{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T23:41:59Z","timestamp":1648770119892},"reference-count":27,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2017,11,25]],"date-time":"2017-11-25T00:00:00Z","timestamp":1511568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,6,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The analysis of transport protocols, along with queue management policies, forms an important aspect of performance evaluation for the Internet. In this article, we study Compound TCP (C-TCP), the default TCP in the Windows operating system, along with the Exponential-RED (E-RED) queue policy and the widely used Drop-Tail queue policy. We consider queuing delay, link utilization and the stability of the queue size as the performance metrics. We first analyse the stability properties of a nonlinear model for C-TCP coupled with the E-RED queue policy. We observe that this system, in its current form, may be difficult to stabilize as the feedback delay gets large. Further, using an exogenous and non-dimensional parameter, we show that the system loses local stability via a Hopf bifurcation, which gives rise to limit cycles. Employing Poincar\u00e9 normal forms and the center manifold theory, we outline an analytical framework to characterize the type of the Hopf bifurcation and to determine the orbital stability of the emerging limit cycles. Numerical examples, stability charts and bifurcation diagrams complement our analysis. We also conduct packet-level simulations, with E-RED and Drop-Tail, in small and large buffer-sizing regimes. With large buffers, E-RED can achieve small queue sizes compared with Drop-Tail. However, it is difficult to maintain the stability of the E-RED policy as the feedback delay gets large. On the other hand, with small buffers, E-RED offers no clear advantage over the simple Drop-Tail queue policy. Our work can offer insights for the design of queue policies that can ensure low latency and stability.<\/jats:p>","DOI":"10.1093\/imamci\/dnx049","type":"journal-article","created":{"date-parts":[[2017,10,11]],"date-time":"2017-10-11T15:11:36Z","timestamp":1507734696000},"page":"399-421","source":"Crossref","is-referenced-by-count":0,"title":["Stability and performance analysis of Compound TCP with the Exponential-RED and the Drop-Tail queue policies"],"prefix":"10.1093","volume":"36","author":[{"given":"Sai","family":"Prasad","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaurav","family":"Raina","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2017,11,25]]},"reference":[{"key":"2019122505174001300_B1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/65.923940","article-title":"REM: active queue management.","volume":"15","author":"Athuraliya,","year":"2001","journal-title":"IEEE Netw.,"},{"key":"2019122505174001300_B2","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.1109\/COMST.2014.2375213","article-title":"Reducing internet latency: a survey of techniques and their merits.","volume":"18","author":"Briscoe,","year":"2016","journal-title":"IEEE Commun. Surveys Tuts.,"},{"key":"2019122505174001300_B3","first-page":"1546","article-title":"Stochastic models for generating synthetic HTTP source traffic.","author":"Cao,","year":"2004","journal-title":"Proceedings of the IEEE INFOCOM."},{"key":"2019122505174001300_B4","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/90.251892","article-title":"Random early detection gateways for congestion avoidance.","volume":"1","author":"Floyd,","year":"1993","journal-title":"IEEE\/ACM Trans. Netw.,"},{"key":"2019122505174001300_B5","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1145\/2063176.2063196","article-title":"Bufferbloat: dark buffers in the internet.","volume":"55","author":"Gettys,","year":"2012","journal-title":"Commun. ACM,"},{"key":"2019122505174001300_B6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.bjp.2014.01.009","article-title":"Fighting the bufferbloat: on the coexistence of AQM and low priority congestion control.","volume":"65","author":"Gong,","year":"2014","journal-title":"Comput. Netw.,"},{"key":"2019122505174001300_B7","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1145\/1400097.1400105","article-title":"CUBIC: a new TCP-friendly high-speed TCP variant.","volume":"42","author":"Ha,","year":"2008","journal-title":"ACM SIGOPS Operating Systems Review,"},{"key":"2019122505174001300_B8","first-page":"6762","article-title":"Synchronization of TCP flows in networks with small Droptail buffers.","author":"Han,","year":"2005","journal-title":"Proceedings of the IEEE Conference on Decision and Control and European Control Conference."},{"key":"2019122505174001300_B9","volume-title":"Theory and Applications of Hopf Bifurcation.","author":"Hassard,","year":"1981"},{"key":"2019122505174001300_B10","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.comnet.2015.08.018","article-title":"On fairness and application performance of active queue management in broadband cable networks.","volume":"91","author":"Hong,","year":"2015","journal-title":"Comput. Netw.,"},{"key":"2019122505174001300_B11","volume-title":"Introduction to Network Simulator NS2.","author":"Issariyakul,","year":"2011"},{"key":"2019122505174001300_B12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3978-7","volume-title":"Elements of Applied Bifurcation Theory.","author":"Kuznetsov,","year":"2004"},{"key":"2019122505174001300_B13","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1109\/TNET.2005.857110","article-title":"Exponential-RED: a stabilizing AQM scheme for low and high-speed TCP protocols.","volume":"13","author":"Liu,","year":"2005","journal-title":"IEEE\/ACM Trans. Netw.,"},{"key":"2019122505174001300_B14","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1023\/B:NETS.0000015657.07692.be","article-title":"A mathematical framework for designing a low-loss, low-delay Internet.","volume":"4","author":"Low,","year":"2004","journal-title":"Netw. Spat. Econ.,"},{"key":"2019122505174001300_B15","first-page":"188","article-title":"Non-linear oscillations in TCP networks with Drop-Tail buffers.","author":"Malangadan,","year":"2013","journal-title":"Proceedings of the Chinese Control and Decision Conference, IEEE."},{"key":"2019122505174001300_B16","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1145\/2209249.2209264","article-title":"Controlling queue delay.","volume":"55","author":"Nichols,","year":"2012","journal-title":"Commun. ACM,"},{"key":"2019122505174001300_B17","doi-asserted-by":"crossref","first-page":"339","DOI":"10.21917\/ijct.2011.0047","article-title":"Drop tail and RED queue management with small buffers: stability and Hopf bifurcation.","volume":"2","author":"Patil,","year":"2011","journal-title":"ICTACT J. Commun. 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