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A ControlTheoretic Approach to Flow Control
, 1991
"... This paper presents a controltheoretic approach to reactive flow control in networks that do not reserve bandwidth. We assume a roundrobinlike queue service discipline in the output queues of the network’s switches, and propose deterministic and stochastic models for a single conversation in a ne ..."
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Cited by 383 (7 self)
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This paper presents a controltheoretic approach to reactive flow control in networks that do not reserve bandwidth. We assume a roundrobinlike queue service discipline in the output queues of the network’s switches, and propose deterministic and stochastic models for a single conversation in a network of such switches. These models motivate the PacketPair rate probing technique, and a provably stable ratebased flow control scheme. A Kalman state estimator is derived from discretetime state space analysis, but there are difficulties in using the estimator in practice. These difficulties are overcome by a novel estimation scheme based on fuzzy logic. We then present a technique to extract and use additional information horn the system to develop a continuoustime system model. This is used to design a wuisnt of the control law that is also provably stable, and, in addition, takes control action as rapidly as possible. Finally, practical issues such as correcting parameter drift and cmmlination with window flow control are described.
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.
On the existence of equilibria in noncooperative optimal flow control
 Journal of the ACM
, 1995
"... Abstract. The existence of Nash equilibria in noncooperative flow control in a general productform network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average timedelay. Previous attempts to study e ..."
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Cited by 71 (10 self)
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Abstract. The existence of Nash equilibria in noncooperative flow control in a general productform network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average timedelay. Previous attempts to study existence of equilibria for this flow control model were not successful, partly because the timedelay constraints couple the strategy spaces of the individual users in a way that does not allow the application of standard equilibrmm existence theorems from the game theory literature. To overcome this difficulty, a more general approach to study the existence of Nash equilibria for decentralized control schemes is introduced. This approach is based on directly proving the existence of a fixed point of the best reply correspondence of the underlying game. For the investigated flow control model, the best reply correspondence is shown to be a function, implicitly defined by means of K interdependent linear programs. Employing an appropriate definition for continuity of the set of optimal solutions of parametrized linear programs, it is shown that, under appropriate conditions, the best reply function is continuous. Brouwer’s theorem implies, then, that the best reply function has a fixed point.
PacketPair Flow Control
 IEEE/ACM Transactions on Networking
, 1994
"... This paper presents the packetpair ratebased feedback flow control scheme. This scheme is designed for networks where individual connections do not reserve bandwidth and for the available bitrate (besteffort) component of integrated networks. We assume a roundrobinlike queue service discipline ..."
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Cited by 44 (2 self)
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This paper presents the packetpair ratebased feedback flow control scheme. This scheme is designed for networks where individual connections do not reserve bandwidth and for the available bitrate (besteffort) component of integrated networks. We assume a roundrobinlike queue service discipline in the output queues of the network's switches, and propose a linear stochastic model for a single conversation in a network of such switches. These model motivates the PacketPair rate probing technique, which forms the basis for provably stable discrete and continuous time ratebased flow control schemes. We present a novel state estimation scheme based on fuzzy logic. We then address several practical concerns: dealing with system startup, retransmission and timeout strategy, and dynamic setpoint probing. We present a finite state machine as well as source code for a model implementation. The dynamics of a single source, the interactions of multiple sources, and the behavior of packetpai...
Flow Control Using The Theory Of Zero Sum Markov Games
 IEEE Transactions on Automatic Control
, 1992
"... We consider the problem of dynamic flow control of arriving packets into an infinite buffer. The service rate may depend on the state of the system, may change in time and is unknown to the controller. The goal of the controller is to design an efficient policy which guarantees the best performance ..."
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Cited by 36 (14 self)
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We consider the problem of dynamic flow control of arriving packets into an infinite buffer. The service rate may depend on the state of the system, may change in time and is unknown to the controller. The goal of the controller is to design an efficient policy which guarantees the best performance under the worst case service conditions. The cost is composed of a holding cost, a cost for rejecting customers (packets) and a cost that depends on the quality of the service. The problem is studied in the framework of zerosum Markov games, and a value iteration algorithm is used to solve it. We show that there exists an optimal stationary policy (such that the decisions depend only on the actual number of customers in the queue); it is of a threshold type, and it uses randomization in at most one state. Keywords: Dynamic flow control, Markov zerosum game, control of queueing networks. 1 Introduction Game theoretical methods seem to be quite promising in the control of queueing systems in...
The Application of Microeconomics to the Design of Resource Allocation and Control Algorithms
, 1989
"... In this thesis, we present a new methodology for resource sharing algorithms in distributed systems. We propose that a distributed computing system should be composed of a decentralized community of microeconomic agents. We show that this approach decreases complexity and can substantially improve ..."
