One of the major sources of pessimism in the response time analysis (RTA) of globally scheduled real-time tasks is the computation of an upper-bound on the inter-task interference. This problem is further exacerbated when intra-task parallelism is permitted because of the complex internal structure of parallel tasks. This paper considers the global fixed-priority (G-FP) scheduling of sporadic real-time tasks when each task is modeled by a directed acyclic graph (DAG) of concurrent subtasks. We present a RTA based on the concept of problem window, a technique that has been extensively used to study the schedulability of sequential task in multiprocessor systems. The problem window approach of RTA usually categorizes interfering jobs in three different groups: carry-in, carry-out and body jobs. In this paper, we propose two novel techniques to derive less pessimistic upper-bounds on the workload produced by the carry-in and carry-out jobs of the interfering tasks. Those new bounds take into account the precedence constraints between subtasks pertaining to the same DAG. We show that with this new characterization of the carry-in and carry-out workload, the proposed schedulability test offers significant improvements on the schedulability of DAG tasks for randomly generated task sets in comparison to state-of-the-art techniques. In fact, we show that, while the state-of-art analysis does not scale with an increasing number of processors when tasks have constrained deadlines, the results of our analysis are barely impacted by the processor count in both the constrained and the arbitrary deadline case.

中文翻译：

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全局固定优先级调度下任意期限DAG任务的可调度性分析

全局调度实时任务的响应时间分析 (RTA) 中悲观的主要来源之一是计算任务间干扰的上限。由于并行任务的内部结构复杂，当允许任务内并行时，这个问题会进一步加剧。当每个任务由并发子任务的有向无环图 (DAG) 建模时，本文考虑了零星实时任务的全局固定优先级 (G-FP) 调度。我们提出了基于问题窗口概念的 RTA，该技术已广泛用于研究多处理器系统中顺序任务的可调度性。RTA 的问题窗口方法通常将干扰作业分为三个不同的组：运入、运出和车身作业。在本文中，我们提出了两种新技术，以推导出干扰任务的执行和执行作业产生的工作量的不那么悲观的上限。这些新边界考虑了属于同一 DAG 的子任务之间的优先约束。我们表明，通过对进位和执行工作负载的这种新表征，与最先进的技术相比，拟议的可调度性测试显着改善了随机生成的任务集的 DAG 任务的可调度性。事实上，我们表明，虽然当任务具有约束期限时，最先进的分析不会随着处理器数量的增加而扩展，但我们的分析结果几乎不受约束和任意期限内处理器数量的影响案件。