# Schedulability Analysis in Fixed-Priority Real-Time Multicore Systems with Contention
## 6 Conclusions  
This paper proposes a schedulability assessment utilizing worst-case response time analysis for hard real-time multicore systems. This analysis assumes fixed-priority and constrained-deadline task models. We assume a general model in which interference is a temporal parameter for each task. In other works, schedulability analysis has previously been proposed for this model for dynamic priorities but did not exist for fixed priorities. With this work, we complete the schedulability analysis of the general interference model proposed in [4]. The proposed test is sufficient, as it is an upper bound of the response time of task sets allocated in multicore systems, where tasks suffer from contention with other tasks running simultaneously in other cores. The test was tested with simulations with synthetic workloads and simulations on a real platform.  
As future work, we would like to explore how to expand our work into the areas of power consumption and interference reduction. To tackle the consumption problem, frequency reduction in idle instants of time might be a feasible approximation. Also, incorporating the modeling of the consumption of each task in the scheduling phase could lead  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**(a) Measured \(WCRT\)**} \\ \hline  & \multicolumn{4}{c}{**Activation k**} \\ \hline  & **0** & **1** & **2** & **3** \\ \(\tau_{0}\) & 55.707 & 59.031 & 55.704 & 55.713 \\ \(\tau_{1}\) & 10.0023 & 10.00231 & 10.00231 & 10.00231 \\ \(\tau_{2}\) & 60.688 & 50.4036 & 50.3931 & - \\ \(\tau_{3}\) & 81.0023 & 81.0021 & 81.0021 & - \\ \hline  & \multicolumn{4}{c}{**(b) \(WCRT^{ub}\)**} \\ \hline  & \multicolumn{4}{c}{**Activation k**} \\ \hline  & **0** & **1** & **2** & **3** \\ \(\tau_{0}\) & 57 & 62 & 62 & 57 \\ \(\tau_{1}\) & 11 & 11 & 11 & 11 \\ \(\tau_{2}\) & 102 & 102 & 102 & - \\ \(\tau_{3}\) & 130 & 135 & 130 & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: \(WCRT\) measured on the platform and the \(WCRT^{ub}\) of each \(k\) activation when the task set is allocated with the WFDU algorithm (Figure 9).  
Figure 9: WFDU allocation applied to the task set defined in Table 5.  
to interesting results. To lessen the effect of interference, the use of AI techniques might lead to a breakthrough in this aspect of scheduling, mainly based on mathematical models.  
Conceptualization, L.O., A.G., P.B., J.S. and A.C.; methodology, L.O., A.G., P.B., J.S. and A.C.; software, L.O., A.G. and P.B.; validation, L.O., A.G. and P.B.; formal analysis, L.O., A.G., P.B., J.S. and A.C.; investigation, L.O., A.G., P.B., J.S. and A.C.; resources, L.O., A.G., P.B., J.S. and A.C.; data curation, L.O., A.G., P.B., J.S. and A.C.; writing--original draft preparation, L.O., A.G. and P.B.; writing--review and editing, L.O., A.G., P.B., J.S. and A.C.; visualization, L.O., A.G., P.B., J.S. and A.C.; supervision, P.B., J.S. and A.C.; project administration, A.G.; funding acquisition, P.B., J.S. and A.C. All authors have read and agreed to the published version of the manuscript.  
This work was funded by MCIN / AEI/10.13039/501100011033/ grant PID2021-124502 OBJECT41 (PRESECREL), and by PAID-10-20 (Universitat Politecnica de Valencia).  
Not applicable.  
The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request. The data are not publicly available due to privacy.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
The following abbreviations are used in this manuscript: