[Paper Review] New Analysis Techniques for Supporting Hard Real-Time Sporadic DAG Task Systems on Multiprocessors

Zheng Dong, Cong Liu|arXiv (Cornell University)|Jul 31, 2018

Real-Time Systems Scheduling27 references4 citations

TL;DR

This paper proposes a novel scheduling and analysis framework for hard real-time sporadic DAG task systems on multiprocessors, introducing the Lazy-Cpath policy and an executing/non-executing interval-based analysis to reduce pessimism from intra-DAG precedence constraints. The resulting utilization-based schedulability test improves schedulability by over 60% on average compared to prior methods, and matches the classical density test when DAGs degenerate to ordinary sporadic tasks.

ABSTRACT

The scheduling and schedulability analysis of real-time directed acyclic graph (DAG) task systems have received much recent attention. The DAG model can accurately represent intra-task parallelim and precedence constraints existing in many application domains. Existing techniques show that analyzing the DAG model is fundamentally more challenging compared to the ordinary sporadic task model, due to the complex intra-DAG precedence constraints which may cause rather pessimistic schedulability loss. However,such increased loss is counter-intuitive because the DAG structure shall better exploit the parallelism provided by the multiprocessor platform. Our observation is that the intra-DAG precedence constraints, if not carefully considered by the scheduling algorithm, may cause very unpredictable execution behaviors of subtasks in a DAG and further cause pessimistic analysis. In this paper, we present a set of novel scheduling and analysis techniques for better supporting hard real-time sporadic DAG tasks on multiprocessors, through smartly defining and analyzing the execution order of subtasks in each DAG. Evaluation demonstrates that our developed utilization-based schedulability test is highly efficient, which dramatically improves schedulability of existing utilization-based tests by over 60% on average. Interestingly, when each DAG in the system is an ordinary sporadic task, our test becomes identical to the classical density test designed for the sporadic task model.

Motivation & Objective

• To address the counter-intuitive pessimism in existing schedulability analysis for DAG task systems, despite their potential to exploit multiprocessor parallelism.
• To identify that intra-DAG precedence constraints cause unpredictable subtask execution behaviors, leading to overly conservative analysis.
• To develop a scheduling and analysis framework that reduces this pessimism by intelligently ordering subtask execution within DAGs.
• To design a utilization-based schedulability test that is both efficient and highly effective for real-time DAG workloads on multiprocessors.

Proposed method

• Introduces the Lazy-Cpath policy to smartly define the execution order of ready subtasks within each DAG, minimizing interference from precedence constraints.
• Develops an executing/non-executing interval-based analysis technique to precisely model workload distribution in the analysis window.
• Proposes a new utilization-based schedulability test that uses cp-utilization and task utilization to bound interference and ensure schedulability under GEDF.
• Derives a sufficient schedulability condition where the sum of subtask utilization terms must satisfy a bound involving the number of processors and critical path utilization.
• Applies the analysis under Global Earliest Deadline First (GEDF) scheduling with the Lazy-Cpath policy to enable efficient, scalable analysis.
• Proves that the test reduces to the classical density test when DAGs are reduced to ordinary sporadic tasks, ensuring backward compatibility.

Experimental results

Research questions

• RQ1 Why do existing schedulability tests for DAG task systems exhibit significantly higher pessimism than those for ordinary sporadic tasks, despite the potential for better parallelism exploitation?
• RQ2 How can intra-DAG precedence constraints be managed in a way that reduces pessimism in schedulability analysis without sacrificing correctness?
• RQ3 Can a novel scheduling policy and analysis technique be designed to better exploit multiprocessor parallelism in DAG task systems while maintaining efficient schedulability tests?
• RQ4 To what extent does the proposed method improve upon existing utilization-based schedulability tests in terms of schedulability gain and efficiency?

Key findings

• The proposed CP-GEDF test improves schedulability by over 60% on average compared to existing utilization-based tests such as CAB and SU.
• In scenarios with short critical paths and medium per-task utilization, CP-GEDF achieves 100% schedulability at total utilization up to 6, while SU and CAB fail at 3.25 and 1.25, respectively.
• When critical paths are long and utilization is heavy, the CAB test fails to schedule any task set, while CP-GEDF maintains high schedulability.
• The CP-GEDF test demonstrates that DAG task systems can be more schedulable than equivalent sporadic task systems due to better exploitation of intra-DAG parallelism, as shown by comparison with the classical density test (U-ordinary).
• The proposed test reduces pessimism by effectively decoupling the analysis from complex intra-DAG precedence constraints through the Lazy-Cpath policy and interval-based workload modeling.
• The test is mathematically proven to be a sufficient condition for schedulability under GEDF with the Lazy-Cpath policy, and reduces to the classical density test when DAGs are degenerate to sporadic tasks.