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.

翻译：网络演算是一种旨在提供最坏情况性能（如延迟或缓冲区占用）上界的理论模型。这是一个同时处理网络建模与网络分析的数学框架，因此它对安全分析所需的函数空间提出了要求。具体而言，由于函数用于建模数据量，它们必须是非负的。这导致分析中存在一些因假设条件而产生的陷阱。Hamscher等人近期的一篇论文指出，在某些非负假设无法处理的情况下（尤其是系统中存在反馈控制时），允许函数取负值也可得出有效的分析结果。本文表明，相反地，在所有提及的案例中，采用更传统的分析方法是可行的，关键在于对次加性函数的详细分析。其次，我们证明Hamscher等人在第二篇论文中提出的采用负值函数对复杂反馈控制系统的分析存在不完善性和稳定性问题。我们在可能的情况下，基于传统假设给出了修正后的分析方法。