# A Reverse Shortest Path Tree-Based Multicast Joining Node Selection Method
## 4 Simulation
### Traffic Congestion Comparison  
In this experiment, we compared the traffic congestion of various methods. The degree of traffic congestion is an important indicator for evaluating MJN selection methods. Reasonable MJN selection methods can effectively reduce traffic congestion and improve multicast scalability. We use max link stress to measure traffic congestion. Max link stress refers to the number of multicast flows carried on the busiest link in the entire topology, measured in units of \"group\". Results are shown in Figure 5, It can be seen that RSPT, like WAVE, can effectively balance the traffic in the network. In the 200 and 2000-node topologies, RSPT and WAVE perform almost identically at certain times, with an average performance difference of less than 5%. This is because the diameter of these two topologies is 5 and 8, respectively, and each DR can explore a topology with a diameter of 6, allowing for the very precise exploration of most of the network. However, the detection of RSPT is not in real-time. In fact, during the experiment process, DR will only initiate a detection and update the cached network state after processing 30 join requests. This delay causes RSPT to not be able to perceive the network state in real-time like WAVE, which results in performance differences between RSPT and WAVE, even in small topologies. In the 200,000-node topology with a diameter of 16, and the 2 million-node topology with a diameter of 34, RSPT can only explore part of the topology with 6 or 8 hops, resulting in performance degradation. The impact of topology size on performance will be further analyzed later. Figure 4: Delay comparison. Moreover, in each topology, the performance of RSPT is far superior to SPT and Near. This is because RSPT can effectively detect the load on the multicast path, while Near and SPT cannot. SPT establishes a long forwarding path from the root node to the receiver, which cannot sense the network load status, and puts a heavy burden on the network due to the long multicast path. Although Near selects the nearest MJN, it also causes traffic congestion because it cannot sense the network load status. To demonstrate the impact of topology size on the performance of RSPT and WAVE, we compare the relative performance gap between the two on topologies of different sizes. Results are shown in Figure 6. To illustrate the gap between RSPT and WAVE, we defined the traffic gap index, that can be expressed by Formula (3). \[TrafficGap=\frac{ML_{RSPT}-ML_{WAVE}}{ML_{WAVE}} \tag{3}\]  
_ML_ represents the max link stress of the network. TrafficGap refers to the difference in traffic congestion level between RSPT and WAVE. As the traffic congestion level of RSPT has always been higher than that of WAVE, this index is greater than 0. The larger the value of this index, the more serious the traffic congestion of RSPT compared to WAVE, and the worse the performance relative to WAVE. The smaller the value, the more similar the traffic congestion level between RSPT and WAVE, and the closer their performance. Through Figure 6, we can observe that as the topology scale increases, the TrafficGap index also gradually increases. However, when the topology size reaches 2 million points, the TrafficGap index sharply drops. This is because as the topology grows, the proportion of the neighbourhood that RSPT can detect in the entire topology decreases, leading to the imprecise evaluation of path cost by DR. This increases the traffic load congestion of RSPT and also increases the traffic gap index. However, when the size of the topology reaches 2 million nodes, the detection radius of RSPT changes from 3 to 4 hops, and DR can perceive a larger range of the network, thereby reducing the traffic load congestion and causing a sudden drop in the traffic gap index. From Figure 6, we can also see that as the number of multicast group members increases, the TrafficGap gradually decreases.