## 5 Experiments
### Results  
In this section, we present the results of the experiments considering different criteria: accuracy, analysis time, and scalability. First we present the impact of the different computation abstraction: Kernel Density Estimation (KDE), Gaussian Distribution (Gauss) and Average execution time (Avg). Then we aim to demonstrate the validation of our proposed communication models by comparing the average iteration delay of our Message Level (ML) model with the Transaction Level (TL) model, the Cycle Accurate (CL) model and the measured data. In Table 2, we compare the analyzed results of the CA model, TL model and ML model with the measured data. In the first column (_Experiment_), the experiments are listed. The second column (_Measured_) presents the average execution time in clock cycles of 1,000,000 iterations. This is the observed measured execution time of the application on a real hardware platform. The next three columns _Average_, _Gaussian_ and _KDE_ show the results of the simulation using different inference techniques: The average computation time of an actor, a fitted Gaussian distribution of possible delays, and a fitted distribution using kernel density estimation. In parentheses, the error in percent (first number) compared to the measured delay is shown, as well as the Bhattacharyya distance [31] (second number) of the analyzed distribution of possible execution times compared to the distribution of measured execution times. The error represents the difference between the average execution time \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Experiment\(\rightarrow\)** & _Jpeg1_ & _Jpeg3_ & _Jpeg7_ & \(\text{Exp.}\rightarrow\) & _Sobel1_ & _Sobel2_ & _Sobel4_ \\
**Actor \(\downarrow\)** & & & & & Actor \(\downarrow\) & & & \\ \hline _Get MCU_ & 0 & 0 & 0 & _GetPixel_ & 0 & 1 & 1 \\ _IQ\({}_{Y}\)_ & 0 & 1 & 1 & _GX_ & 0 & 2 & 2 \\ _IQ\({}_{Cr}\)_ & 0 & 1 & 2 & _GY_ & 0 & 1 & 3 \\ _IQ\({}_{Cb}\)_ & 0 & 1 & 3 & _ABS_ & 0 & 2 & 0 \\ _IDCT\({}_{Y}\)_ & 0 & 4 & 4 & & & & \\ _IDCT\({}_{Cr}\)_ & 0 & 4 & 5 & & & & \\ _IDCT\({}_{Cb}\)_ & 0 & 4 & 6 & & & & \\ _YCrb RGB_ & 0 & 0 & 0 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mapping of the Sobel and JPEG experiments on the tiles of the hardware platform. Cp. [2]. Figure 6: Overview of all experiments done using different computation and communication performance models. Experiments that challenge our approach are highlighted in blue and will be discussed in detail. for all iterations. The Bhattacharyya distance shows the similarity between the distribution of the execution times (lower value is better). For all experiments, the Bhattacharyya distance between the simulated distribution of execution times and the observed distribution is within a range of 3.388 for _Sobel-ML/TL1-Avg_ and 0.059 for _JPEG-ML1-KDE_. The JPEG use case with less communication relative to its computation times has a much lower Bhattacharyya distance compared to the Sobel experiments for all computation models. The less influences the communication has, the closer comes the analyzed distribution to the observed one. The communication heavy Sobel application analysis shows higher similarities in its distribution with the Gaussian distribution of computation delays. The simulated distribution of the computation heavy JPEG use-case is best with the kernel density estimation inference technique. The experiments using our ML communication model show a high accuracy result that over-approximate the measured data. The error is within a range of 4.7% for _Sobel-ML2-Avg_ and 0.01% for _JPEG-ML7-Avg/KDE_. The TL communication model leads to errors within the range of \(-5.12\%\) for _Sobel-TL4-KDE_ to 0.11% for _Sobel-TL2-KDE_. All JPEG decoder experiments using the TL communication model show very low errors with the highest value of \(-1.47\%\) for _JPEG-TL7-Avg/KDE_. Compared to this, the Cycle Accurate (CA) model leads to relative high errors of up to 1.57% for _JPEG-CA3_. For the _Sobel-CA4_ experiments the error is up to 49.69%.