Multi-cores are becoming mainstream hardware platforms for embedded and real-time systems. To fully utilize the processing capacity of multi-cores, software should be parallelized. Recently, much work has been done on real-time scheduling of parallel tasks modeled as directed acyclic graphs (DAG), motivated by the parallel task structures supported by popular parallel programming frameworks such as OpenMP. The DAG-based task models in existing real-time scheduling research assume well-nested graph structures recursively composed by single-source-single-sink parallel and conditional components. However, realistic OpenMP task systems in general have more flexible structures that do not comply with those assumptions. In this article, we model the behavior of general OpenMP task systems with non-well-nested structures. The worst-case response time analysis problem for such systems is more difficult due to the flexible graph structure. As the major technical contribution, we develop two efficient algorithms to compute the worst-case response time bounds, with different trade-offs between efficiency and precision. Evaluation with both randomly generated task graphs and realistic OpenMP programs shows good performance of our approaches in terms of both precision and efficiency.

中文翻译：

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使用条件分支计算 OpenMP 任务系统的 WCRT 边界的算法

多核正在成为嵌入式和实时系统的主流硬件平台。为了充分利用多核的处理能力，软件应该并行化。最近，在流行的并行编程框架（如 OpenMP）支持的并行任务结构的推动下，在建模为有向无环图 (DAG) 的并行任务的实时调度方面做了很多工作。现有实时调度研究中基于 DAG 的任务模型假设由单源单汇并行和条件组件递归组成的良好嵌套图结构。然而，现实的 OpenMP 任务系统通常具有更灵活的结构，不符合这些假设。在本文中，我们对具有非良好嵌套结构的通用 OpenMP 任务系统的行为进行建模。由于灵活的图形结构，此类系统的最坏情况响应时间分析问题更加困难。作为主要的技术贡献，我们开发了两种有效的算法来计算最坏情况的响应时间界限，在效率和精度之间进行不同的权衡。随机生成的任务图和真实的 OpenMP 程序的评估显示了我们的方法在精度和效率方面的良好性能。