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International Workshop on Automated Verification of Critical Systems

International Workshop on Formal Methods for Industrial Critical Systems

AVoCS 2017, FMICS 2017: Critical Systems: Formal Methods and Automated Verification pp 100–115Cite as

A Unified Formalism for Monoprocessor Schedulability Analysis Under Uncertainty

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10471))

Abstract

The schedulability analysis of real-time systems (even on a single processor) is a very difficult task, which becomes even more complex (or undecidable) when periods or deadlines become uncertain. In this work, we propose a unified formalism to model monoprocessor schedulability problems with several types of tasks (periodic, sporadic, or more complex), most types of schedulers (including \(\mathsf {EDF}\), \(\mathsf {FPS}\) and \(\mathsf {SJF}\)), with or without preemption, in the presence of uncertain timing constants. Although the general case is undecidable, we exhibit a large decidable subclass. We demonstrate the expressive power of our formalism on several examples, allowing also for robust schedulability.

This work is partially supported by the ANR national research program PACS (ANR-14-CE28-0002).

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Notes

  1. 1.

    As this definition is a contribution of this paper, it would better fit outside of the preliminaries section; however, it is convenient to define it first so as to then define task automata, and (parametric) timed automata in a straightforward manner.

  2. 2.

    In the literature, TAs are often defined using integer constants in guards and invariants; it is well-known that using rationals preserves decidability results, as rationals can be translated to integers using an appropriate constants rescaling.

  3. 3.

    Sources, binaries, models and results are available at imitator.fr/static/FMICS17.

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Authors and Affiliations

  1. Université Paris 13, LIPN, CNRS, UMR 7030, 93430, Villetaneuse, France

    Étienne André

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  1. Étienne André
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Correspondence to Étienne André .

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Editors and Affiliations

  1. Paris 13 University, Villetaneuse, France

    Laure Petrucci

  2. Mälardalen University, Västerås, Sweden

    Cristina Seceleanu

  3. University of York, York, United Kingdom

    Ana Cavalcanti

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André, É. (2017). A Unified Formalism for Monoprocessor Schedulability Analysis Under Uncertainty. In: Petrucci, L., Seceleanu, C., Cavalcanti, A. (eds) Critical Systems: Formal Methods and Automated Verification. AVoCS FMICS 2017 2017. Lecture Notes in Computer Science(), vol 10471. Springer, Cham. https://doi.org/10.1007/978-3-319-67113-0_7

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  • DOI: https://doi.org/10.1007/978-3-319-67113-0_7

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  • Print ISBN: 978-3-319-67112-3

  • Online ISBN: 978-3-319-67113-0

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