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43
Optimization Flow Control, I: Basic Algorithm and Convergence
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1999
"... We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In thi ..."
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Cited by 518 (55 self)
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We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In this system sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial and timevarying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly timevarying environment.
Analysis and Design of an Adaptive Virtual Queue (AVQ) Algorithm for Active Queue Management
 In Proceedings of ACM SIGCOMM
, 2001
"... Virtual Queuebased marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to mai ..."
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Cited by 206 (19 self)
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Virtual Queuebased marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to maintain small queue lengths and its robustness in the presence of extremely short flows (the socalled web mice). Using a mathematical tool motivated by the earlier work of Hollot et al, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several wellknown AQM schemes such as RED, REM, PI controller and a nonadaptive virtual queue algorithm. With a view towards implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code. 1
Adaptive RED: An Algorithm for Increasing the Robustness of RED
, 2001
"... Approval for the Report and Comprehensive Examination: Committee: ..."
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Cited by 167 (1 self)
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Approval for the Report and Comprehensive Examination: Committee:
Global Stability of Congestion Controllers for the Internet
 IEEE Transactions on Automatic Control
, 2002
"... We consider a single link accessed by a single source which responds to congestion signals from the network. The design of controllers for such sources in the presence of feedback delay has received much attention recently. Here we present conditions for the global, asymptotic stability and semi ..."
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Cited by 62 (6 self)
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We consider a single link accessed by a single source which responds to congestion signals from the network. The design of controllers for such sources in the presence of feedback delay has received much attention recently. Here we present conditions for the global, asymptotic stability and semiglobal exponential stability of congestion controllers which are natural extensions of earlier linearized analysis of such systems. Our result on exponential stability provides the missing link in the proof of how one obtains a single deterministic congestion control equation from a system with many congestioncontrolled sources and random disturbances. Using numerical examples, we compare the conditions on the congestioncontrol parameters obtained using local and global stability analysis.
Congestion Control for Fair Resource Allocation in Networks with Multicast Flows
, 2001
"... The problem of congestion control in networks with multicast multirate traffic along with unicast sessions has been addressed in this paper. We present a decentralized algorithm which enables the different rateadaptive receivers in different multicast sessions to adjust their rates to satisfy some ..."
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Cited by 42 (3 self)
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The problem of congestion control in networks with multicast multirate traffic along with unicast sessions has been addressed in this paper. We present a decentralized algorithm which enables the different rateadaptive receivers in different multicast sessions to adjust their rates to satisfy some fairness criterion. We propose a onebit ECN marking strategy to be used at the nodes. The congestion control mechanism does not require any perflow state information for unicast flows at the nodes. Per receiver state information may be required for each multicast flow. The congestion control mechanism takes into account the diverse user requirements when different receivers within a multicast session have different utility functions, but does not assume the network to have any knowledge about the receiver utility functions and also converges under certain reasonable assumptions.
How Good are Deterministic Fluid Models of Internet Congestion Control?
, 2002
"... Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introdu ..."
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Cited by 36 (4 self)
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Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the simulation tractable, often deterministic fluid model approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional differential equations. We justify the use of deterministic models for proportionallyfair congestion controllers under a limiting regime where the number of sources in a network is large. We verify our results through simulations of windowbased implementations of proportionally fair controllers and TCP.
Mean FDE Models for Internet Congestion Control Under a ManyFlows Regime
 IEEE Transactions on Information Theory
, 2001
"... Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduc ..."
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Cited by 30 (11 self)
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Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the analysis or simulation tractable, often deterministic fluid approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional differential equations (FDEs). In this paper, we ignore the complexity introduced by the windowbased implementation of such algorithms and focus on the randomness in the network. We justify the use of deterministic models for proportionallyfair congestion controllers under a limiting regime where the number of flows in a network is large.
Optimization Flow Control with Online Measurement or Multiple Paths
 In Proceedings of the ITC
, 1999
"... We proposed earlier an optimization approach to reactive flow control where the objective of the control is to maximize the total utility of all sources over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. In this paper we cons ..."
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Cited by 28 (10 self)
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We proposed earlier an optimization approach to reactive flow control where the objective of the control is to maximize the total utility of all sources over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. In this paper we consider two extensions to the basic algorithm. First, the basic algorithm requires communication from sources of their rates to links in their paths in order to carry out the gradient projection algorithm. We prove that it is possible for the links to estimate the gradient using only local information, thus eliminating the need for explicit communication. Second, the basic algorithm assumes that each source is served by a single path. We generalize the model to the case where there are multiple paths between a sourcedestination pair. This allows flow control and routing to be jointly optimized. 1 Introduction We have proposed previously an optimization approach to flow control where the cont...
RateBased versus QueueBased Models of Congestion Control
 in Proceedings of ACM SIGMETRICS
, 2004
"... Mathematical models of congestion control capture the congestion indication mechanism at the router in two different ways: ratebased models, where the queuelength at the router does not explicitly appear in the model, and queuebased models, where the queue length at the router is explicitly a p ..."
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Cited by 26 (3 self)
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Mathematical models of congestion control capture the congestion indication mechanism at the router in two different ways: ratebased models, where the queuelength at the router does not explicitly appear in the model, and queuebased models, where the queue length at the router is explicitly a part of the model. Even though most congestion indication mechanisms use the queue length to compute the packet marking or dropping probability to indicate congestion, we argue that, depending upon the choice of the parameters of the AQM scheme, one would obtain a ratebased model or a rateandqueuebased model as the deterministic limit of a stochastic system with a large number of users.
An Adaptive Virtual Queue (AVQ) Algorithm for Active Queue Management
 IEEE/ACM Transactions on Networking
, 2004
"... Virtual Queuebased marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to mai ..."
Abstract

Cited by 26 (0 self)
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Virtual Queuebased marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to maintain small queue lengths and its robustness in the presence of extremely short flows (the socalled web mice). Using a linearized model of the system dynamics, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several wellknown AQM schemes such as RED, REM, PI controller and a nonadaptive virtual queue algorithm. With a view towards implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code.