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215
A Duality Model of TCP and Queue Management Algorithms
 IEEE/ACM Trans. on Networking
, 2002
"... We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates as p ..."
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Cited by 307 (37 self)
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We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates as primal variables and congestion measures as dual variables, and congestion control as a distributed primaldual algorithm carried out over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas, and the dual iteration is carried out by queue management such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction.
REM: Active Queue Management
 IEEE NETWORK
, 2000
"... REM is an active queue management scheme that measures congestion not by a performance measure such as loss or delay, but by a quantity we call price. Price is computed by each link distributively using local information and is fed back to the sources through packet dropping or marking. This decoupl ..."
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Cited by 273 (22 self)
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REM is an active queue management scheme that measures congestion not by a performance measure such as loss or delay, but by a quantity we call price. Price is computed by each link distributively using local information and is fed back to the sources through packet dropping or marking. This decoupling of congestion and performance measures allows REM to achieve high utilization with negligible delays and buffer overflow regardless of the number of. sources. We prove that REM is asymptotically stable and compare its performance with RED using simulations.
A tutorial on crosslayer optimization in wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2006
"... This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable my ..."
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Cited by 248 (29 self)
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This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a cleanslate optimization based approach to the multihop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.
Impact of Fairness on Internet Performance
 IN PROCEEDINGS OF ACM SIGMETRICS
, 2000
"... We discuss the relevance of fairness as a design objective for congestion control mechanisms in the Internet. Specifically, we consider a backbone network shared by a dynamic number of shortlived flows, and study the impact of bandwidth sharing on network performance. In particular, we prove that f ..."
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Cited by 220 (15 self)
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We discuss the relevance of fairness as a design objective for congestion control mechanisms in the Internet. Specifically, we consider a backbone network shared by a dynamic number of shortlived flows, and study the impact of bandwidth sharing on network performance. In particular, we prove that for a broad class of fair bandwidth allocations, the total number of ows in progress remains finite if the load of every link is less than one. We also show that provided the bandwidth allocation is "sufficiently" fair, performance is optimal in the sense that the throughput of the ows is mainly determined by their access rate. Neither property is guaranteed with unfair bandwidth allocations, when priority is given to one class of ow with respect to another. This suggests current proposals for a differentiated services Internet may lead to suboptimal utilization of network resources.
Internet Congestion Control.
 IEEE Control Systems Magazine,
, 2002
"... Abstract This article reviews the current TCP congestion control protocols and overviews recent advances that have brought analytical tools to this problem. We describe an optimizationbased framework that provides an interpretation of various flow control mechanisms, in particular, the utility bei ..."
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Cited by 194 (25 self)
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Abstract This article reviews the current TCP congestion control protocols and overviews recent advances that have brought analytical tools to this problem. We describe an optimizationbased framework that provides an interpretation of various flow control mechanisms, in particular, the utility being optimized by the protocol's equilibrium structure. We also look at the dynamics of TCP and employ linear models to exhibit stability limitations in the predominant TCP versions, despite certain builtin compensations for delay. Finally, we present a new protocol that overcomes these limitations and provides stability in a way that is scalable to arbitrary networks, link capacities, and delays.
Mathematical modelling of the Internet
"... Modern communication networks are able to respond to randomly uctuating demands and failures by adapting rates, by rerouting traffic and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The des ..."
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Cited by 191 (0 self)
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Modern communication networks are able to respond to randomly uctuating demands and failures by adapting rates, by rerouting traffic and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. This paper outlines how mathematical models are being used to address current issues concerning the stability and fairness of rate control algorithms for the Internet.
Crosslayer congestion control, routing and scheduling design in ad hoc wireless networks
 PROC. IEEE INFOCOM
, 2006
"... This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless ..."
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Cited by 151 (10 self)
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This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or singlerate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multirate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with timevarying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dualbased algorithm remains stable and optimal when the constraint set is modulated by an irreducible finitestate Markov chain. This paper thus presents a step toward a systematic way to carry out crosslayer design in the framework of “layering as optimization decomposition ” for timevarying channel models.
Joint Congestion Control and Media Access Control Design for Ad Hoc Wireless Networks
 In Proc. IEEE INFOCOM
, 2005
"... Abstract—We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from content ..."
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Cited by 120 (4 self)
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Abstract—We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from contention for channel access. We present two algorithms that are not only distributed spatially, but more interestingly, they decompose vertically into two protocol layers where TCP and MAC jointly solve the system problem. The first is a primal algorithm where the MAC layer at the links generates congestion (contention) prices based on local aggregate source rates, and TCP sources adjust their rates based on the aggregate prices in their paths. The second is a dual subgradient algorithm where the MAC subalgorithm is implemented through scheduling linklayer flows according to the congestion prices of the links. Global convergence properties of these algorithms are proved. This is a preliminary step towards a systematic approach to jointly design TCP congestion control algorithms and MAC algorithms, not only to improve performance, but more importantly, to make their interaction more transparent.
Scalable Laws for Stable Network Congestion Control
 In Proceedings of Conference on Decision and Control
, 2001
"... This paper discusses flow control in networks, in which sources control their rates based on feedback signals received from the network links, a feature present in current TCP protocols. We develop a congestion control system which is arbitrarily scalable, in the sense that its stability is maintain ..."
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Cited by 115 (26 self)
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This paper discusses flow control in networks, in which sources control their rates based on feedback signals received from the network links, a feature present in current TCP protocols. We develop a congestion control system which is arbitrarily scalable, in the sense that its stability is maintained for arbitrary network topologies and arbitrary amounts of delay. Such a system can be implemented in a decentralized way with information currently available in networks plus a small amount of additional signaling.