Probabilistic schedulability tests for uniprocessor fixed-priority scheduling under soft errors

Due to rising integrations, low voltage operations, and environmental influences such as electromagnetic interference and radiation, transient faults may cause soft errors and corrupt the execution state. Such soft errors can be recovered by applying fault-tolerant techniques. Therefore, the execution time of a job of a sporadic/periodic task may differ, depending upon the occurrence of soft errors and the applied error detection and recovery mechanisms. We model a periodic/sporadic real-time task under such a scenario by using two different worst-case execution times (WCETs), in which one is with the occurrence of soft errors and another is not. Based on a probabilistic soft-error model, the WCETs are hence with different probabilities. In this paper, we present efficient probabilistic schedulability tests that can be applied to verify the schedulability based on probabilistic arguments under fixed-priority scheduling on a uniprocessor system. We demonstrate how the Chernoff bounds can be used to calculate the task workloads based on their probabilistic WCETs. In addition, we further consider how to calculate the probability of `-consecutive deadline misses of a task. The pessimism and the efficiency of our approaches are evaluated against the tighter and approximated convolution-based approaches, by running extensive evaluations under different soft-error rates. The evaluation results show that our approaches are effective to derive the probability of deadline misses and efficient with respect to the needed calculation time.