ContentionFree Scheduling for MixedCriticality Multiprocessor RealTime System
Abstract
:1. Introduction
 We propose a method to calculate an upper bound of the number of contentionfree slots for each task;
 We then propose MCCF;
 We develop the DA test for MCCF.
2. Related Work
3. System Model
 ${X}_{i}\in \{HI,LO\}$ is the criticality of a task, and a task ${\tau}_{i}$ with ${X}_{i}=HI$ or ${X}_{i}=LO$ is either a HIcriticality or LOcriticality task, respectively.
 ${C}_{i}^{LO}$ and ${C}_{i}^{HI}$ denote the worstcase execution times (WCETs) for the low and high criticalities, respectively. We assume that ${C}_{i}^{LO}\le {C}_{i}^{HI}$ because a task with higher criticality requires a more conservative analysis for WCET.
 ${D}_{i}$ and ${T}_{i}$ represent the relative deadline and the period of the task, respectively, and ${D}_{i}={T}_{i}$ is satisfied.
 In the LOmode, every task ${\tau}_{i}\in \tau $ is schedulable; and
 In the HImode, every task ${\tau}_{i}\in {\tau}^{HI}$ is schedulable.
4. MCCF
4.1. MCCF Scheme
Algorithm 1 CF policy for MC multiprocessor systems. 

4.2. Lower Bound of ContentionFree Slots
5. Schedulability Analysis for MCCF
5.1. Schedulability Analysis for LOMode
5.2. Schedulability Analysis for HIMode
6. Evaluation
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Notation  Description  Notation  Description 

m  the number of processors  $\tau $  a task set 
${\tau}_{i}$  a task in $\tau $  ${X}_{i}$  the criticality of ${\tau}_{i}$ 
${C}_{i}^{LO}$  WCET for the low criticality  ${C}_{i}^{HI}$  WCET for high criticality 
${D}_{i}$  the relative deadline of ${\tau}_{i}$  ${T}_{i}$  the period of ${\tau}_{i}$ 
${\tau}^{LO}$  a set of tasks of which the criticality is low  ${\tau}^{HI}$  a set of tasks of which the criticality is high 
${J}_{i}^{n}$  the nth job invoked by ${\tau}_{i}$  ${r}_{i}$  the release time of ${J}_{i}$ 
${f}_{i}$  the finishing time of ${f}_{i}$  ${d}_{i}$  the absolute deadline of ${J}_{i}$ 
$hep\left({\tau}_{i}\right)$  a set of tasks of which the priority of each is higher than ${\tau}_{i}$  ${\Phi}_{i}^{LO}$  the lower bound of the contentionfree slots for ${\tau}_{i}\in {\tau}^{LO}$ 
${\Phi}_{i}^{HI}$  the lower bound of the contentionfree slots for ${\tau}_{i}\in {\tau}^{HI}$  ${C}_{i}^{\left(t\right)}$  the remaining execution time of ${J}_{i}$ at t 
${\Phi}_{i}^{\left(t\right)}$  the remaining contentionfree slots of ${J}_{i}$ at t  ${Q}^{H}$  the queue in which tasks have their original priorities 
${Q}^{L}$  the queue in which tasks have demoted priorities  ${\Phi}_{k}^{HI}\left({\ell}^{\prime}\right)$  the lower bound of the contentionfree slots for ${\tau}_{i}\in {\tau}^{HI}$, assuming that a mode transition occurs at ${r}_{i}+{\ell}^{\prime}$ 
${I}_{k\leftarrow i}^{LO}(\ell )$  the interference of ${\tau}_{i}$ on ${\tau}_{k}\in \tau $ in the LOmode  ${I}_{k\leftarrow i}^{HI}(\ell ,{\ell}^{\prime})$  the interference ${I}_{k\leftarrow i}^{HI}(\ell ,{\ell}^{\prime})$ of ${\tau}_{i}$ on ${\tau}_{k}\in {\tau}^{HI}$, assuming that a mode transition occurs at ${r}_{i}+{\ell}^{\prime}$ 
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Baek, H.; Lee, K. ContentionFree Scheduling for MixedCriticality Multiprocessor RealTime System. Symmetry 2020, 12, 1515. https://doi.org/10.3390/sym12091515
Baek H, Lee K. ContentionFree Scheduling for MixedCriticality Multiprocessor RealTime System. Symmetry. 2020; 12(9):1515. https://doi.org/10.3390/sym12091515
Chicago/Turabian StyleBaek, Hyeongboo, and Kilho Lee. 2020. "ContentionFree Scheduling for MixedCriticality Multiprocessor RealTime System" Symmetry 12, no. 9: 1515. https://doi.org/10.3390/sym12091515