Sub-additive service curves in the Network Calculus analysis

2026-04-20

AI Summary

This study addresses the limitations of traditional network calculus, which assumes non-negative service curves and struggles to analyze complex systems with feedback control. By rigorously examining the properties of subadditive functions, the authors reveal that allowing negative service curves in feedback systems often leads to unstable analyses. To overcome this issue while preserving the non-negativity assumption, they develop a refined network calculus framework that integrates network calculus theory, subadditive function analysis, and system stability verification. Applying this approach to the complex feedback system proposed by Hamscher et al., the method achieves accurate modeling and tight performance bounds, effectively circumventing the instability inherent in prior techniques and significantly enhancing the applicability and reliability of network calculus in closed-loop systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

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.

Problem

• Network Calculus
• sub-additive functions
• feedback control
• service curves
• stability

Innovation

• Network Calculus
• sub-additive functions
• feedback control
• service curves
• stability analysis