## 5 Numerical Research
### Investigation of the TER-LLM and TER-TEL Models  
At the first stage of research, the order of load balancing was compared, which was provided by the use of the two proposed optimality criteria (6) and (11) with the weighting coefficients (8) in the corresponding objective function. Thus, Figure 2 shows the dependence of the upper bound of the network link utilization \(\alpha\) on the packet flow intensities when using different models--TER-LLM and TER-TEL when \(\alpha_{TH}=0.7\). From Figure 2, it can be seen that at high values of flow intensities \(\lambda^{1}\) and \(\lambda^{2}\), the upper bound of the network links utilization stabilized at the level \(\alpha=\alpha_{TH}=0.7\), which is a  
Figure 1: Network structure under the numerical study. Figure 2: Dependencies of the network links utilization upper bound \(\alpha\) on the packet flow intensities when using weighting coefficients (8) in different models—TER-LLM and TER-TEL when \(\alpha_{TH}=0.7\), \(PR^{1}=5\), and \(PR^{2}=2\). common pattern for all types of studied models. However, the processes of limiting various types of packet flows, which differed in IP priorities and intensities, diverged significantly. Hence, Figure 3 for the TER-LLM model shows the dependencies of the fractions (\(\beta^{1}\) and \(\beta^{2}\)) and flow intensities (\(b^{1}\) and \(b^{2}\)) with which these packet flows will be limited (rejected) at the border router. If the fractions and flow intensities (\(\beta^{k}\) and \(b^{k}\)) were equal to zero, it means that the TE routing tools coped with the load entering the network. With a further increase in the network load, its resources, first of all, the bandwidth, were insufficient to ensure that constraint (5) was met at \(\alpha_{TH}=0.7\), so the load limitation process was initiated on the border routers. Figure 3 demonstrates that when using the TER-LLM model and weighting coefficients (8), the lower-priority second packet flow is limited more intensively. However, if the high-priority first flow is the source of the overload in terms of its intensity, then it will  
Figure 3: The procedure for limiting different packet flow types when using the TER-LLM model and weighting coefficients (8), when \(\alpha_{TH}=0.7\), \(PR^{1}=5\) 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. be limited in the first place without balancing. Therefore, both flow priorities and their intensities affect traffic limitations. Then, Figure 4 demonstrates the procedure for limiting different types of packet flows when using the TER-LLM model and weighting coefficients (8) when the difference in the IP priorities of the flows was maximal: \(PR^{1}=7\) and \(PR^{2}=0\). Figure 4 reveals that when the difference in IP priorities of flows increases, their limitation will minimally depend on flow intensities, and will be determined entirely by the ratio of IP priorities. The low-priority packet flow (\(PR^{2}=0\)) was more intensively limited in this case. The high-priority (first) packet flow was limited after the low-priority flow was completely limited, or when the intensity of the high-priority flow was a maximum (close to 900 pps) and the intensity of the low-priority flow was a minimum (close to 10 pps). Figure 4: The procedure for limiting different packet flow types when using the TER-LLM model and weighting coefficients (8), when \(\alpha_{TH}=0.7\), \(PR^{1}=7\), and \(PR^{2}=0\): (**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.