Exact and sufficient schedulability tests for adaptive weakly-hard real-time mixed-criticality systems

This paper presents enhanced schedulability analysis techniques for Adaptive Mixed-Criticality systems with Weakly-Hard constraints (AMC-WH), where the low-criticality (LO) task jobs can continue to execute when the system switches to high-criticality (HI) mode. Prior AMC-WH studies typically adopt the skip-over model, in which up to s out of m consecutive LO task deadlines may be missed without violating system constraints. These approaches evaluate the Worst-Case Response Times (WCRT) of LO tasks under a fixed job execution pattern. In contrast, this work introduces a novel schedulability analysis framework based on the more general $(m,k)$-firm model, where each LO task must meet at least m out of any k consecutive deadlines. This extension allows for more flexible and configurable execution patterns for LO tasks after a mode transition, improving the adaptability of the system to varying operational conditions. Additionally, we propose an exact schedulability test for AMC-WH based on Response Time Analysis (RTA), which incorporates the $(m,k)$-firm model to precisely analyze schedulability by dynamically managing LO task execution patterns post-mode switch. Comprehensive experimental evaluations confirm the effectiveness and practicality of the proposed tests. In particular, our approach achieves an 18% improvement in schedulability compared to the AMC-WH skip-over baseline, while also optimizing resource utilization. By leveraging the flexibility of the $(m,k)$-firm model, our method supports a wide range of real-time applications with diverse tolerance levels for deadline misses, offering enhanced adaptability in LO task execution strategies.