# The Design and Implementation of a Novel Open Source Massive Deployment System
## 5 Discussion  
### Performance of Massive Deployment by Using Local Connection  
The speedup, \(S\), for the first experiment is defined as:  
\[S=\frac{T_{s}}{T_{p}} \tag{1}\]  
where \(T_{s}\) is the time to deploy multiple USB flash drives in sequence and \(T_{p}\) is the time to deploy multiple USB flash drives in parallel.  
When an image of size \(D\) is deployed to \(n\) USB flash drives in parallel on a machine, the bandwidth of the USB bus is \(B_{w}\), and the writing rate for each flash drive is \(H_{w}\). The total deployment time \(T_{n}\) can be formulated as:  
\[T_{n}=Max\left[\frac{D\times n}{B_{w}},\frac{D\times n}{H_{w}\times n}\right] =D\times n\frac{1}{Min[B_{w},H_{w}\times n]} \tag{2}\]  
where \(Max\) and \(Min\) are the maximum and minimum functions, respectively.  
When \(n\leq B_{w}/H_{w}\), \(T_{n}=D/H_{w}\), but when \(n>B_{w}/H_{w}\), \(T_{n}=D\times n/B_{w}\). Thus, the speedup, \(S\), can be formulated as:  
\[S=\left\{\begin{array}{c}\frac{\frac{D}{H_{w}}}{H_{w}\times\frac{1}{n}}=n,n \leq\frac{B_{w}}{H_{w}}\\ \frac{H_{w}}{B_{w}}\frac{1}{H_{w}}=\frac{B_{w}}{H_{w}},n>\frac{B_{w}}{H_{w}} \end{array}\right. \tag{3}\]  
Therefore, from Equation (3), \(Bw/Hw\) is the key factor to judge the speedup for massive deployment by using the local connection. In theory, the maximum transfer rate of the USB 2.0 is 480 Mb/s. From Figure 5a, the average writing rates for Types 1 and 2 flash drives were 9.2 MB/s and 4.1 MB/s, respectively. For the two types of USB flash drives, the ratio of the bandwidth to the writing rate is demonstrated in Table 3. For the Type 1 flash drives, when the number of drives was less than 4, the speedup increased almost linearly. When the number of drives was more than 6, the speedup increased more slowly. When the number of drives was more than 10, the speedups were almost the same, which was about 5. For Type 2 flash drives, when the number of drives was less than 10, the speedup increased almost linearly. When the number of drives was more than 16, the speedup is almost the same, which was about 10 to 11. The number of the total USB flash drives versus the speedup for each configuration is illustrated in Figure 8. Due to the overhead during the system deployment, including the USB bus constraints, the time to create the partition table, and the time to install the boot loader on the flash drives, the theoretic ratio of bandwidth to the writing rate \(Bw/Hw\) being demonstrated in Table 3 cannot match the experimental values in Figure 8 exactly when checking Equation (3). Nevertheless, the trend matches well between the theory and experiments, since for both Types 1 and 2, when the number of drives being deployed \"\(n\)\" is smaller than \(Bw/Hw\), the speedup values that were obtained in the experiments increased almost linearly. Conversely, the speedup values obtained in the experiments became almost the same, which are roughly the value of \(Bw/Hw\) when the number of drives being deployed \"\(n\)\" is larger than \(Bw/Hw\).  
\begin{table}
\begin{tabular}{c c c c} \hline
**USB Type** & \(B_{w}\) **(MB/s)** & \(H_{w}\) **(MB/s)** & \(B_{w}\)/\(H_{w}\) \\ \hline Type 1 & 60.0 (in theory) & 9.2 & 6.5 \\ Type 2 & 60.0 (in theory) & 4.1 & 14.3 \\ \hline \end{tabular}
\end{table}
Table 3: The ratio of bandwidth to the writing rate.