{"title":"Local stability of congestion control protocols: A MIMO gain and phase perspective","authors":"Ding Zhang , Ioannis Lestas , Li Qiu","doi":"10.1016/j.automatica.2025.112435","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"179 ","pages":"Article 112435"},"PeriodicalIF":4.8000,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109825003292","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
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.
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.