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471
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 936 (7 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 694 (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.
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 350 (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.
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 238 (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.
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 214 (18 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...
Efficiency Loss in a Network Resource Allocation Game: The Case of Elastic Supply
, 2008
"... We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on ..."
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Cited by 211 (12 self)
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We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on prices, a simple proportional pricing mechanism can maximize the sum of users’ utilities minus the cost (called aggregate surplus). Continuing previous efforts to quantify the effects of selfish behavior in network pricing mechanisms, we consider the possibility that users anticipate the effect of their actions on link prices. Under the assumption that the links’ marginal cost functions are convex, we establish existence of a Nash equilibrium. We show that the aggregate surplus at a Nash equilibrium is no worse than a factor of 4 √ 2 − 5 times the optimal aggregate surplus; thus, the efficiency loss when users are selfish is no more than approximately 34%.
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 optimization for OFDM wireless network Part I: Theoretical framework
 IEEE TRANS. WIRELESS COMMUN
, 2005
"... In this paper, we provide a theoretical framework for crosslayer optimization for orthogonal frequency division multiplexing (OFDM) wireless networks. The utility is used in our study to build a bridge between the physical layer and the media access control (MAC) layer and to balance the efficien ..."
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Cited by 128 (3 self)
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In this paper, we provide a theoretical framework for crosslayer optimization for orthogonal frequency division multiplexing (OFDM) wireless networks. The utility is used in our study to build a bridge between the physical layer and the media access control (MAC) layer and to balance the efficiency and fairness of wireless resource allocation. We formulate the crosslayer optimization problem as one that maximizes the average utility of all active users subject to certain conditions, which are determined by adaptive resource allocation schemes. We present necessary and sufficient conditions for utilitybased optimal subcarrier assignment and power allocation and discuss the convergence properties of optimization. Numerical results demonstrate a significant performance gain for the crosslayer optimization and the gain increases with the number of active users in the networks.
Stability and Performance Analysis of Networks Supporting Elastic Services
 IEEE/ACM Transactions on Networking
, 2001
"... AbstractWe consider the stability and performance of a model for networks supporting services that adapt their transmission to the available bandwidth. Not unlike real networks, in our model, connection arrivals are stochastic, each has a random amount of data to send, and the number of ongoing co ..."
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Cited by 119 (6 self)
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AbstractWe consider the stability and performance of a model for networks supporting services that adapt their transmission to the available bandwidth. Not unlike real networks, in our model, connection arrivals are stochastic, each has a random amount of data to send, and the number of ongoing connections in the system changes over time. Consequently, the bandwidth allocated to, or throughput achieved by, a given connection may change during its lifetime as feedback control mechanisms react to network loads. Ideally, if there were a fixed number of ongoing connections, such feedback mechanisms would reach an equilibrium bandwidth allocation typically characterized in terms of its &quot;fairness &quot; to users, e.g., maxmin or proportionally fair. In this paper we prove the stability of such networks when the offered load on each link does not exceed its capacity. We use simulation to investigate performance, in terms of average connection delays, for various fairness criteria. Finally, we pose an architectural problem in TCP/IPs decoupling of the transport and network layer from the point of view of guaranteeing connectionlevel stability, which we claim may explain congestion phenomena on the Internet. Index TermsABR service, bandwidth allocation, Lyapunov functions, performance analysis, proportional fairness, rate control, stability, TCP/IP, weighted maxmin fairness. F I.
Auctionbased spectrum sharing
 WiOpt '04
, 2004
"... Abstract. We study auctionbased mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at collocated receivers. The users access the channel using spread spectrum signaling and thus generate interference with each other. Each user receives a ..."
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Cited by 119 (18 self)
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Abstract. We study auctionbased mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at collocated receivers. The users access the channel using spread spectrum signaling and thus generate interference with each other. Each user receives a utility that is a function of the received signaltointerference plus noise ratio. We propose two auction mechanisms for allocating the received power. The first is an SINRbased auction, which, when combined with logarithmic utilities, leads to a weighted maxmin fair SINR allocation. The second is a powerbased auction that maximizes the total utility when the bandwidth is large enough. Both auction mechanisms achieve social optimality in a large system limit where bandwidth, power and the number of users are increased in a fixed proportion. We also give sufficient conditions for global convergence of a distributed updating algorithm and discuss the convergence speed. 1