## 5 Numerical Research
### Investigation of the OSPF-TS Model  
To analyze the proposed models' effectiveness, we compared them with a model based on known technological solutions. It was taken into account that firstly, in practice, for example, in IP networks, decisions to limit traffic on border routers, unfortunately, are not coordinated with routing decisions in any way. Secondly, IP routing protocols cannot guarantee the maximum level of the network and its links utilization. Thirdly, traffic shaping (TS) mechanisms equalize and limit traffic according to the previously agreed rate of packets entering the network through mostly static settings.  
Therefore, the _OSPF-TS_ model was chosen for the compared technological solution, based on reasonably common traffic management tools in IP networks--the OSPF routing  
Figure 8: The procedure for limiting different packet flow types when using the TER-TEL model and weighting coefficients (9), 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.  
protocol and the traffic shaping mechanism at the network edge [1]. The OSPF IP routing protocol supported uniform load balancing along paths with the same metric, influenced by the number of links in the route and their bandwidth. The traffic shaping mechanism limited the intensity of the aggregated flow to ensure that condition (5) was met.  
As shown by the study results of the selected network topology (Figure 1), the use of the OSPF protocol functionality, its routing metrics, and balancing schemes has led to a change in the utilization of communication links and the network as a whole (Figure 9). Compared to Figure 2, the changes concerned the value of the total load when the link utilization reached the threshold level \(\alpha_{TH}=0.7\). When using the TER-LLM and TER-TEL models, traffic limitation began at a network load of 760 pps, whereas when using the OSPF-TS model, the limitation began much earlier, at a lower network load of 320 pps. Consequently, balancing based on the principles of traffic engineering within the TER-LLM and TER-TEL models was more effective than load balancing using the OSPF protocol. This made it possible to increase the network performance (the amount of load served without failures) by almost 2.4 times, subject to condition (5).  
The application of traffic shaping led to a uniform intensity limitation of the analyzed packet flows entering the network (Figure 10). The limitation uniformity was manifested in the fact that for both flows, the proportions of their intensities that received a denial of service (\(\beta^{1}\) and \(\beta^{2}\)) were always the same (Figure 10a,b) because traffic shaping worked with the aggregated packet flow, and the limitation rates differed (Figure 10c,d). Thus, it can be concluded that when using the OSPF-TS model for load balancing, its key characteristics (neither priority nor intensity) were taken into account, which in practice leads to ignoring the requirements for DiffServ and localization of the overload source.  
Figure 9: Dependencies of the network links utilization upper bound \(\alpha\) on the packet flow intensities when using OSPF-TS model, when \(\alpha_{TH}=0.7\), \(PR^{1}=5\), and \(PR^{2}=2\).