Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems

Authors Binqi Sun , Tomasz Kloda , Marco Caccamo



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Binqi Sun
  • TUM School of Engineering and Design, Technical University of Munich, Germany
Tomasz Kloda
  • LAAS-CNRS, Insa de Toulouse, France
Marco Caccamo
  • TUM School of Engineering and Design, Technical University of Munich, Germany

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Binqi Sun, Tomasz Kloda, and Marco Caccamo. Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 17:1-17:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ECRTS.2024.17

Abstract

We present a response time analysis for global fixed-priority preemptive scheduling of constrained-deadline tasks upon a uniform multiprocessor where each processor can be characterized by a different speed. A fixed-priority scheduler assigns the jobs with the highest priorities to the fastest processors. Since determining whether all tasks can meet their deadlines is generally intractable even with identical processors, we propose two sufficient schedulability tests that calculate upper bounds on the task’s worst-case response time within polynomial and pseudo-polynomial time. The proposed tests leverage the linear programming model to upper bound the interference of the higher-priority tasks. Furthermore, we identify specific conditions and platforms upon which the problem can be solved more efficiently within linear time. These formulations are used to iteratively evaluate and refine possible solutions until a safe upper bound on the task’s worst-case response time is found. Additionally, we demonstrate that, with specific minor modifications, the proposed tests are compatible with Audsley’s optimal priority assignment. Experimental evaluations performed on synthetic task sets show that the proposed approach outperforms the state-of-the-art methods.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
Keywords
  • Real-time scheduling
  • Uniform multiprocessor
  • Response time analysis

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