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Cited by 19 (4 self)
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In this thesis, we present a new methodology for resource sharing algorithms in distributed systems. We propose that a distributed computing system should be composed of a decentralized community of microeconomic agents. We show that this approach decreases complexity and can substantially improve performance. We compare the performance, generality and complexity of our algorithms with noneconomic algorithms. To validate the usefulness of our approach, we present economies that solve three distinct resource management problems encountered in large, distributed systems. The first economy performs CPU load balancing and demonstrates how our approach limits complexity and effectively allocates resources when compared to noneconomic algorithms. We show that the economy achieves better performance than a representative noneconomic algorithm. The load balancing economy spa...
Why is Flow Control Hard: Optimality, Fairness, Partial and Delayed Information
 IN PROC. 2ND ORSA TELECOMMUNICATIONS CONFERENCE
, 1992
"... Flow control has been studied since the early stages of research in telecommunication networks. In these early studies the term flow control has been used to describe almost any type of network control. With the rapid growth of telecommunication networks control and management, flow control has evol ..."
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Cited by 15 (1 self)
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Flow control has been studied since the early stages of research in telecommunication networks. In these early studies the term flow control has been used to describe almost any type of network control. With the rapid growth of telecommunication networks control and management, flow control has evolved as a distinct class of algorithms and substantial research effort has been devoted to its study. An extensive survey of the most representative of these efforts is presented in this paper. The motivation for this work is the need for of a thorough, deep understanding of the flow control problem in gigabit, multiclass networks. A broad class of flow control schemes, namely optimal flow control, is considered within a game theoretic framework. The class of adaptive flow control mechanisms is not presented extensively, but valuable insight about the performance of such schemes can be gained from the study of optimal flow control policies. A number of important efforts to define and study fa...
Oblivious AQM and Nash Equilibria
 in INFOCOM ’03
, 2003
"... An oblivious Active Queue Management scheme is one which does not differentiate between packets belonging to different flows. In this paper, we study the existence and the quality of Nash equilibria imposed by oblivious AQM schemes on selfish agents. Oblivious AQM schemes are of obvious importance b ..."
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Cited by 13 (2 self)
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An oblivious Active Queue Management scheme is one which does not differentiate between packets belonging to different flows. In this paper, we study the existence and the quality of Nash equilibria imposed by oblivious AQM schemes on selfish agents. Oblivious AQM schemes are of obvious importance because of the ease of implementation and deployment, and Nash equilibrium offers valuable clues into network performance under noncooperative user behavior. Specifically, we ask the following three questions: 1) Do there exist oblivious AQM schemes that impose Nash equilibria on selfish agents? 2) Are the imposed equilibria, if they exist, efficient in terms of the goodput obtained and the drop probability experienced at the equilibrium? 3) How easy is it for selfish users to reach the Nash equilibrium state? We assume that the traffic sources are Poisson but the users can control the average rate. We show that droptail and RED do not impose Nash equilibria. We modify RED slightly to obtain an oblivious scheme, VLRED, that imposes a Nash equilibrium, but is not efficient. We then present another AQM policy, ENAQM, that can impose an efficient Nash equilibrium. Finally, we show that for any oblivious AQM, the Nash equilibrium imposed on selfish agents is highly sensitive as the number of agents increases, thus making it hard for the users to converge to the Nash equilibrium, and motivating the need for equilibriaaware protocols.
Gametheoretic Analysis of Internet Switching with Selfish Users
 In Proceedings of the First International Workshop on Internet and Network Economics (WINE 2005), volume 3828 of Lecture Notes in Computer Science
, 2005
"... Abstract. We consider the problem of Internet switching, where traffic is generated by selfish users. We study a packetized (TCPlike) traffic model, which is more realistic than the widely used fluid model. We assume that routers have FirstInFirstOut (FIFO) buffers of bounded capacity managed by ..."
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Cited by 4 (0 self)
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Abstract. We consider the problem of Internet switching, where traffic is generated by selfish users. We study a packetized (TCPlike) traffic model, which is more realistic than the widely used fluid model. We assume that routers have FirstInFirstOut (FIFO) buffers of bounded capacity managed by the droptail policy. The utility of each user depends on its transmission rate and the congestion level. Since selfish users try to maximize their own utility disregarding the system objectives, we study Nash equilibria that correspond to a steady state of the system. We quantify the degradation in the network performance called the price of anarchy resulting from such selfish behavior. We show that for a single bottleneck buffer, the price of anarchy is proportional to the number of users. Then we propose a simple modification of the Random Early Detection (RED) drop policy, which reduces the price of anarchy to a constant. 1
A Mechanism for Congestion Control in Computer Networks
 the Existence of Equilibria in Noncooperative Optimal Flow Control", Proceedings of ITC Workshop
, 1989
"... this paper, we present an economic model of a computer network. We then make some simplifying assumptions to derive a mechanism for congestion control. Subsequently we relax some of the assumptions and generalize the solution. We will not present details of implementation of the scheme in reallife ..."
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Cited by 3 (0 self)
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this paper, we present an economic model of a computer network. We then make some simplifying assumptions to derive a mechanism for congestion control. Subsequently we relax some of the assumptions and generalize the solution. We will not present details of implementation of the scheme in reallife networks: these will be discussed in a forthcoming thesis.