model in terms of ensuring the level of QoE in terms of quality rating when transmitting VoIP traffic along the primary and backup paths.

The overview of a mathematical model for multicast routing supporting shared explicit reservation of link resource was presented, which is introduced by linear expressions that responsible for ensuring the connectivity of the calculated multicast routes, as well as the absence of loops in them. The novelty of the model consists in introducing conditions for preventing congestion of communication links when implementing a shared explicit reservation, in which a link resource is allocated to several flows simultaneously, but the list of these flows is strictly defined. The task of routing multicast flows supporting shared explicit reservation of link resource is formulated as an optimization problem of mixed integer linear programming. The use of the proposed model makes it possible to exploit the available link resource more efficiently (on average, from 15 to 25%) by ensuring the consistency of solutions for multicast routing tasks and organizing of the shared explicit reservation.

The paper proposes to improve the mathematical model of multicast routing with balanced use of network resource in accordance with the requirements of the concept of Traffic Engineering (TE). The model is based on the optimality criterion, which quantitatively equals the minimization of the utilization rate of the most downloaded network link. A research of the proposed improved model on the number of network structures was conducted. The research found that when using the optimization criterion of minimization of the utilization rate of the most loaded network link, inappropriately loaded links occur. This is caused by the fact that utilization coefficients of these links are not the highest in the network, and they are not critical to the value of the optimality criterion, and therefore the flow of packets in those links was not prohibited. To solve this problem in the work it is proposed to introduce two additional conditions into the model, the fulfillment of the first condition implies that the flow can come from no more than one adjacent node to an arbitrary node; and the second condition is that the flow of packets on the incoming interfaces of the transit node can only appear if its outgoing interfaces are used. Using the proposed conditions, it was possible to solve the problem of misuse of the links resource without reducing the efficiency of the calculation solutions. The use of an advanced model allows balanced use of the network resource, especially for the traffic structure, which consists of a large number of multicast flows with relatively low intensity compared to the bandwidth of the links.

Practical implementation of Software-Defined Networks (SDN) focuses on increasing the centralization of network management. This requires a high computing power of SDN controller, which implements routing functions also. The effective direction of increasing the productivity of an SDN controller is the use of multicore/multiprocessor computing architectures. In this architecture each core (processor) is functionally responsible for solving a given separate network problem. However, most mathematical methods and calculation algorithms, which are the basis of existing routing protocols, are not adapted for parallel computing. Therefore, in this paper a two-level routing method in a Software-Defined Network is proposed. The method is adapted for use on an SDN controller with multicore architecture. Within the method, a two-tier hierarchy of calculations is introduced by using the goal coordination principle: each core of the lower level of hierarchy is responsible for solving the flow-based routing problem on a separate border router during the solving of the optimization problem of quadratic programming. The functionality of the upper level is implemented on the core-coordinator, which coordinates the lower level solutions to prevent overload of the links in the SDN network. Time to solve routing tasks on an SDN controller and its load directly depends on the convergence rate of the coordination procedure. During studying the proposed method, it is shown that it converges to optimal solutions for the finite number of iterations.

In this paper the hierarchical method of load balancing routing on SDN controllers with multicore architecture is proposed. The implementation of a two-level hierarchy of calculations is proposed on the SDN controllers with multicore architecture where the lower level is responsible for calculating the routing variables, and the upper level is for solutions obtained from the lower level coordination. In proposed multicore architecture of SDN controller the border routers of the network will be matched by the controller core, which performs the function of calculation the routing variables. The separate core of the controller will act as a coordinator with function of link overload prevention. Application of the proposed method allows to increase the scalability of routing solutions, reduce the amount of service information that circulates in the network, as well as reduce the complexity of the whole method.

Two-level routing method with priority link resource allocation balancing in software defined telecommunication network is proposed. The proposed method is based on the use of a flow-based mathematical model, which allowed providing a coherent solution of routing and link bandwidth allocation. On the other hand, the basis of the proposed method is the interaction prediction principle of the theory of hierarchical multi-level control system, which allowed the introduction of a two-level hierarchy of calculations: the lower level was responsible for calculating routing variables, and the upper level was responsible for the link resource allocation. The numerical example confirms the correspondence of the method to optimal solutions for the finite number of iterations. Also, due to the use of the interaction prediction principle, the solution of the problem of recalculating routes and the order of link resource allocation can be completed on an arbitrary iteration, and the resulting solution will be permissible and meet all the conditions and limitations.

