Conference Paper

# Synchronization of TCP Flows in Networks with Small DropTail Buffers

Electrical and Computer Engineering Department, University of Massachusetts, Amherst, MA 01003, USA.

DOI: 10.1109/CDC.2005.1583249 In proceeding of: Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on Source: IEEE Xplore

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**ABSTRACT:**In this note we analyse various stability properties of the max-min fair Rate Control Protocol (RCP) operating with small buffers. We first tackle the issue of stability for networks with arbitrary topologies. We prove that the max-min fair RCP fluid model is globally stable in the absence of propagation delays, and also derive a set of conditions for local stability when arbitrary heterogeneous propagation delays are present. The network delay stability result assumes that, at equilibrium, there is only one bottleneck link along each route. Lastly, in the simpler setting of a single link, single delay model, we investigate the impact of the loss of local stability via a Hopf bifurcation.IEEE Transactions on Automatic Control 12/2007; · 2.72 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The past few years have witnessed a lot of debate on how large Internet router buers should be. The widely believed rule-of- thumb used by router manufacturers today mandates a buer size equal to the delay-bandwidth product. This rule was rst challenged by researchers in 2004 who argued that if there are a large number of long-lived TCP connections owing through a router, then the buer size needed is equal to the delay- bandwidth product divided by the square root of the number of long-lived TCP ows. The publication of this result has since reinvigorated interest in the buer sizing problem with numerous other papers exploring this topic in further detail - ranging from papers questioning the applicability of this result to proposing alternate schemes to developing new congestion control algorithms, etc. This paper provides a synopsis of the recently proposed buer sizing strategies and broadly classies them according to their desired objective: link utilisation, and per-ow per- formance. We discuss the pros and cons of these dierent approaches. These prior works study buer sizing purely inComputer Communication Review. 01/2009; 39:34-39. - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a non-equilibrium analysis and control approach for the Active Queue Management (AQM) problem in communication networks. Using simplified fluid models, we carry out a bifurcation study of the complex dynamic queue behavior to show that non-equilibrium methods are essential for analysis and optimization in the AQM problem. We investigate an ergodic theoretic framework for stochastic modeling of the non-equilibrium behavior in deterministic models and use it to identify parameters of a fluid model from packet level simulations. For computational tractability, we use set-oriented numerical methods to construct finite-dimensional Markov models, including control Markov chains and hidden Markov models. Subsequently, we develop and analyze an example AQM algorithm using a Markov Decision Process (MDP) based control framework. The control scheme developed is optimal with respect to a reward function, defined over the queue size and aggregate flow rate. We implement and simulate our illustrative AQM algorithm in the ns-2 network simulator. The results obtained confirm the theoretical analysis and exhibit promising performance when compared with well-known alternative schemes under persistent non-equilibrium queue behavior.Automatica. 01/2008;

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