# DAG Hierarchical Schedulability Analysis for Avionics Hypervisor in Multicore Processors
## 6 Results
### Evaluations
#### 6.1.2 Usefulness of The Proposed Schedulability  
The proposed algorithm is compared with the advanced joint-level priority allocation method (namely He2019). In short, it is proved that the WC achieves maximum CT considering priority allocation. The goal is to prove the WC He2019 of improvement, grouped by the numeral of processors \(m\), \(p=8\), \"?\" means beat the market. Scenarios are realized through priority allocation. Overall, 1000 random task sets will be generated under every configuration. This evaluation compares two indicators: (i) time suggested rta-cpf-eo is more than the comparison algorithm, (ii) the latency of standardized CT in the improvement cases. Figure 9 shows the extended comparison between the proposed ranking algorithm and the algorithm in He2019 in the case of different numerals of processors. The frequency denotes the number of cases where the proposed timetable is red or blue. The WC maximum CT analysis for explicit orders is applicable to both orders, so the performance difference comes from the order strategy. From the results, the proposed algorithm is generally superior to it at higher frequencies, especially in the case of a small numeral of cores, for example, in the case of \(m=2\) near the frequency of 600. With the increase of \(m\), the frequency difference of the method gradually decreases, and it becomes difficult to distinguish when \(m=8\). In these cases, most joints can execute in parallel, so the influence of different sequences on the final maximum CT becomes less significant. Figure 8: Sensitivity of CP ratio (\(m=4\), \(p=8\)). Figure 7: Sensitivity of parallelism parameter (\(m=4\)). Table 1 compares the advantages of the two algorithms in detail, expressed as a percentage. For EO > He2019 (that is, the proposed schedule is better than it), the average optimization was observed (in terms of the WC maximum CT) is higher than 5.42% (as high as 7.88%) in all cases. In the case of EO < He2019, the optimization is always lower than that of EO > He2019. Table 2 shows the number of advantageous cases and the scientific significance of improvement, He2019 > EO, He2019 < EO. The values in Table 2 are category values to report its importance. Namely, the importance determines if any difference is more than random, and the size of the difference. The data column illustrates the number of times that an algorithm has a lower CT than another. As far as all of the circumstances are concerned, the algorithm is superior to the most advanced algorithm. This order of magnitude further proves the advantages of our algorithm. For example, when \(m=4\), when EO is superior to He2019, the effect size is medium, but when He2019 is superior to EO, the effect size is small; For \(m=8\), even if data have similar values, the effect size is small and can be ignored. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**He2019 \textgreater{} EO**} \\ \hline
**Core (\(m\))** & **Min.** & **Avg.** & **Max.** \\ \hline
2 & 0.05 & 7.88 & 30.62 \\
4 & 0.02 & 7.20 & 33.38 \\
8 & 0.03 & 5.42 & 25.28 \\ \hline  & \multicolumn{2}{c}{**He2019 \textless{} EO**} \\ \hline
**Core (\(m\))** & **Min.** & **Avg.** & **Max.** \\ \hline
2 & 0.01 & 6.48 & 30.67 \\
4 & 0.02 & 4.54 & 23.84 \\
8 & 0.03 & 1.64 & 19.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Advantage: percentage of improvement in joint ordering policy. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Core (\(m\))** & **Data** & **Dataset** \\ \hline
2 & 262 & He2019 \textgreater{} EO \\
670 & He2019 \textless{} EO \\ \hline
4 & 275 & He2019 \textgreater{} EO \\
451 & He2019 \textless{} EO \\ \hline
8 & 184 & He2019 \textgreater{} EO \\
191 & He2019 \textless{} EO \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The joint-level priority allocation realized in (\(\alpha\), \(\beta\)). Figure 9: Compare priority sorting with sorting in He2019. Similarly, by applying the same ranking to the two methods, we compared our analysis with that in He2019, and found consistent results.