## 4 Experimental Evaluation  
In this section, we implement several schedulability tests and compare their performance through extensive simulations. In the first set of experiments, we demonstrate that BSF-EDF has the best schedulability. Then, we further verify that BSF-EDF schedules more task sets than the other two processor assignment strategies. Then, we find that as the proportion of fast processors increases, so does the proportion of the task set that the algorithm can schedule. We also compare the number of task migrations and effective processor utilization (EPU), where SSF-EDF performs best. We randomly generate various parameters on a performance asymmetric multiprocessor platform \(\pi\). The total number \(m\) of processors is randomly selected from a range of \([1,10]\). While satisfying \(q\leq m\), the number \(q\) of the slowest processors is also selected from the same range. The speed of the processor is randomly generated within \([1,10]\). Table 2 is the parameter range for each task. We generated \(10,000\) task sets, and each task set contained \(2(m+1)\) tasks. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Parameter Range** \\ \hline \(T_{i}\) & \(10\leq T_{i}\leq 100\) \\ \(D_{i}\) & \(\frac{D_{i}}{D_{i}}=T_{i}\) \\ \(E_{i}\) & \(0\leq E_{i}\leq 50\) and \(E_{i}\leq D_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Task parameters. Figure 3 shows that BSF-EDF performs better than FSF-EDF and SSF-EDF on four-core performance asymmetric multiprocessors. The results show that the schedulability of BSF-EDF is the highest for different system utilization cases. The \(X\)-axis represents the system utilization rate, and the system utilization rate is defined as \(U_{sum}/S_{m}\). When the system utilization rate reaches 40-50%, the task set that can be scheduled by the three processor allocation strategies begins to decrease. When the system utilization reaches 80-90%, BSF-EDF can still schedule up to 93% task sets, while the other two processor allocation strategies can only schedule 81.4% and 75.1% task sets. After this, the proportion that the algorithm can schedule decreases rapidly. When the system utilization reaches 90-100%, the three processor allocation strategies can only schedule 8.9%, 0%, and 0% task sets. Figure 4 shows the experimental results on seven-core performance asymmetric multiprocessors. When the system utilization is low, the three algorithms perform well. BSF-EDF performs better than the other two processor allocation strategies at high system utilization. When the system utilization reaches 80-90%, the BSF-EDF can schedule up to 88.9% of the task set, which is lower than the performance on four-core processors. However, it still schedules 10.5% and 20.8% more task sets than the other two processor allocation strategies. When the system utilization reaches 90-100%, the three processor allocation strategies can only schedule 8.7%, 0%, and 0% task sets. Figure 4: Performance comparison of BSF, FSF, and SSF under different system utilization values (\(m=7\)). Figure 3: Performance comparison of BSF, FSF, and SSF under different system utilization values (\(m=4\)). When \(m=10\), the experiment further verifies the leading position of BSF-EDF. In Figure 5, BSF-EDF outperforms the other two processor allocation strategies at high system utilization. When the system utilization reaches 80-90%, the BSF-EDF can schedule 82.6% of the task set, which is lower than the performance on seven-core processors. However, it still schedules 9.8% and 29.5% more task sets than the other two processor allocation strategies. When the system utilization reaches 90-100%, the three processor allocation strategies can only schedule 8.3%, 0%, and 0% task sets. In the first set of simulation experiments, we did not limit the number of high-utilization tasks in the task set, and the data were generated randomly. Now, we limit the proportion of high-utilization tasks in the task set, in which we define high-utilization tasks as a utilization rate of 80-100%.