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DOI: 10.4230/LIPIcs.ECRTS.2024.9

Switching Between Left and Right Continuity in Network Calculus

Authors: Damien Guidolin--Pina and Marc Boyer

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract

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.

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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)

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@InProceedings{guidolinpina_et_al:LIPIcs.ECRTS.2024.9,
  author =	{Guidolin--Pina, Damien and Boyer, Marc},
  title =	{{Switching Between Left and Right Continuity in Network Calculus}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.9},
  URN =		{urn:nbn:de:0030-drops-203129},
  doi =		{10.4230/LIPIcs.ECRTS.2024.9},
  annote =	{Keywords: Worst-case analysis, Real-time and embedded systems, Network Calculus}
}

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Switching Between Left and Right Continuity in Network Calculus

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