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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 523 (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.
Resource pricing and the evolution of congestion control
, 1999
"... We describe ways in which the transmission control protocol of the Internet may evolve to support heterogeneous applications. We show that by appropriately marking packets at overloaded resources and by charging a fixed small amount for each mark received, endnodes are provided with the necessary i ..."
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Cited by 308 (7 self)
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We describe ways in which the transmission control protocol of the Internet may evolve to support heterogeneous applications. We show that by appropriately marking packets at overloaded resources and by charging a fixed small amount for each mark received, endnodes are provided with the necessary information and the correct incentive to use the network efficiently.
Bandwidth Sharing: Objectives and Algorithms
 IEEE/ACM Transactions on Networking
, 1999
"... This paper concerns the design of distributed algorithms for sharing network bandwidth resources among contending flows. The classical fairness notion is the socalled maxmin fairness; F. Kelly [8] has recently introduced the alternative proportional fairness criterion; we introduce a third crit ..."
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Cited by 270 (12 self)
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This paper concerns the design of distributed algorithms for sharing network bandwidth resources among contending flows. The classical fairness notion is the socalled maxmin fairness; F. Kelly [8] has recently introduced the alternative proportional fairness criterion; we introduce a third criterion, which is naturally interpreted in terms of the delays experienced by ongoing transfers. We prove that fixed size window control can achieve fair bandwidth sharing according to any of these criteria, provided scheduling at each link is performed in an appropriate manner. We next consider a distributed random scheme where each traffic source varies its sending rate randomly, based on binary feedback information from the network. We show how to select the source behaviour so as to achieve an equilibrium distribution concentrated around the considered fair rate allocations. This stochastic analysis is then used to assess the asymptotic behaviour of deterministic rate adaption proc...
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 243 (33 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 209 (18 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.
The price of stability for network design with fair cost allocation
 In Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS
, 2004
"... Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite differ ..."
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Cited by 209 (26 self)
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Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite different from the centrally enforced optimum. We study the quality of the best Nash equilibrium, and refer to the ratio of its cost to the optimum network cost as the price of stability. The best Nash equilibrium solution has a natural meaning of stability in this context — it is the optimal solution that can be proposed from which no user will defect. We consider the price of stability for network design with respect to one of the most widelystudied protocols for network cost allocation, in which the cost of each edge is divided equally between users whose connections make use of it; this fairdivision scheme can be derived from the Shapley value, and has a number of basic economic motivations. We show that the price of stability for network design with respect to this fair cost allocation is O(log k), where k is the number of users, and that a good Nash equilibrium can be achieved via bestresponse dynamics in which users iteratively defect from a starting solution. This establishes that the fair cost allocation protocol is in fact a useful mechanism for inducing strategic behavior to form nearoptimal equilibria. We discuss connections to the class of potential games defined by Monderer and Shapley, and extend our results to cases in which users are seeking to balance network design costs with latencies in the constructed network, with stronger results when the network has only delays and no construction costs. We also present bounds on the convergence time of bestresponse dynamics, and discuss extensions to a weighted game.
Endtoend congestion control schemes: Utility functions, random losses and ECN marks
 In Proceedings of IEEE Infocom
, 2000
"... We present a framework for designing endtoend congestion control schemes in a network where each user may have a different utility function and may experience noncongestionrelated losses. We first show that there exists an additive increasemultiplicative decrease scheme using only endtoend me ..."
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Cited by 180 (1 self)
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We present a framework for designing endtoend congestion control schemes in a network where each user may have a different utility function and may experience noncongestionrelated losses. We first show that there exists an additive increasemultiplicative decrease scheme using only endtoend measurable losses such that a sociallyoptimal solution can be reached. We incorporate roundtrip delay in this model, and show that one can generalize observations regarding TCPtype congestion avoidance to more general window flow control schemes. We then consider explicit congestion notification (ECN) as an alternate mechanism (instead of losses) for signaling congestion and show that ECN marking levels can be designed to nearly eliminate losses in the network by choosing the marking level independently for each node in the network. While the ECN marking level at each node may depend on the number of flows through the node, the appropriate marking level can be estimated using only aggregate flow measurements, i.e., perflow measurements are not required. 1
A game theoretic framework for bandwidth allocation and pricing in broadband networks
 IEEE/ACM Trans. on Networking
, 2000
"... Abstract—In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in highspeed networks. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto opti ..."
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Cited by 178 (5 self)
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Abstract—In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in highspeed networks. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto optimal from the point of view of the whole system, but are also consistent with the fairness axioms of game theory. We first consider the centralized problem and then show that this procedure can be decentralized so that greedy optimization by users yields the system optimal bandwidth allocations. We propose a distributed algorithm for implementing the optimal and fair bandwidth allocation and provide conditions for its convergence. The paper concludes with the pricing of elastic connections based on users ’ bandwidth requirements and users’ budget. We show that the above bargaining framework can be used to characterize a rate allocation and a pricing policy which takes into account users ’ budget in a fair way and such that the total network revenue is maximized. Index Terms—Bandwidth allocation, elastic traffic, game theory, Nash bargaining solution, pricing. I.
Bandwidth Sharing and Admission Control for Elastic Traffic
 Telecommunication Systems
, 1998
"... We consider the performance of a network like the Internet handling socalled elastic traffic where the rate of flows adjusts to fill available bandwidth. Realized throughput depends both on the way bandwidth is shared and on the random nature of traffic. We assume traffic consists of point to point ..."
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Cited by 163 (15 self)
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We consider the performance of a network like the Internet handling socalled elastic traffic where the rate of flows adjusts to fill available bandwidth. Realized throughput depends both on the way bandwidth is shared and on the random nature of traffic. We assume traffic consists of point to point transfers of individual documents of finite size arriving according to a Poisson process. Notable results are that weighted sharing has limited impact on perceived quality of service and that discrimination in favour of short documents leads to considerably better performance than fair sharing. In a linear network, maxmin fairness is preferable to proportional fairness under random traffic while the converse is true under the assumption of a static configuration of persistent flows. Admission control is advocated as a necessary means to maintain goodput in case of traffic overload. 1 Introduction Traffic in a multiservice network is essentially composed of individual transactions or flows...
Opportunistic transmission scheduling with resourcesharing constraints in wireless networks
 IEEE Journal on Selected Areas in Communications
, 2001
"... We present an “opportunistic ” transmission scheduling policy that exploits timevarying channel conditions and maximizes the system performance stochastically under a certain resource allocation constraint. We establish the optimality of the scheduling scheme, and also that every user experiences ..."
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Cited by 161 (8 self)
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We present an “opportunistic ” transmission scheduling policy that exploits timevarying channel conditions and maximizes the system performance stochastically under a certain resource allocation constraint. We establish the optimality of the scheduling scheme, and also that every user experiences a performance improvement over any nonopportunistic scheduling policy when users have independent performance values. We demonstrate via simulation results that the scheme is robust to estimation errors, and also works well for nonstationary scenarios, resulting in performance improvements of 20–150 % compared with a scheduling scheme that does not take into account channel conditions. Last, we discuss an extension of our opportunistic scheduling scheme to improve “shortterm ” performance.