## 5 Experiments
### Discussion  
The Kernel Density Estimation is the best computation modeling approach of the three inference techniques we applied. For the JPEG Use-Case, the resulting execution time distribution is closest to the observed one using KDE. In most cases, the overall error of the average execution time is also smallest with the exception of experiment _JPEG-CA3_ where the Gaussian distribution leads to the lowest error. Table 2 shows that for the Sobel experiment, the Gaussian distribution is a bit better than the KDE approach when it comes \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Experiment** & **Measured** & \multicolumn{2}{c}{**CA Model**} & \multicolumn{2}{c}{**TL Model**} & \multicolumn{2}{c}{**ML Model**} & \multicolumn{2}{c}{**TL/ML Speed-up**} \\ \hline _Sobel-1-KDE_ & 0:07:40 & 0:03:12 & (2.40) & 0:03:04 & (2.50) & 0:01:44 & (4.42) & 1.77 \\ _Sobel-2-KDE_ & 0:07:03 & 0:12:32 & (0.56) & 0:05:05 & (1.39) & 0:02:11 & (3.23) & 2.33 \\ _Sobel-4-KDE_ & 0:07:13 & 0:20:00 & (0.36) & 0:05:21 & (1.35) & 0:02:18 & (3.14) & 2.33 \\ _Jpeg-1-KDE_ & 13:14:31 & 0:52:29 & (15.14) & 0:51:35 & (15.40) & 0:19:03 & (41.71) & 2.71 \\ _Jpeg-3-KDE_ & 5:12:58 & 67:31:00 & (0.08) & 1:20:56 & (3.87) & 0:23:41 & (13.22) & 3.42 \\ _Jpeg-7-KDE_ & 5:13:02 & 56:19:42 & (0.10) & 1:20:57 & (3.87) & 0:25:29 & (12.28) & 3.18 \\ \hline \hline \end{tabular}
\begin{tabular}{c} AMD OpteronTM Processor 6328 (3.5 GHz) at OFFIS e.V. www.offis.de, accessed on 24 May 2021. Simulation split into 16 processes, each on a dedicated processor. \\ \end{tabular}
\end{table} 
Table 3: Simulation time (HH:MM:SS) with Kernel Density Estimation computation model for 1,000,000 iterations. to similarity of the distribution function. Considering the overall error, the KDE approach is in many cases also slightly better for the Sobel use-case. For the ML model applying the KDE technique for the Sobel filter experiments _Sobel-MLx-KDE_, the analyzed results present a similar error as in the ML model applying the Gaussian Distribution. The Bhattacharyya distance in this experiment is much higher than in the ML model applying KDE. This can be explained because in the case of the \(GX\) and \(GY\) actors, their measured computation time were constant. However, the KDE technique created unexpected computation time for these actors. This led to variation in the iteration delay of the ML model KDE for Sobel filter application which made the Bhattacharyya distance higher. Our ML model applying the KDE technique for the JPEG decoder experiments also shows a very good level of accuracy to the measured data. Figure 7(a) compares all Bhattacharyya distances of the different experiments compared to their observed behavior, using different delay distributions for modeling the individual actors. For the more complex compute intensive JPEG decoder, applying a kernel density estimation leads to a much more accurate distribution of iteration delays compared to other inference techniques. For simple applications like the Sobel-Filter, a Gaussian distribution is more suitable. This is because its distribution of actor's computation delays is closer to the average delay, which is beneficial for actors with low variance in its execution time. Figure 7(b) shows that there is no significant change in accuracy regarding analyzing the average execution time between different distribution functions. Since the different inference techniques have also no influence to the simulation time, they are only relevant when the possible distribution function of the iterations of the application shall be analyzed. For only estimating the average execution time, the selection of communication model is more relevant. Table 2 shows that the communication model performs different depending on the amount of communicating tiles. For mappings with less communication, the Transaction Level (TL) model leads to the lowest error (Sobel, 2 Tiles and JPEG, 1 Tile). For the 1 Tile mapping of the Sobel Use-Case, the Cycle Accurate (CA) model is slightly better than the TL model.