Switching Between Left and Right Continuity in Network Calculus

Authors Damien Guidolin--Pina , Marc Boyer

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Damien Guidolin--Pina
  • RealTime-at-Work, 54000, Nancy, France
Marc Boyer
  • DTIS, ONERA, Université de Toulouse, 31000, Toulouse, France


The authors express their gratitude to Pierre Roux for his assistance on various mathematical aspects in the proofs, and to the ECRTS reviewers and shepherd, whose valuable feedback significantly enhanced the presentation of the results.

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Damien Guidolin--Pina and Marc Boyer. Switching Between Left and Right Continuity in Network Calculus. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


The Network Calculus theory has been designed to compute upper bounds on delay and backlog in data networks. A lot of results have been developed to address different aspects. However, they are not all compatible with each other since they make different assumptions on the continuity of a core aspect of the model (the cumulative curves). However, real systems may mix several mechanisms. When modeling such a system, one has to choose one continuity hypothesis and limit the analysis to a subset of existing results. This paper addresses the continuity problem and argues formally that continuity issues are mathematical details that can be solved as long as the min-plus properties are used (minimal and maximal service, shaping). Conversely, it gives a counter-example for properties based on strict service, requiring a generalisation of the backlogged interval notion.

Subject Classification

ACM Subject Classification
  • Networks → Network performance modeling
  • Networks → Network performance analysis
  • Worst-case analysis
  • Real-time and embedded systems
  • Network Calculus


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