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129
FAST TCP: Motivation, Architecture, Algorithms, Performance
, 2004
"... We describe FAST TCP, a new TCP congestion control algorithm for highspeed longlatency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties, at both packet and flow levels, which the current TCP implementation has at large windows. W ..."
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Cited by 364 (19 self)
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We describe FAST TCP, a new TCP congestion control algorithm for highspeed longlatency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties, at both packet and flow levels, which the current TCP implementation has at large windows. We describe the architecture and characterize the equilibrium and stability properties of FAST TCP. We present experimental results comparing our first Linux prototype with TCP Reno, HSTCP, and STCP in terms of throughput, fairness, stability, and responsiveness. FAST TCP aims to rapidly stabilize highspeed longlatency networks into steady, efficient and fair operating points, in dynamic sharing environments, and the preliminary results are promising.
Stability criteria for switched and hybrid systems
 SIAM Review
, 2007
"... The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, an ..."
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Cited by 103 (7 self)
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The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability, and also represent problems in which significant progress has been made. We also comment on the inherent difficulty of determining stability of switched systems in general which is exemplified by NPhardness and undecidability results. We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell time requirements and state dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems is reviewed. We briefly comment on the classical Lur’e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.
Linear Stability of TCP/RED and a Scalable Control
, 2003
"... We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise tra#c. We develop a general multilink multisource model for TCP/RED and derive a local stability condition in the case of a single link wit ..."
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Cited by 74 (21 self)
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We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise tra#c. We develop a general multilink multisource model for TCP/RED and derive a local stability condition in the case of a single link with heterogeneous sources. We validate our model with simulations and illustrate the stability region of TCP/RED. These results suggest that TCP/RED becomes unstable when delay increases, or more strikingly, when link capacity increases. The analysis illustrates the di#culty of setting RED parameters to stabilize TCP: they can be tuned to improve stability, but only at the cost of large queues even when they are dynamically adjusted.
One More Bit Is Enough
 in Proceedings of ACM SIGCOMM
, 2005
"... Achieving efficient and fair bandwidth allocation while minimizing packet loss and bottleneck queue in high bandwidthdelay product networks has long been a daunting challenge. Existing endtoend congestion control (e.g., TCP) and traditional congestion notification schemes (e.g., TCP+AQM/ ECN) have ..."
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Cited by 64 (1 self)
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Achieving efficient and fair bandwidth allocation while minimizing packet loss and bottleneck queue in high bandwidthdelay product networks has long been a daunting challenge. Existing endtoend congestion control (e.g., TCP) and traditional congestion notification schemes (e.g., TCP+AQM/ ECN) have significant limitations in achieving this goal. While the XCP protocol addresses this challenge, it requires multiple bits to encode the congestionrelated information exchanged between routers and endhosts. Unfortunately, there is no space in the IP header for these bits, and solving this problem involves a nontrivial and timeconsuming standardization process. In this paper, we design and implement a simple, lowcomplexity protocol, called Variablestructure congestion Control Protocol (VCP), that leverages only the existing two ECN bits for network congestion feedback, and yet achieves comparable performance to XCP, i.e., high utilization, negligible packet loss rate, low persistent queue length, and reasonable fairness. On the downside, VCP converges significantly slower to a fair allocation than XCP. We evaluate the performance of VCP using extensive ns2 simulations over a wide range of network scenarios and find that it significantly outperforms many recentlyproposed TCP variants, such as HSTCP, FAST, and CUBIC. To gain insight into the behavior of VCP, we analyze a simplified fluid model and prove its global stability for the case of a single bottleneck shared by synchronous flows with identical roundtrip times. 1.
A positive systems model of TCPlike congestion control: Asymptotic results
 IEEE/ACM Transactions on Networking
, 2004
"... In this paper we study communication networks that employ droptail queueing and AdditiveIncrease MultiplicativeDecrease (AIMD) congestion control algorithms. We show that the theory of nonnegative matrices may be employed to model such networks. In particular, we show that important network p ..."
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Cited by 59 (10 self)
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In this paper we study communication networks that employ droptail queueing and AdditiveIncrease MultiplicativeDecrease (AIMD) congestion control algorithms. We show that the theory of nonnegative matrices may be employed to model such networks. In particular, we show that important network properties such as: (i) fairness; (ii) rate of convergence; and (iii) throughput; can be characterised by certain nonnegative matrices that arise in the study of AIMD networks. We demonstrate that these results can be used to develop tools for analysing the behaviour of AIMD communication networks. The accuracy of the models is demonstrated by means of several NSstudies.
Understanding XCP: Equilibrium and fairness
 in Proc. IEEE INFOCOM, 2005
"... Abstract—We prove that the XCP equilibrium solves a constrained maxmin fairness problem by identifying it with the unique solution of a hierarchy of optimization problems, namely those solved by maxmin fair allocation, but solved by XCP under an additional constraint. This constraint is due to the ..."
