Precise Response Time Analysis for Multiple DAG Tasks with Intra-task Priority Assignment.

In many real-time application domains, there are execution dependencies, such tasks may be formulated as multiple Directed Acyclic Graphs (DAGs) and scheduled with intra-task (i.e., intra-DAG) priority assignment. The worst-case completion time of a DAG must be bounded and schedulability analysis must be conducted during the design phase to estimate the required hardware resources. Typical examples include automotive systems and Ultra-Reliable Low Latency Communications (URLLC), which is the "to-business" protocol in 5G technologies, deployed in industrial automation for instance. To bound the execution time of multiple DAGs, there are two key factors to analyze: the intra-task interference for a single DAG and the inter-task interference between DAGs. While extensive efforts have been invested, the existing methods either still contain a large degree of pessimism or are even erroneous due to errors in the derived analysis. In this paper, we first provide an in-depth analysis of the limitation and defects of the existing methods. Inspired by these observations, we construct novel response time analysis for multiple DAG tasks with arbitrary intra-task priority assignment. Our analysis precisely accounts for both the intra- and inter-task interference by fully exploring the node parallelism in each DAG as well as between DAGs. Extensive experimental results show that the proposed analysis obtains tighter bounds and improves the system scheduability by at least 300% compared to state-of-the-art approaches. This improvement is even larger when the scheduling pressure is relatively high, up to 100% versus 0% in many cases. This work notably advances the use of response time analysis in industry. Practitioners have to resort to either potentially unsafe measurement results or significant resource over-provisioning when precise analysis is unavailable.