Sub-additive service curves in the Network Calculus analysis
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910148959666176 |
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| author | Bouillard, Anne |
| author_facet | Bouillard, Anne |
| contents | Network Calculus is a theoretical model that aims at providing upper bounds of worst-case performance (such as delay or buffer occupancy). This is a mathematical framework that handles both network modeling and network analysis. As such it has requirements regarding the space of functions needed for a safe analysis. Namely, the functions need to be non-negative, as they model a quantity of data. This results in some pitfall for the analysis, where hypothesis matter.
A recent paper by Hamscher et al. states that allowing functions with negative values can also lead to a valid analysis, in cases that would be untractable with the non-negative assumption results, especially when feedback control is present in the system.
In this paper, we show that, on the contrary, a more conventional analysis is possible in all the mentioned cases. The key is a detailed analysis of sub-additive functions. Second, we show that the analysis of complex feedback control systems, presented by Hamscher et al. in a second paper that uses functions with negative values, is unsound and has stability issues. We give a corrected analysis, when possible, with conventional hypotheses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_18370 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sub-additive service curves in the Network Calculus analysis Bouillard, Anne Networking and Internet Architecture C.4; B.8.m Network Calculus is a theoretical model that aims at providing upper bounds of worst-case performance (such as delay or buffer occupancy). This is a mathematical framework that handles both network modeling and network analysis. As such it has requirements regarding the space of functions needed for a safe analysis. Namely, the functions need to be non-negative, as they model a quantity of data. This results in some pitfall for the analysis, where hypothesis matter. A recent paper by Hamscher et al. states that allowing functions with negative values can also lead to a valid analysis, in cases that would be untractable with the non-negative assumption results, especially when feedback control is present in the system. In this paper, we show that, on the contrary, a more conventional analysis is possible in all the mentioned cases. The key is a detailed analysis of sub-additive functions. Second, we show that the analysis of complex feedback control systems, presented by Hamscher et al. in a second paper that uses functions with negative values, is unsound and has stability issues. We give a corrected analysis, when possible, with conventional hypotheses. |
| title | Sub-additive service curves in the Network Calculus analysis |
| topic | Networking and Internet Architecture C.4; B.8.m |
| url | https://arxiv.org/abs/2604.18370 |