# A Reverse Shortest Path Tree-Based Multicast Joining Node Selection Method
## 4 Simulation
### The Comparison of the Control Message Numbers  
In this section, we compared the average number of control messages required for each algorithm to establish a multicast tree. As the number of control messages increases, the network burden becomes heavier, making this indicator very important. In the RSPT algorithm, the DR sends a request to the leaf nodes every certain period, which is set to send a request every time the DR processes 30 new multicast group members. In the WAVE algorithm, DR needs to detect all nodes in the multicast tree whenever a new group member joins. Therefore, we can anticipate that the control message count in RSPT will be much lower than that of WAVE. In contrast, the Near and SPT methods do not require any control message, so their control message count is zero.  
In the left graph of Figure 3, we compared the control message counts of different algorithms in topologies of different sizes. Firstly, as the topology expands, the control message count gradually increases. The reason is that for the WAVE algorithm, as the topology grows, the size of the multicast tree also increases, and DR needs to probe more nodes; thus, the control message count gradually increases. For the RSPT algorithm, the larger the topology, the more nodes covered by DR neighbours, so the control message count also increases accordingly. In the topologies of 200, 2k, and 200k nodes, their diameters are 6, 8, and 13, respectively, and the DR's probing diameter is 6. According to statistics,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Topology** & **Waxman200** & **Waxman2000** & **Waxman200k** & **Waxman2000k** \\ \hline DR Number & 20 & 200 & 2000 & 4000 \\ Group Size & 6 & 20 & 200 & 400 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Traffic generation model.  
in these three topologies, the average number of nodes probed by DR is 134, 623, and 932, respectively. In the topology of 2 million nodes, the DR's probing diameter expands to 4, so the number of probed nodes will increase significantly, with an average of 6789 nodes probed. In summary, for RSPT, the larger the topology, the more nodes DR needs to probe, and the more control messages are required. Secondly, we can see that the control message count of RSPT is about one-tenth to one-hundredth of that of WAVE, and the cost brought by RSPT to the network is much lower than that of WAVE.  
In the right graph of Figure 3, we compared the number of control messages for various algorithms in a topology with 2 million nodes. When each multicast group has 200 members, the number of control messages for RSPT is only 6034, while for WAVE it is 80,096, which is 7.5% of WAVE. As the number of group members increases, the number of control messages for WAVE gradually increases, while for RSPT it remains constant, eventually accounting for only about 1% of WAVE. The reason why RSPT can maintain the same number of control messages is that RSPT only detects the neighbourhood of DR, and its detection behaviour is not related to the size of the multicast tree. However, WAVE must detect the entire multicast tree. Therefore, as the number of group members increases and the multicast tree becomes larger, the number of control messages for WAVE will gradually increase.  
The control messages of RSPT will not impose a heavy burden on the network. The control message payload of RSPT is relatively small, only about 20 bytes, and the sending period is relatively long. In this experiment, DR triggers a detection only after processing 30 multicast group requests, which takes about 10 s. Therefore, the bandwidth occupied by RSPT's control message is below 1 Kb/s. In contrast, WAVE's bandwidth usage can reach over 100 times that of RSPT, reaching the 1 Mb/s level. When the bandwidth usage of each multicast stream is in the Mb/s range, WAVE's control message bandwidth usage will impose a significant burden on the bandwidth and network devices, while RSPT will not.  
In short, RSPT is a cost-effective method.