Probabilistic Response Time Analysis for Fixed Preemption Point Selection

Preemption point selection has a significant impact on the schedulability of Real-Time tasks under the Fixed Preemption Point approach in Limited Preemptive Scheduling. Many real time systems can occasionally tolerate deadline misses as long as their occurrence does not exceed a specified probabilistic threshold. However, the existing approaches for preemption point selection are inappropriate for such systems, as they are mainly aiming to provide hard guarantees, considering worst case (upper bounded) preemption overheads. Additionally, the worst case preemption overheads typically occur with very low probabilities. In this paper, we propose a novel preemption point selection approach, and an associated probabilistic response time analysis, considering preemption related overheads modelled as probabilistic distributions. The method is suitable for providing solutions in systems that can occasionally tolerate deadline misses and can be interesting in the context of mixed criticality systems. Our method is able to find solutions, in terms of preemption point selections, in all cases where the existing approaches do. Moreover, it provides preemption point selections for additional tasksets that guarantees the overall taskset schedulability with a certain probability. The evaluation results show an improvement with respect to increasing the number of tasksets for which a preemption point selection is possible compared to existing, upper-bound based, selection approaches. The results show that the deadline miss probabilities of the tasksets and associated preemption point selections are considerably low.