# Advanced Tensor Solution to the Problem of Inter-Domain Routing with Normalized Quality of Service
###### Abstract
In turn, the promising direction is the use of a concept of Software-Defined Networking in a Wide Area Network (SD-WAN) and multidomain SDN [4; 5; 10; 11; 12], the advantages of which are as follows:  
* Optimal utilization of network resource (bandwidth);
* Manageability aimed at reducing the cost of the network administration;
* Enhanced capabilities for providing network security;
* Flexibility and scalability when reallocating network bandwidth in differentiated service users flows, which should receive guaranteed network service;
* High performance of SD-WAN, which can be equated to MPLS networks. In turn, multidomain SDN must provide the interconnection of distinct SDN domains and interoperability between them through domain controllers [5]. Even though SDN offers flexibility in managing the flows inside a network, deploying a multidomain network increases its size and complexity. The other multidomain SDN challenge is concerned with the controller scalability factor. Usually, a logically centralized control plane consists of a set of distributed controllers, due to reliability issues. Moreover, such an approach allows for load balancing among controllers and reduces the controller's response time. However, synchronization mechanisms can cause network overload by the overhead. They must be adapted to improve scalability in line with load reduction regarding maintaining sufficient and consistent information about the controller's states. Additionally, the controller placement challenge is related to the number of controllers and their location influence on SDN performance [5]. Next, the corresponding communication protocol and coordination method between controllers, essential mechanisms in multidomain SDN, must be selected. Within the current work, a generalized architecture of hierarchical coordination inter-domain routing with normalized Quality of Service has the following components, as shown in Figure 1. First and foremost, it contains three planes: the data plane; the domain control plane, represented by a set of SDN controllers of the distinct domains; and the control plane with the central SDN controller. Here, the domain control plane optimizes inter-domain routing processes with normalized QoS. In addition, the upper-level control plane is responsible for routing metrics adjustment during multipath calculation. The data plane consists of SDN routers and domain border routers, e.g., SD-WAN routers. Figure 1: Generalized architecture of hierarchical coordination inter-domain routing with normalized Quality of Service. Therefore, the remainder of this article is structured as follows: Section 2 contains a research background in SDN-based inter-domain routing and provides an analysis of existing solutions. Section 3 proposes the decomposition model of inter-domain QoS routing in a communication network. Section 4 focuses on formulating conditions for ensuring end-to-end Quality of Service in a multidomain network. Section 5 is devoted to the method formulation of hierarchical coordination inter-domain routing in communication networks under a provision of normalized QoS. Section 6 contains the numerical research of the proposed hierarchical coordination SDN inter-domain routing method. Finally, Section 7 discusses the obtained research results, and Section 8 presents the conclusions of the work and directions for future investigations.