# Maximizing the Capacity of Edge Networks with Multicasting
## 8 Simulation Results and Performance Evaluation
### Simulation Results  
Figure 3 plots the networks topology and the construction process of the multicast tree. In Figure 3a, one hundred SBSs and two hundred users are distributed according to the Poisson distribution intensity \(\lambda_{u}\) and \(\lambda_{e}\), respectively. Figure 3b,c show the proportional regional caching scheme, where the copy number 7 is used as an example. Figure 3d illustrates the construction process of the multicast. When one user (green dot) makes a content request, the adjacent SBS starts to request cooperation from the nearest SBS. When the SBS (small blue circle) of the content cache is found, the multicast transmission structure is established. The content is stored at the root node and starts being transmitted to the adjacent SBS with each branch. Then, if the requesting SBS is found, the transmission is stopped. Otherwise, the SBS that has received the content as the relay SBS continues to search for the most adjacent SBS and looks downstream for the transmission target until \begin{table}
\begin{tabular}{c c} \hline Simulation area & 100 \(\times\) 100 \\ \hline Number of SBSs & 100 \\ \hline Number of users & 200 \\ \hline \(\lambda_{e}\) & 10 \\ \hline \(\lambda_{u}\) & 20 \\ \hline Number of files & 5000 \\ \hline Buffer size of SBSs & 50 \\ \hline Communication range & 20 \\ \hline \end{tabular}
\end{table} 
Table 1: Initial settings of Parameters. the requesting SBS is found, and the transmission process stops. Here, to facilitate viewing, the fork number of the multicast tree is taken as  
Figure 4 shows the impact of the number of branches of the multicast tree on the capacity of the edge caching network. With an increase in \(k\), the network capacity of the two schemes shows a growing trend. Multicast can directly improve the network capacity by reducing the traffic load and shortening the transmission distance. However, in the case of the full \(k\)-ary tree, when \(k\) is greater than 25, the growth trend slows down and begins to decline. Note that the rapid increase in capacity is because the cooperative transmission between SBS has changed from one-to-one unicast communication to one-to-\(k\) multicast communication, so that SBSs can simultaneously transmit content to more adjacent SBSs, reducing the transmission distance of multi-path repeated transmission; however, when the number of SBSs is kept at a certain level and is larger than its reasonable range, the overall transmission distance is limited because it is transmitted to SBSs with a longer distance, which makes the capacity growth trend worse or even lower. For the multicast tree with only the last hop, the distance reduction through multicast is very limited. When \(k\) increases, although the network capacity can be improved, the improvement speed is low. In fact, it is for this reason that only the last hop multicast tree can steadily improve the network performance with an increase in \(k\). The number of content copies can directly affect the transmission distance of content. Figure 5 shows that when the number of content copies increases gradually, the network capacity can grow steadily. However, as the copy number increases, the growth rate of network capacity becomes slow, and the upper and lower bounds on capacity gradually approach and tend to be stable. The reason for this trend is that when the number of content copies becomes large, the number of SBS in each subarea is small, and users in the network can obtain the requested content in the adjacent SBS. There is no need to cooperate with the remote SBS. All requests can be completed in two hops, or even one hop. In this case, all the leaf nodes are close to the root node, and the advantage of multicast becomes limited. Figure 3: Constructing process of multicast tree. Figure 6 is the distribution diagram of the influence of the distribution intensity at the SBS on the network's capacity.