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.

Most current real-time parallel applications can be modeled as a directed acyclic graph (DAG) task. Existing worst-case response time (WCRT) bounds (e.g., Graham's bound) derived for DAGs may be very pessimistic. No one precisely knows the gap between the WCRT bound and the actual WCRT. In this paper, we aim to derive the exact WCRT of a DAG task under the list scheduling upon multi-core platforms. We encode the WCRT analysis problem into a satisfaction modular theoretical (SMT) formulation based on insights into the list scheduling algorithm, and prove that our SMT program can solve the WCRT precisely, providing an accurate baseline to measure the tightness of the existing WCRT bounds. Experiments show that our method significantly improves the tightness of the WCRT bound, and is practically quite efficient, e.g., it can analyze DAGs with more than 40 vertices in a few seconds.

OpenMP is a promising framework to develop parallel real-time software on multi-cores. Although similar to the DAG task model, OpenMP task systems are significantly more difficult to analyze due to constraints posed by OpenMP specifications. One of the most interesting features in OpenMP is the support for nested parallelism, enjoying benefits in enhancing performance transparency of parallel libraries and promoting reuse of black-box code. Previous researches on DAG task scheduling mainly restrict to only one level of parallelism. The problem whether OpenMP tasks with multiple levels of parallelism are suitable to real-time systems remains open. In this paper, we study the real-time scheduling and analysis of OpenMP task systems supporting nested parallelism. First, we show that under existing scheduling algorithms in OpenMP implementations, nested parallelism indeed may lead to extremely bad timing behaviors where the parallel workload is sequentially executed completely. To solve this problem, we propose a new scheduling algorithm and develop two sound response time bounds by considering the trade-off between simplicity and analysis precision. Experiments demonstrate the efficiency of our methods.

Capacity augmentation bound (CAB) is a widely used quantitative metric in theoretical analysis for directed acyclic graph (DAG) parallel real-time tasks, which reveals the key factors the schedulability of DAG tasks heavily depending on: the normalized utilization (the ratio of the total utilization to the core numbers) and the tensity (the maximum ratio of task's longest path length to task's deadline). However, CAB requires both factors of a schedulable task system to be capped by the same threshold. A task system with a normalized utilization slightly larger than that threshold but very small tensity, or very smaller normalized utilization but slightly larger than that threshold has good chance to be scheduled are both denied by CAB. To this end, we propose a new concept called capacity augmentation function (CAF) to better characterize the schedulability of parallel real-time tasks, which provides a more loose and different threshold for both factors. In particular, we derive a CAF-based linear-time schedulability test for real-time constrained-deadline DAG tasks under global EDF, which entirely dominates the state-of-the-art CAB-based test for constrained-deadline settings. Finally, we conduct experiments to compare the acceptance ratio of our CAF-based test with the existing schedulability tests also having linear-time complexity. The results show that CAF-based test significantly outperforms the existing linear-time schedulability test under different parameter settings.