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Charging and rate control for elastic traffic
 European Transactions on Telecommunications
, 1997
"... This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max–min fairness of rates emerges as a limiting special case; more generally, the ..."
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Cited by 926 (6 self)
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This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max–min fairness of rates emerges as a limiting special case; more generally, the charges users are prepared to pay influence their allocated rates. In the preferred version of the model, a user chooses the charge per unit time that the user will pay; thereafter the user’s rate is determined by the network according to a proportional fairness criterion applied to the rate per unit charge. A system optimum is achieved when users ’ choices of charges and the network’s choice of allocated rates are in equilibrium. 1
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 690 (64 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.
A game theoretic framework for bandwidth allocation and pricing in broadband networks
 IEEE/ACM TRANS. ON NETWORKING
, 2000
"... 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 ..."
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Cited by 237 (11 self)
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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.
Internet congestion control
 IEEE CONTROL SYSTEMS MAGAZINE
, 2002
"... This article reviews the current transmission control protocol (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 parti ..."
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Cited by 191 (26 self)
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This article reviews the current transmission control protocol (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.
An Approach to Pricing and Resource Sharing for Available Bit Rate (ABR) Services
 INSTITUTE FOR COMPUTER
, 1997
"... Traditional ABR flow control mechanisms share, in a fair way, the available bandwidth according to the instantaneous peak rate requirements of active traffic streams. Such an approach does not allow bursty users, who besides the peak rate value additional measures of burstiness (e.g., the mean rate) ..."
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Cited by 7 (1 self)
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Traditional ABR flow control mechanisms share, in a fair way, the available bandwidth according to the instantaneous peak rate requirements of active traffic streams. Such an approach does not allow bursty users, who besides the peak rate value additional measures of burstiness (e.g., the mean rate), to express their true preferences for network usage. Furthermore, fair sharing is achieved at the short time scales of the duration of the bursts, and cannot express fairness properties defined over longer time scales, such as average throughput. We describe an approach where resource sharing is done according to effective usage. Users bid for some amount of effective bandwidth, and the network controls the effective bandwidth of their traffic by adjusting the explicit rate ER (maximum rate the user is allowed to send traffic) in order to achieve economically fair resource sharing. The feedback loop operates in much longer time scales than the round trip delays, and its performance relies ...
A Comparison of Feedback Based and Fair Queuing Mechanism for Handling Unresponsive Traffic
, 2001
"... The stability of the current Internet depends on the endtoend congestion control mechanism provided by TCP. Recently, popular multimedia applications (RealAudio, RLM) started using more aggressive forms of congestion control. It is not clear yet how wide uncooperation will become in Internet, bu ..."
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Cited by 2 (0 self)
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The stability of the current Internet depends on the endtoend congestion control mechanism provided by TCP. Recently, popular multimedia applications (RealAudio, RLM) started using more aggressive forms of congestion control. It is not clear yet how wide uncooperation will become in Internet, but it seems dangerous to base the Internet congestion control solely on the assumption of endhost cooperation. In this paper we examine the impact of router based congestion control mechanisms in the presence of uncooperative trac. We consider two classes of congestion control mechanisms (1) fair queuing mechanisms (FRED, DRR, CSFQ) and (2) feedback based mechanisms (ERAF, NBP). Within the subclass of feedback based mechanisms we distinguish between binary feedback mechanisms (ERAF) and rate feedback mechanisms (NBP). The criteria we use for our comparison are: eciency, fairness, convergence and scalability. Our results indicate that the feedback based mechanisms are able to shield responsive trac competing with uncooperative trac on a single link with the same eciency as the fair queuing mechanisms. For more complex topologies, the feedback based mechanisms oer better bandwidth allocations than the fair queuing mechanisms alone. In particular, the binary feedback mechanism we examine is able to provide allocations close to proportional fairness.
Estimation of the Number of Virtual Connections in a RateBased Flow Control Problem
, 2003
"... In this paper we deal with the ratebased flow control problem which we formulate as a tracking problem where the goal is to track a reference queue size chosen by the network administrator. We consider the single bottleneck link topology and use a nonlinear model for the queueing dynamics. A known ..."
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Cited by 1 (1 self)
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In this paper we deal with the ratebased flow control problem which we formulate as a tracking problem where the goal is to track a reference queue size chosen by the network administrator. We consider the single bottleneck link topology and use a nonlinear model for the queueing dynamics. A known algorithm is then extended to improve performance. Integral action is added to remove any steady state errors and the control signal is then normalized by the estimated number of flows. The main contribution of this work is the estimation algorithm that we propose, which is based on online parameter identification techniques and is shown analytically to converge to the correct number of flows exponentially fast. The algorithm does not require maintenance of per flow states and can thus form the basis for the development of an endtoend congestion control protocol. The performance of the proposed algorithm is evaluated through simulations carried out on the Ns simulator. Good estimation of the number of sessions and good tracking of the reference queue size are observed.
Rate Control for Communication Networks:
"... This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalizations to largescale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum ch ..."
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This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalizations to largescale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterized by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimization problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimization problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalized to include routing control, and provide natural implementations of proportionally fair pricing
Resource Pricing for ConnectionOriented Networks
, 2004
"... Network pricing has important implications in the revenue generation, resource management, system optimization and congestion control of computer networks. We depart from the prevalent idea of marginal cost pricing and provide a holistic, bilevel optimization framework to model the interaction betw ..."
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Network pricing has important implications in the revenue generation, resource management, system optimization and congestion control of computer networks. We depart from the prevalent idea of marginal cost pricing and provide a holistic, bilevel optimization framework to model the interaction between network entities in a connection oriented network. Users are treated as utility maximizing entities who allocate the available bandwidth among themselves by playing a distributed, noncooperative rate game. The ensuing Nash equilibrium is analyzed for the single link Erlang network and the multilink product form networks. Variants based on the upper bound of the blocking are also studied owing to their role in reducing computational complexity. Theoretical results are then validated using numerical simulation for varying network scenarios. An extension of the rate adaptation game based on Recursive Least Squares is proposed for dealing with the imperfect information scenario. These exhibited favorable convergence, accuracy and scalability properties. Gradientfree schemes are then developed for revenue maximization. These are based on novel stochastic approximation techniques such as Finite Difference Stochastic Approximation (FDSA) and Simultaneous Perturbation Stochastic Approximation (SPSA). It is observed that the network employed price discrimination for optimizing its objective function and partitioning its available capacity among competing users.
Rate control for communication networks: shadow
"... This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to largescale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum ch ..."
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This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to largescale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system de®ned by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.