## 7 Conclusions  
The study substantiates the current scientific problem of load balancing process optimization in the network. It is noted that an effective mechanism for balancing the load in the network is the implementation of traffic engineering concept principles to ensure the effective use of the available network resource, first of all, the bandwidth of communication links. That is why, in theory and practice, mathematical and protocol solutions related to implementing traffic engineering routing, queuing, etc., are increasingly proposed and implemented. It is essential to ensure the predictability of the QoS level and manageability following traffic engineering requirements, routing processes, and load limitation at the network edge. Therefore, appropriate mathematical models and methods should be developed, which are the basis of any communication protocol, to adequately describe the abovementioned network processes. Thus, this research proposed mathematical optimization models (1)-(5) and (10), which, depending on the selected type of optimality criterion (6) or (11), received two modifications: TER-LLM and TER-TEL. Each of these modifications aims to provide solutions for load balancing within the traffic routing and rate limitation problems, based on different principles related to the flow parameters consideration. During the research, a comparative analysis of the proposed solutions TER-LLM and TER-TEL (Figures 2-8) was carried out for different variants of the initial data regarding the ratio of the flows' parameters served by the network. A system of recommendations is presented related to the preferential use of the proposed solutions under their features and advantages. Thus, it was established that the TER-LLM solution is better for servicing packet flows based on the so-called absolute priorities when low-priority flows are first limited. The TER-TEL solution is recommended for balanced flow limitation based on flow priorities and their rates. Thus, considering IP priorities, precisely those flows that directly create overload in the network are more intensively limited. The comparison results indicate that the solution of routing and load balancing problems coordinated on the principles of traffic engineering, represented by the TER-LLM and TER-TEL models, will significantly improve network performance. In the example shown in Figure 1, compared to the OSPF-TS model, it was possible to increase the performance (the amount of traffic served without limitations) by almost 2.4 times. In contrast to the OSPF-TS model, the proposed solutions for network overload allowed differential traffic limitation, considering such key packet flow characteristics as their intensities and priorities. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Flow Intensity**} & \multicolumn{4}{c}{**OSPF-TS**} \\ \hline \(\mathbf{\lambda^{1}}\) & \(\mathbf{\lambda^{2}}\) & \(\mathbf{\beta^{1}}\) & \(\mathbf{b^{1}}\) & \(\mathbf{\beta^{2}}\) & \(\mathbf{b^{2}}\) \\ \hline
850 & 50 & 0.1444 & 122,778 & 0.1444 & 7222 \\
450 & 450 & 0.1444 & 65 & 0.1444 & 65 \\
900 & 900 & 0.5722 & 515 & 0.5722 & 515 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Traffic limitation under \(\varpi_{TH}=0.7\), \(PR^{1}=5\), and \(PR^{2}=2\) for OSPF-TS model. This fits into the DiffServ paradigm and ensures the localization of the overload source, if necessary. When the upper bound of the network links utilization increases, it is worth switching to a nonlinear flow-based network model, for example, as described in [31]. Due to tensor generalization, it considers the packet loss probability at network routers. Such an approach analyzes and calculates network performance, average end-to-end delays, and packet loss probabilities. This option is proposed as a direction for further development of the solution obtained in this research.