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285
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 690 (5 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 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.
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 306 (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
"... 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 176 (4 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 160 (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...
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 153 (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.
Tsitsiklis. Efficiency loss in a network resource allocation game
 Mathematics of Operations Research
"... 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 144 (10 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%. The current Internet is used by a widely heterogeneous population of users; not only are different types of traffic sharing the same network, but different end users place different values on their perceived network performance. This has led to a surge of interest in congestion pricing, where
Differentiated endtoend internet services using weighted proportional fair sharing tcp
, 1998
"... In this document we study the application of weighted proportional fairness to data flows in the Internet. We let the users set the weights of their connections in order to maximise the utility they get from the network. When combined with a pricing scheme where connections are billed by weight and ..."
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Cited by 94 (0 self)
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In this document we study the application of weighted proportional fairness to data flows in the Internet. We let the users set the weights of their connections in order to maximise the utility they get from the network. When combined with a pricing scheme where connections are billed by weight and time, such a system is known to maximise the total utility of the network. Our study case is a national Web cache server connected to long distance links. We propose two ways of weighting TCP connections by manipulating some parameters of the protocol and present results from simulations and prototypes. We finally discuss how proportional fairness could be used to implement an Internet with differentiated services.
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 88 (5 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 "fairness " 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.
A Framework for Robust MeasurementBased Admission Control
 IEEE/ACM Transactions on Networking
, 1999
"... Measurementbased admission control (MBAC) is an attractive mechanism to concurrently offer quality of service (QoS) to users, without requiring a priori traffic specification and online policing. However, several aspects of such a system need to be clearly understood in order to devise robust MBAC ..."
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Cited by 87 (3 self)
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Measurementbased admission control (MBAC) is an attractive mechanism to concurrently offer quality of service (QoS) to users, without requiring a priori traffic specification and online policing. However, several aspects of such a system need to be clearly understood in order to devise robust MBAC schemes, i.e., schemes that can match a given QoS target despite the inherent measurement uncertainty, and without the tuning of external system parameters. We study the impact of measurement uncertainty, flow arrival, departure dynamics, and of estimation memory on the performance of a generic MBAC system in a common analytical framework. We show that a certainty equivalence assumption, i.e., assuming that the measured parameters are the real ones, can grossly compromise the target performance of the system. We quantify the improvement in performance as a function of the length of the estimation window and an adjustment of the target QoS. We demonstrate the existence of a critical time scale over which the impact of admissin decisions persists. Our results yield new insights into the performance of MBAC schemes, and represent quantitative and qualitative guidelines for the design of robust schemes.