On Strong and Weak Sustainability, with an Application to Self-Suspending Real-Time Tasks

Authors Felipe Cerqueira, Geoffrey Nelissen, Björn B. Brandenburg

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Author Details

Felipe Cerqueira
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
Geoffrey Nelissen
  • CISTER Research Centre, ISEP, Polytechnic Institute of Porto (IPP), Porto, Portugal
Björn B. Brandenburg
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany

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Felipe Cerqueira, Geoffrey Nelissen, and Björn B. Brandenburg. On Strong and Weak Sustainability, with an Application to Self-Suspending Real-Time Tasks. In 30th Euromicro Conference on Real-Time Systems (ECRTS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 106, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Motivated by an apparent contradiction regarding whether certain scheduling policies are sustainable, we revisit the topic of sustainability in real-time scheduling and argue that the existing definitions of sustainability should be further clarified and generalized. After proposing a formal, generic sustainability theory, we relax the existing notion of (strongly) sustainable scheduling policy to provide a new classification called weak sustainability. Proving weak sustainability properties allows reducing the number of variables that must be considered in the search of a worst-case schedule, and hence enables more efficient schedulability analyses and testing regimes even for policies that are not (strongly) sustainable. As a proof of concept, and to better understand a model for which many mistakes were found in the literature, we study weak sustainability in the context of dynamic self-suspending tasks, where we formalize a generic suspension model using the Coq proof assistant and provide a machine-checked proof that any JLFP scheduling policy is weakly sustainable with respect to job costs and variable suspension times.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Real-time schedulability
  • real-time scheduling
  • sustainability
  • self-suspending tasks
  • machine-checked proofs


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