A Mathematical Comparison Between Response-Time Analysis and Real-Time Calculus for Fixed-Priority Preemptive Scheduling

Authors Victor Pollex, Frank Slomka

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Author Details

Victor Pollex
  • INCHRON AG, Erlangen, Germany
Frank Slomka
  • Institute of Embedded Systems/Real-Time Systems, Faculty of Engineering and Computer Science, Universität Ulm, Germany

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Victor Pollex and Frank Slomka. A Mathematical Comparison Between Response-Time Analysis and Real-Time Calculus for Fixed-Priority Preemptive Scheduling. In 34th Euromicro Conference on Real-Time Systems (ECRTS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 231, pp. 7:1-7:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Fixed-priority preemptive scheduling is a popular scheduling scheme for real-time systems. This is accompanied by a vast amount of research on how to analyse and check whether these systems satisfy their real-time requirements. Two methods that emerged from this research are the response-time analysis and the real-time calculus. These two methods have been compared empirically on the basis of several abstract systems showing that for some systems one method gives better results than the other and for other systems both methods appear to give the same results. However, empirical analyses inherently contain uncertainty. To get a definitive answer we compare both methods mathematically and we show that both methods give the same results for systems that use fixed-priority preemptive scheduling and independent tasks.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • Computer systems organization → Embedded and cyber-physical systems
  • Software and its engineering → Scheduling
  • real-time systems
  • fixed-priority scheduling
  • response-time analysis
  • real-time calculus


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