## 6 Summary of Experimental Results  
In this section, the results of the experiments performed in this paper are summarized. Tables 1-4 compare the performance improvement rate of Python communication and C communication in the Host and four Docker Containers environments. Table 1 shows the ratio of DDR4 and MCDRAM communication times when performing Python buffer communication in Flat mode. Table 2 is a table comparing the performance of C communication in Flat mode. Tables 3 and 4 are tables comparing the experimental results in the four Docker Containers environment. Table 5 compares the communication time according to the Host environment and the increase of Docker Containers. Tables 6 and 7 compare the communication performance according to the Cluster mode. All experiments in the previous section increase the number of processes. However, in this summary, the communication time is compared in the number of processes with the best performance improvement. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **DDR4/MCDRAM (\%)** & **Number of Processes** \\ \hline Broadcast & 545 & 16 \\ Gather & 159 & 64 \\ AllReduce & 262 & 68 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of Python buffer communication time between Double Data Rate 4 (DDR4) and MCDRAM in Host environment (Flat mode). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **DDR4/MCDRAM (\%)** & **Number of Processes** \\ \hline Broadcast & 271 & 16 \\ Gather & 103 & 16 \\ AllReduce & 201 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of C communication time between DDR4 and MCDRAM in Host environment (Flat mode). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **DDR4/MCDRAM (\%)** & **Number of Processes** \\ \hline Broadcast & 202 & 68 \\ Gather & 131 & 64 \\ AllReduce & 217 & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of Python buffer communication time between DDR4 and MCDRAM in four Docker Containers environment (Flat mode). In Table 1, when Broadcast performed MPI collective communication with 16 processes, it was confirmed that MCDRAM performance improved 445% over DDR4. In addition, Gather improved the performance by 59% in 64 processes, and AllReduce confirmed performance improvement by 162% in 68 processes. As can be seen in Table 2, Broadcast showed 171% performance improvement in 16 processes, Gather showed 3% performance improvement in 16 processes, and, finally, AllReduce showed 101% performance improvement in 32 processes. From Tables 1 and 2, it can be confirmed that the rate of performance improvement in the same Host experiment environment is greater in Python buffer communication than in C communication. Similarly, in Tables 3 and 4, the Python buffer communication in the four Containers environment showed a higher performance improvement rate than with C communication. Table 5 shows the communication time results of Python buffer communication in 32 processes and MCDRAM in Flat mode. In Table 5, the Host environment and one Container show almost the same communication time. In addition, when the number of Containers increases, it can be seen that all collective communication time increases. In Table 5, it was confirmed that there was little difference in performance between Host and one Docker, as claimed by Docker. However, multiple Containers show relatively less efficient communication than communication in the Host environment. The experimental results in Tables 6 and 7 are the communication time results of the Python buffer communication in 68 processes and MCDRAM in Flat mode. In Tables 6 and 7, Quadrant mode and SNC-4 mode are similar, or SNC-4 mode shows slow communication time. This experimental result shows that the advantages of SNC-4 mode cannot be utilized. Due to the MPI communication feature, it seems that the advantages of SNC-4 mode cannot be utilized when the communication process is not in the same domain. As a result, in MPI communication, the Quadrant mode that can maintain transparency may be more efficient than the SNC-4 mode.