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Cited by 56 (4 self)
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Abstract—We prove that the XCP equilibrium solves a constrained maxmin fairness problem by identifying it with the unique solution of a hierarchy of optimization problems, namely those solved by maxmin fair allocation, but solved by XCP under an additional constraint. This constraint is due to the “bandwidth shuffling ” necessary to obtain fairness. We describe an algorithm to compute this equilibrium and derive a lower and upper bound on link utilization. While XCP reduces to maxmin allocation at a single link, its behavior in a network can be very different. We illustrate that the additional constraint can cause flows to receive an arbitrarily small fraction of their maxmin fair allocations. We confirm these results using ns2 simulations. Index Terms—Congestion control, maxmin, optimization.
Nonlinear stability analysis of a class of TCP/AQM networks
 in Proc. 40th IEEE Conference on Decision and Control
, 2001
"... Recent work has shown the benefit of using proportional feedback in TCP/AQM networks. By proportional feedback we mean the marking probability is proportional to the instantaneous queue length. Our earlier work relied on linearization of nonlinear fluidflow models of TCP. In this work we address ..."
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Cited by 51 (1 self)
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Recent work has shown the benefit of using proportional feedback in TCP/AQM networks. By proportional feedback we mean the marking probability is proportional to the instantaneous queue length. Our earlier work relied on linearization of nonlinear fluidflow models of TCP. In this work we address these nonlinearities directly and establish some stability results when the marking is proportional. In the case of delayfree marking, we show the system’s equilibrium point to be asymptotically stable for all proportional gains. In the more realistic case of delayed feedback, we establish local asymptotic stability and quantify a region of attraction. 1
Fast tcp: From theory to experiments
 IEEE Network
, 2005
"... he congestion control algorithm in the current TCP has performed remarkably well and is generally believed to have prevented severe congestion as the Internet scaled up by six orders of magnitude in size, speed, load, and connectivity in the last 15 years. It is also well known, however, that as ban ..."
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Cited by 46 (9 self)
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he congestion control algorithm in the current TCP has performed remarkably well and is generally believed to have prevented severe congestion as the Internet scaled up by six orders of magnitude in size, speed, load, and connectivity in the last 15 years. It is also well known, however, that as bandwidthdelay product continues to grow, the current TCP implementation will eventually become a performance bottleneck. In this article we describe a different congestion control algorithm for TCP, called FAST [1]. FAST TCP has three key differences. First, it is an equationbased algorithm and hence eliminates packetlevel oscillations. Second, it uses queuing delay as the primary measure of congestion, which can be more reliably measured by end hosts than loss probability in fast longdistance networks. Third, it has stable flow dynamics and achieves weighted proportional fairness in equilibrium that does not penalize long flows, as the current congestion control algorithm does. Alternative approaches are described in [2–6]. The details of the architecture, algorithms, extensive experimental evaluations of FAST TCP, and comparison with other TCP variants can be found in [1, 7]. In this article we highlight the motivation, background theory, implementation, and our first major experimental results. The scientific community is singular in its urgent need for efficient highspeed data transfer. We explain why this community has been driving the development and deployment of ultrascale networking. The design of FAST TCP builds on an emerging theory that allows us to understand the equilibrium and stability properties of large networks under endtoend control. It provides a framework to understand issues, clarify ideas, and suggest directions, leading to a more robust and better performing design. We summarize this theory and explain FAST TCP. We report the results of our first global experiment and conclude the article.
Modeling and stability of FAST TCP
 In IMA Volumes in Mathematics and its Applications, Volume 143: Wireless Communications
, 2006
"... Abstract — We introduce a discretetime model of FAST TCP that fully captures the effect of selfclocking, and compare it with the traditional continuoustime model. While the continuoustime model predicts instability for homogeneous sources sharing a single link when feedback delay is large, exper ..."
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Cited by 32 (9 self)
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Abstract — We introduce a discretetime model of FAST TCP that fully captures the effect of selfclocking, and compare it with the traditional continuoustime model. While the continuoustime model predicts instability for homogeneous sources sharing a single link when feedback delay is large, experiments suggest otherwise. Using the discretetime model, we prove that FAST TCP is locally asymptotically stable in general networks when all sources have a common roundtrip feedback delay, no matter how large the delay is. We also prove global stability for a single bottleneck link in the absence of feedback delay. The techniques developed here are new and applicable to other protocols.
Unresponsive flows and AQM performance
 In Proceedings of IEEE/INFOCOM
, 2003
"... Abstract — Routers handle data packets from sources unresponsive to TCP’s congestion avoidance feedback. We are interested in the impact these sources have on AQM’s control of longlived TCP traffic. In this paper, we combine models of TCP/AQM dynamics with models of unresponsive traffic to analyze ..."
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Cited by 23 (3 self)
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Abstract — Routers handle data packets from sources unresponsive to TCP’s congestion avoidance feedback. We are interested in the impact these sources have on AQM’s control of longlived TCP traffic. In this paper, we combine models of TCP/AQM dynamics with models of unresponsive traffic to analyze the effects on AQM performance. I.