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Response time analysis of multiframe mixed-criticality systems with arbitrary deadlines

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Abstract

The well-known model of Vestal aims to avoid excessive pessimism in the quantification of the processing requirements of mixed-criticality systems, while still guaranteeing the timeliness of higher-criticality functions. This can bring important savings in system costs, and indirectly help meet size, weight and power constraints. This efficiency is promoted via the use of multiple worst-case execution time (WCET) estimates for the same task, with each such estimate characterized by a confidence associated with a different criticality level. However, even this approach can be very pessimistic when the WCET of successive instances of the same task can vary greatly according to a known pattern, as in MP3 and MPEG codecs or the processing of ADVB video streams. In this paper, we present a schedulability analysis for the new multiframe mixed-criticality model, which allows tasks to have multiple, periodically repeating, WCETs in the same mode of operation. Our work extends both the analysis techniques for Static Mixed-Criticality scheduling (SMC) and Adaptive Mixed-Criticality scheduling (AMC), on one hand, and the schedulability analysis for multiframe task systems on the other. A constrained-deadline model is initially targeted, and then extended to the more general, but also more complex, arbitrary-deadline scenario. The corresponding optimal priority assignment for our schedulability analysis is also identified. Our proposed worst-case response time (WCRT) analysis for multiframe mixed-criticality systems is considerably less pessimistic than applying the static and adaptive mixed-criticality scheduling tests oblivious to the WCET variation patterns. Experimental evaluation with synthetic task sets demonstrates up to 20% and 31.4% higher scheduling success ratio (in absolute terms) for constrained-deadline analyses and arbitrary-deadline analyses, respectively, when compared to the best of their corresponding frame-oblivious tests.

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Notes

  1. The more general case of arbitrary deadlines is considered later in Sect. 7.

  2. We note that, if such jobs are instead immediately discarded at the mode switch, then assuming \(\lceil \frac{s}{T_j} \rceil\) interfering jobs is safe. In Hussain et al. (2019), when discussing the original AMC-max, we inadvertently used the expression with \(\lceil \frac{s}{T_j} \rceil\) for \(IL_j(s),\) instead of Eq. (7). That typo did not propagate to the experiments in that paper.

  3. In Eq. (18) of Hussain et al. (2019) (which corresponds to Eq. (22)), the regular \(G^L\) function was inadvertently used, instead of \(G^{L+},\) to upper-bound the number of such jobs. This is still safe, as long as all jobs by low-criticality tasks are terminated immediately at mode switch, but unsafe, if they are allowed to continue executing to completion for up to their L-WCET. In any case, the typo did not propagate to the experiments in Hussain et al. (2019), which were in fact consistent with Eq. (22).

  4. For convenience, without loss of generality (since shift-rotating the order of the frames results in an equivalent multiframe task), the first frame has the biggest L-WCET. Please note that our analyses make no assumptions regarding the WCET of the first frame being the greatest.

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Acknowledgements

This work was partially supported by National Funds through FCT/MCTES (Portuguese Foundation for Science and Technology), within the CISTER Research Unit (UIDB/04234/2020); also by the Operational Competitiveness Programme and Internationalization (COMPETE 2020) under the PT2020 Partnership Agreement, through the European Regional Development Fund (ERDF), and by national funds through the FCT, within project POCI-01-0145-FEDER-029119 (PREFECT). This work was also supported by the Netherlands Organization for Applied Scientific Research TNO.

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Authors and Affiliations

  1. CISTER Research Center and ISEP/IPP, Porto, Portugal

    Ishfaq Hussain, Muhammad Ali Awan, Konstantinos Bletsas & Eduardo Tovar

  2. FEUP-Faculty of Engineering and CISTER Research Centre, University of Porto, Porto, Portugal

    Pedro F. Souto

  3. ESI (TNO), Eindhoven, The Netherlands

    Benny Akesson

  4. University of Amsterdam, Amsterdam, The Netherlands

    Benny Akesson

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  1. Ishfaq Hussain
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  2. Muhammad Ali Awan
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  3. Pedro F. Souto
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  4. Konstantinos Bletsas
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  6. Eduardo Tovar
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Correspondence to Ishfaq Hussain.

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Hussain, I., Awan, M.A., Souto, P.F. et al. Response time analysis of multiframe mixed-criticality systems with arbitrary deadlines. Real-Time Syst 57, 141–189 (2021). https://doi.org/10.1007/s11241-020-09357-w

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