## 5 Discussion
### Performance of Massive Deployment by the Proposed BT Solution  
According to the authors' earlier definition [34], the speedup of the massive deployment for a large number of computers is the ratio of time required to deploy multiple computers in sequence versus the time required to deploy multiple computers by the BT or multicast solution. Figure 11 demonstrates the speedup measured in the experimental environments consisting of one to 32 clients. Table 4 further summarizes the speedup for the BT and multicast solutions. As the authors assumed no overhead for the ideal case in the massive deployments, the speedup increases linearly as the number of client machines increases. However, in the real world, the speedup becomes smaller as more computers are deployed using the BT or multicast solution. Compared to the multicast solution, the speedup of the BT solution increases as more computers are deployed (see Figure 10a and Table 4). As the number of clients increases, the speedup ratio of the BT-based solution to the multicast-based one also increases. When deploying 32 machines, which was the largest number in the experiment, the ratio hit 1.927, which means that the BT-based mass deployment solution proposed in this research can enhance the performance by about two times that of the traditional multicast solution in the experimental environment. In Figure 10a, when there is only one client machine, the time to complete the deployment is the shortest in the BT-based solution. In this case, there is only one seeder (image repository server), so it is dedicated to serving the only client. However, when there are two or more client machines to be deployed, the available system resource and network bandwidth from the image repository server will be shared; hence, the performance decreases temporarily before the number of client machines can increase to a large enough number. Nevertheless, as the number of client machines grows large \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Client(s)** & **SFBT** & **SFMC** & **SRBTMC** & **Time-Saving Ratio (\%)** & **LOOCV (\%)** \\ \hline  
\hline \hline \end{tabular} Remarks: (1) SFBT means the speedup factors for mass deployment using the BT solution; (2) SFMC means the speedup factors for deployment using the multicast solution; (3) SRBTMC means the speedup ratio of the BT solution to that of the multicast one.  
\end{table} 
Table 4: _Cont._enough, the merit of the BT solution is shown in Figure 10a; that is, the more peers that join the swarm, the more the access speed and availability increases, thereby contributing to the overall provisioning performance [90]. In addition, Figure 10a shows that the total time required by the BT solution is almost constant when the number of client machines is equal to or more than 10. In the BT-based solution, the available service capacity grows exponentially with time [91]. Hence, the total time required to complete the download tasks will be shortened. In the ideal case, assume that no bottlenecks exist in the CPUs, RAMs, or network(s). Meanwhile, no disk errors happen while reading or writing data. If the BT connections among all of the peers are in the topology of a complete tree-typed network [92; 93] with \(n\) nodes, where the degree of each node is defined as \(c\). Here, the degree of some specific node means that the number of connections of the node to other nodes. Assume that the child node does not send data to the parent node, and the nodes in the same level of the tree do not send data to each other; then, the total number of peers (\(n\)) can be formulated as [91]:  
\[n=\sum_{i=0}^{l}c^{i} \tag{1}\]  
where \(c^{i}\) is the capacity of service in the \(i\)th level of the tree, and \(l\) is the total number of levels in the tree. As only the leaf nodes in the tree cannot provide data in the BT-based solution, the total number of nodes in the tree that can provide the data is \(n-c^{l}\). \(n-c^{l}\) can be expressed as \((n-1)/c\).