A Formal Link Between Response Time Analysis and Network Calculus

Authors Pierre Roux , Sophie Quinton , Marc Boyer

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Author Details

Pierre Roux
  • ONERA, Toulouse, France
  • DTIS - Université de Toulouse, F-31055 Toulouse, France
Sophie Quinton
  • Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, F-38000 Grenoble, France
Marc Boyer
  • ONERA, Toulouse, France
  • DTIS - Université de Toulouse, F-31055 Toulouse, France

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Pierre Roux, Sophie Quinton, and Marc Boyer. A Formal Link Between Response Time Analysis and Network Calculus. In 34th Euromicro Conference on Real-Time Systems (ECRTS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 231, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Classical Response Time Analysis (RTA) and Network Calculus (NC) are two major formalisms used for the verification of real-time properties. We offer mathematical links between these two different theories. Based on these links, we then prove the equivalence of various key notions in both frameworks. This enables specialists of both formalisms to get increase confidence on their models, or even, like the authors, to discover errors in theorems by investigating apparent discrepancies between some notions expected to be equivalent. The presented mathematical results are all mechanically checked with the interactive theorem prover Coq, building on existing formalizations of RTA and NC. Establishing such a link between NC and RTA paves the way for improved real-time analyses obtained by combining both theories to enjoy their respective strengths (e.g., multicore analyses for RTA or clock drifts for NC).

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time system specification
  • Networks → Formal specifications
  • Software and its engineering → Formal methods
  • General and reference → Verification
  • Response Time Analysis
  • Network Calculus
  • dense time
  • discrete time
  • response time
  • formal proof
  • Coq


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