## 5 Numerical Research
### Investigation of the TER-LLM and TER-TEL Models
Conversely, when the flows' IP priorities were almost the same (\(PR^{1}=4\) and \(PR^{2}=3\)), the differentiation in limitation was determined only by their intensities (Figure 5), i.e., whichever flow had a higher intensity, it was restricted more strongly. When using the TER-TEL model and weighting coefficients (8), the order of traffic limitation is presented in Figure 6. In this way, limiting the load entering the network was more balanced than when using the TER-LLM model (Figure 6), but also considering both flows' IP priorities and intensities. In the present case, when the network was overloaded, both flows were limited at the network edge at once. However, the flow of packets with a higher intensity (i.e., its contribution to the overload was more significant) and a lower IP priority was limited more. Figure 5: The procedure for limiting different packet flow types when using the TER-LLM model and weighting coefficients (8), when \(\alpha_{TH}=0.7\), \(PR^{1}=4\), and \(PR^{2}=3\): (**a**) the proportion of the first flow intensity that receives a denial of service; (**b**) the proportion of the second flow intensity that receives a denial of service; (**c**) the limitation intensity of the first flow at the border router; (**d**) the limitation intensity of the second flow at the border router. The load balancing order was again compared at the second research stage. It was provided under the application of the two proposed optimality criteria (6) and (11), but with weighting coefficients (9) for the TER-LLM and TER-TEL solutions. At the same time, the dependence character of the upper bound of the network link utilization on the packet flows' intensities when using different models, TER-LLM and TER-TEL, with weighting coefficients (9), when \(\alpha_{TH}=0.7\), \(PR^{1}=5\), and \(PR^{2}=2\), entirely coincides with Figure 2. However, the nature of failures when using weighting coefficients (9) was significantly different (Figures 7 and 8) from the results obtained when using weighting coefficients (8) in optimality criteria (6) and (11). Figure 7 for the TER-LLM model indicates the procedure for limiting the load in the network using weighting coefficients (9). Figure 7 shows that using the TER-LLM model and weighting coefficients (9) leads to the primary limitation of low-priority flows (\(PR^{2}=2\)). Only when the low-priority flow is wholly blocked will the higher-priority flow  
Figure 6: The procedure for limiting different packet flow types when using the TER-TEL model and weighting coefficients (8), when \(\alpha_{TH}=0.7\), \(PR^{1}=5\), and \(PR^{2}=2\): (**a**) the proportion of the first flow intensity that receives a denial of service; (**b**) the proportion of the second flow intensity that receives a denial of service; (**c**) the limitation intensity of the first flow at the border router; (**d**) the limitation intensity of the second flow at the border router. (\(PR^{1}=5\)) begin to be limited. Thus, within the TER-LLM solution, balancing is supported only within the network when solving routing problems, and balancing is not supported when limiting the load. Figure 8, as an example, demonstrates the research results on the TER-TEL model. As shown in Figure 8, the limitations of different types of flows are carried out in a balanced way, considering only their priorities. In the case of overload, the low-priority flow (\(PR^{2}=2\)) was more intensively limited, and the high-priority flow (\(PR^{1}=5\)) was restricted, but less intensively. In contrast to the use of weighting coefficients (8), in this case, the flow intensity does not significantly affect the order of traffic limitation. That is, the identification of the overload source is not supported.