Local stability of congestion control protocols: A MIMO gain and phase perspective

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-06-19 DOI:10.1016/j.automatica.2025.112435

Ding Zhang , Ioannis Lestas , Li Qiu

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引用次数: 0

Abstract

This paper presents a systematic approach to analyzing the stability of linearized models of network congestion control protocols from a novel multi-input multi-output (MIMO) gain and phase perspective. We leverage a recently developed MIMO phase concept to revisit several classical stability results of congestion control protocols and enhance this analysis by entangling gain and phase information. This entanglement allows us to study protocols with significant phase lag or networks with delays. Particularly, the gain-phase entanglement is realized through two methods: (1) an explicit method based on frequency partitioning, which yields a set of easily verifiable, distributed stability conditions for typical TCP networks; and (2) an implicit method based on the Davis–Wielandt shell, which refines (1) but is more difficult to verify. Both methods exploit global phase bounds on network switches, resulting in partially decentralized conditions that emphasize phase characteristics. These conditions are advantageous in networks where switches exhibit similar phase responses. The effectiveness of the proposed conditions is demonstrated by a numerical example showcasing the stabilization of a Reno/RED network.

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拥塞控制协议的局部稳定性：MIMO增益和相位视角

本文从一种新的多输入多输出（MIMO）增益和相位角度，系统地分析了网络拥塞控制协议线性化模型的稳定性。我们利用最近开发的MIMO相位概念来重新审视拥塞控制协议的几个经典稳定性结果，并通过纠缠增益和相位信息来增强这种分析。这种纠缠使我们能够研究具有显著相位滞后的协议或具有延迟的网络。具体而言，增益相位纠缠通过两种方法实现：(1)基于频率划分的显式方法，该方法为典型TCP网络提供了一组易于验证的分布式稳定性条件；(2)基于Davis-Wielandt壳的隐式方法，该方法对(1)进行了改进，但更难验证。这两种方法都利用网络交换机上的全局相位边界，从而产生强调相位特征的部分分散条件。这些条件在开关具有相似相位响应的网络中是有利的。通过一个Reno/RED网络的稳定算例验证了所提条件的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.