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.
@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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