# Schedulability Analysis in Fixed-Priority Real-Time Multicore Systems with Contention
## 5 Evaluation
### Simulations with Synthetic Workload  
In this section, we present the evaluation of the proposed schedulability test with a synthetic load in an experimental environment, as depicted in Figure 6. First, the load was generated. Then, for each task set, the scheduling problem was solved. Finally, the results were validated to evaluate some parameters. In parallel, the proposed schedulability test was applied to the task sets, and all results were compared. Let us explain each of these steps. We used the same synthetic task generator as in [9] with the experimental parameters defined in Table 4.  
With the total system utilization and a specified number of tasks for each set, the utilization was distributed among the tasks by using the UUniFast discard algorithm from [32]. Periods were randomly generated within the range [20, 1000], and computation times were determined based on system utilization. Deadlines were constrained to be less than or equal to periods, and they were set to \(D_{i}\in[0.5T_{i},T_{i}]\). The theoretical utilization ranges from 50 and 75% of the system's maximum potential load. For instance, the maximum load of a system with eight cores is 8; so, for evaluation purposes, the initial utilization was set to the range 4.1 (\(\approx\)50%) to 6 (75%). Figure 6: Experimental simulation. The number of broadcasting tasks was configured to be 25% of the total number of tasks, except for scenarios 1-6 (two cores), where it was set to 50%. In the latter case, if only one task is a broadcasting task, no interference is generated. We evaluated every combination of core count and utilization by testing interference levels of 10%, 20%, and 30% relative to the WCET. It is important to note that not all tasks in a task set have the same interference value, but they all experience the same percentage of interference with the WCET. Once the load was generated, to solve the scheduling problem, tasks were allocated to cores by different algorithms. On the one hand, we considered bin-packing algorithms such as Worst Fit (WF) and First Fit (FF) [7,8] to allocate the tasks to cores. Tasks are ordered in descending order of utilization (DU). On the other hand, the interference-aware Wmin algorithm [4] assigns tasks to cores aiming to reduce contention. Following the task allocation phase, we now move to the task scheduling phase. For this purpose, we employed the contention-aware scheduling algorithm, as also proposed in [4]. Specifically, we chose Deadline Monotonic (DM) as the priority-based algorithm serving as the basis for this scheduling approach. Next, the obtained scheduling plans were evaluated, and different parameters were measured (validation phase). In this case, we focused on measuring the response times of the activations of the tasks. Independently of the above, the schedulability test stated in Theorem 2 was applied to the task sets. This was compared with the results obtained in the validation phase. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Number** \\ **of Cores** \\ \end{tabular}  & **Utilization** & **Tasks** & \begin{tabular}{c} **Broadcasting** \\ **Tasks** \\ \end{tabular}  & \ \begin{tabular}{c} **Interference** \\ **with** \\ **WCET (\%)** \\ \end{tabular}  & \begin{tabular}{c} **Scenario** \\ \end{tabular}  \\ \hline \multirow{4}{*}{2} & 1.1 & & & & 10 & 1 \\  & 1.1 & & & & 20 & 2 \\  & 1.5 & & & & 30 & 3 \\  & 2.4 & & & & 20 & 5 \\  & 3 & & & & 30 & 6 \\ \hline \multirow{4}{*}{4} & 2.4 & & & & 10 & 7 \\  & 2.4 & & & & 20 & 8 \\  & & 12 & & 3 & 30 & 9 \\  & 3 & & & & 10 & 10 \\  & 3 & & & & 20 & 11 \\  & 3 & & & & 30 & 12 \\ \hline \multirow{4}{*}{6} & 3.1 & & & & 10 & 13 \\  & 3.1 & & & & 20 & 14 \\  & 3.0 & & & & 30 & 15 \\  & 3.1 & & & & 10 & 16 \\  & 4.5 & & & & 20 & 17 \\  & & & & & 30 & 18 \\ \hline \multirow{4}{*}{8} & 4.1 & & & & 1  
Figure 7 shows the actual schedulability rates measured in the validation phase. As expected, when the number of cores and broadcasting tasks increased, the percentage of schedulability decreased.