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The shape of a DAG: bounding the response time using long paths

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Abstract

In 1969, Graham developed a well-known response time bound for a DAG task using the total workload and the longest path of the DAG, which has been widely applied to solve many scheduling and analysis problems of DAG-based task systems. This paper presents a new response time bound for a DAG task using the total workload and the lengths of multiple long paths of the DAG, instead of the longest path in Graham’s bound. Our new bound theoretically dominates and empirically outperforms Graham’s bound. Based on the insight of the new bound, we propose a new task model called the multi-path model, which intuitively describes the shape of a DAG task. We further extend the proposed approach to multi-task systems using the new task model under both federated scheduling and global scheduling. Our schedulability test theoretically dominates federated scheduling and significantly outperforms the state-of-the-art.

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Notes

  1. In a box plot, the middle line of the box indicates the median of data. The bottom and top edges of the box represent the 25th and 75th percentiles, respectively. The whiskers extending from the box show the range of data. And the outliers are plotted individually using the ’+’ symbol.

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Acknowledgements

This work is supported by the Research Grants Council of Hong Kong (GRF 11208522, 15206221) and the National Natural Science Foundation of China (NSFC 62102072). The authors also thank the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. The Hong Kong Polytechnic University, Hong Kong, China

    Qingqiang He & Mingsong Lv

  2. City University of Hong Kong, Hong Kong, China

    Nan Guan

  3. Northeastern University, Shenyang, China

    Mingsong Lv & Xu Jiang

  4. Hunan University, Changsha, China

    Wanli Chang

  5. Huawei Technologies, Shenzhen, China

    Wanli Chang

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  1. Qingqiang He
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  2. Nan Guan
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  3. Mingsong Lv
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Correspondence to Nan Guan.

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He, Q., Guan, N., Lv, M. et al. The shape of a DAG: bounding the response time using long paths. Real-Time Syst 60, 199–238 (2024). https://doi.org/10.1007/s11241-023-09397-y

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