Mixed-criticality (MC) scheduling of sequential tasks (with no intra-task parallelism) has been well-explored by the real-time systems community. However, till date, there has been little progress on MC scheduling of parallel tasks. MC scheduling of parallel tasks is highly challenging due to the requirement of various assurances under different criticality levels. In this work, we address the MC scheduling of parallel tasks of gang model that allows workloads to execute on multiple cores simultaneously, as well as the change to degree of parallelism of a task upon a mode switch. It represents an efficient mode-based parallel processing scheme with many potential applications. To schedule such task sets, we propose a new technique GEDF-VD, which integrates Global Earliest Deadline First (GEDF) and Earliest Deadline First with Virtual Deadline (EDF-VD). We prove the correctness of GEDF-VD and provide a detailed quantitative evaluation in terms of speedup bound in both the MC and the non-MC cases. Specifically, we show that GEDF provides a speedup bound of 2 for non-MC gang tasks, while the speedup for GEDF-VD considering MC gang tasks is \(\sqrt{5}+1\). Experiments on randomly generated gang task sets are conducted to validate our theoretical findings and to demonstrate the effectiveness of the proposed approach.

实时系统社区已经很好地探索了顺序任务的混合关键度（MC）调度（没有任务内并行性）。但是，到目前为止，并行任务的MC调度还没有什么进展。由于要求在不同关键性级别下进行各种保证，因此并行任务的MC调度非常具有挑战性。在这项工作中，我们解决了帮派模型并行任务的MC调度，该调度允许工作负载同时在多个内核上执行，以及在模式切换时任务并行度的更改。它代表了一种有效的基于模式的并行处理方案，具有许多潜在的应用程序。为了安排此类任务集，我们提出了一项新技术GEDF-VD，它将全球最早截止日期优先（GEDF）和最早截止日期优先与虚拟截止日期（EDF-VD）集成在一起。我们证明了GEDF-VD的正确性，并针对MC和非MC案例中的加速限制提供了详细的定量评估。具体来说，我们显示GEDF为非MC帮派任务提供了2的加速范围，而考虑了MC帮派任务的GEDF-VD的提速为\（\ sqrt {5} +1 \）。进行了随机生成的帮派任务集的实验，以验证我们的理论发现并证明所提出方法的有效性。