In this paper, a method of inter-area routing in a telecommunications network based on the principles of Traffic Engineering is proposed. The method is based on a diakoptical approach that involves splitting a general routing problem into several routing over areas subtasks of lower dimensionality and complexity and then obtaining a generalized solution based on combining solutions obtained in individual areas. The application of the proposed method is focused on improvement of the scalability of routing solutions without losing their efficiency, which is evaluated by the upper threshold of network link utilization.

In this paper, we propose a How-based model and the hierarchical method of routing and resource allocation in DiffServ-TE network. This method is based on the interaction prediction principle due to a two-level functional hierarchy of calculation is organized in the method, and aimed at increasing their scalability and reducing computational complexity. At the lower level, the routing order is determined, and at the upper level, the link resource is allocated between flows with different classes of service. The numerical example confirms the convergence of the method to optimal solutions for a finite number of iterations. Also due to the use of the interaction prediction principle, the solution of the problem of route recalculation and the order of link resource allocation can be completed at an arbitrary iteration and the resulting solution will be acceptable and satisfy all the conditions and constraints.

In this paper, in order to increase the scalability of the communication network, a three-level method of hierarchical coordination routing in multi-area network is proposed, which is based on the principle of goal coordination. The method is based on the decomposition representation of the flow-based routing model and it includes three levels of the calculation hierarchy: at the zero level, the routing variables are calculated by the border routers of each area; at the first level, coordination of zero-level decisions is carried out to prevent congestion of communication links in each individual area, and the task of the second-level coordinator is to ensure inter-area interaction.

In this paper hierarchical method of load-balancing routing in MPLS network. Method identified tasks of two hierarchical levels: realization of source routing (lower level) and prevention of link overload in MPLS-network (upper level). Method oriented on procuring of Load-Balancing Routing in MPLS-network on principles of conceptions of Traffic Engineering. Modification of conditions of load balancing of links allows to reduce number of coordination iterations about 2 to 5 times which in practice will lead to a proportional decrease in the amount of service information circulating in the network associated with the implementation of hierarchical routing, as well as to increase the efficiency of network management in general.

The method of segment hierarchical coordination routing in multi-area network has been proposed. The method based on decomposed implementation of How-based model of inter-area routing and goal coordination principle. In this method on the lower level, there is the calculation of the routing variables, and on the upper level, there is the coordination of the solutions obtained from lower level for providing the connectivity of inter-area routes. The analysis of method convergence to optimal solutions of hierarchical routing was performed.

The paper proposes a method of hierarchical QoS routing based on reservation of network resources. It describes the case of organization of distributed source routing when one of the border routers consistently solves two interconnected network tasks: calculation of the required routes and determination of the allocation order of link resource to be reserved in order to meet end-to-end QoS-requirements for the packet rate and the average packet delay. It has been found that the method provides iterative calculation of the desired control variables; the number of such iterations depended on the network structure, amount of available network resources, the number of flows and their requirements for QoS level.

In this paper, in order to increase the scalability and fault-tolerance of routing solutions the hierarchical method of inter-area fast rerouting in communication networks was presented. The method is based on the decomposed representation of the flow-based routing model with the introduction of the area interaction conditions to ensure connectivity of the inter-area routes. The model includes conditions for border routers protection, adapted for both single path and multipath routing. During the research it was established that the efficiency of the proposed method in terms of the speed of the coordinating procedure convergence was most influenced by the number of border routers and the implemented routing strategy.

In this paper for the first time the mathematical model and the two-level method of fault-tolerant inter-domain routing in telecommunications networks was presented. The novelty of the model is its decomposed representation and formulation the inter-area interworking conditions. The implementation of these conditions guaranteed the connectivity of calculated inter-area paths. The research of the proposed method of hierarchical routing showed that on increase of the number of coordinating iterations is affect the network load, if it was accompanied by the implementation of multipath routing strategy, as well as increasing the number of border routers.