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Abstract Response-Time Analysis: A Formal Foundation for the Busy-Window Principle

Authors Sergey Bozhko, Björn B. Brandenburg

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Author Details

Sergey Bozhko
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany
Björn B. Brandenburg
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 803111). Funded in part by Deutsche Forschungsgemeinschaft (DFG) - 391919384.

Acknowledgements

We thank the members of the ANR-DFG joint project RT-PROOFS, in particular Maxime Lesourd and Sophie Quinton, for their valuable feedback and suggestions.

Cite As Get BibTex

Sergey Bozhko and Björn B. Brandenburg. Abstract Response-Time Analysis: A Formal Foundation for the Busy-Window Principle. In 32nd Euromicro Conference on Real-Time Systems (ECRTS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 165, pp. 22:1-22:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ECRTS.2020.22

Abstract

This paper introduces the first general and rigorous formalization of the classic busy-window principle for uniprocessors. The essence of the principle is identified as a minimal set of generic, high-level hypotheses that allow for a unified and general abstract response-time analysis, which is independent of specific scheduling policies, workload models, and preemption policy details. From this abstract core, the paper shows how to obtain concrete analysis instantiations for specific uniprocessor schedulers via a sequence of refinement steps, and provides formally verified response-time bounds for eight common schedulers and workloads, including the widely used fixed-priority (FP) and earliest-deadline first (EDF) scheduling policies in the context of fully, limited-, and non-preemptive sporadic tasks. All definitions and proofs in this paper have been mechanized and verified with the Coq proof assistant, and in fact form the common core and foundation for verified response-time analyses in the Prosa open-source framework for formally proven schedulability analyses.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • Software and its engineering → Scheduling
  • Theory of computation → Scheduling algorithms
Keywords
  • hard real-time systems
  • response-time analysis
  • uniprocessor
  • busy window
  • fixed priority
  • EDF
  • verification
  • Coq
  • Prosa
  • preemptive
  • non-preemptive
  • limited-preemptive

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