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How bad is selfish routing?
 JOURNAL OF THE ACM
, 2002
"... We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route t ..."
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Cited by 506 (27 self)
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We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimumlatency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total
Architecting Noncooperative Networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 1995
"... In noncooperative networks users make control decisions that optimize their own performance measure. Focusing on routing, we devise two methodologies for architecting noncooperative networks, that improve the overall network performance. These methodologies are motivated by problem settings arising ..."
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Cited by 124 (16 self)
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In noncooperative networks users make control decisions that optimize their own performance measure. Focusing on routing, we devise two methodologies for architecting noncooperative networks, that improve the overall network performance. These methodologies are motivated by problem settings arising in the provisioning and the run time phases of the network. For either phase, Nash equilibria characterize the operating point of the network. The goal of the provisioning phase is to allocate link capacities that lead to systemwide efficient Nash equilibria. In general, the solution of such design problems is counterintuitive, since adding link capacity might lead to a degradation of user performance. We show that, for systems of parallel links, such paradoxes cannot occur and the optimal solution coincides with the solution in the singleuser case. We derive some extensions to general network topologies. During the run time phase, a manager controls the routing of part of the network flow. The manager is aware of the noncooperative behavior of the users and makes its routing decisions based on this information while aiming at improving the overall system performance. We obtain necessary and sufficient conditions for enforcing an equilibrium that coincides with the global systemwide optimum, and indicate that these conditions are met in many cases of interest.
Stackelberg scheduling strategies
 In Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing
, 2001
"... AbstractWe study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with loaddependent latency functions specifying the length of time necessary to complete a job; we measure ..."
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Cited by 108 (6 self)
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AbstractWe study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with loaddependent latency functions specifying the length of time necessary to complete a job; we measure system performance by the total latency of the system. Assigning jobs according to the selfish interests of individual users (who wish to minimize only the latency that their own jobs experience) typically results in suboptimal system performance. However, in many systems of this type there is a mixture of "selfishly controlled " and "centrally controlled " jobs; as the assignment of centrally controlled jobs will influence the subsequent actions by selfish users, we aspire to contain the degradation in system performance due to selfish behavior by scheduling the centrally controlled jobs in the best possible way. We formulate this goal as an optimization problem via Stackelberg games, games in which one player acts a leader (here, the centralized authority interested in optimizing system performance) and the rest as followers (the selfish users). The problem is then to compute a strategy for the leader (a Stackelberg strategy) that induces the followers to react in a way that (at least approximately) minimizes the total latency in the system. In this paper, we prove that it is NPhard to compute the optimal Stackelberg strategy and present simple strategies with provable performance guarantees. More precisely, we give a simple algorithm that computes a strategy inducing a job assignment with total latency no more than a constant times that of the optimal assignment of all of the jobs; in the absence of centrally controlled jobs and a Stackelberg strategy, no result of this type is possible. We also prove stronger performance guarantees in the special case where every machine latency function is linear in the machine load.
Programming telecommunication networks
 IEEE Network
, 1997
"... The recent move towards market deregulation and open competition has sparked a wave of serious introspection in the telecommunications service industry. Telecom providers and operators are now required to open up their primary revenue channels to competing industries. In this paper, we examine the s ..."
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Cited by 81 (4 self)
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The recent move towards market deregulation and open competition has sparked a wave of serious introspection in the telecommunications service industry. Telecom providers and operators are now required to open up their primary revenue channels to competing industries. In this paper, we examine the service structure of two major global communication networks  the Telephone Network and the Internet and explore their weaknesses and strengths. Building upon the experience we gained during the development of the initial xbind prototypes, we discuss the realization of an open programable networking environment based on a new service architecture for advanced telecommunication services. Our approach to the problem stems from two angles  one conceptual, the other implementational. In the first, we attempt to develop a service model that is open and reflects the economic market structure of the future telecommunications service industry. We believe that investigating such a model will help cl...
Capacity Allocation under Noncooperative Routing
, 1997
"... The capacity allocation problem in a network that is to be shared by noncooperative users is considered. Each user decides independently upon its routing strategy, so as to optimize its individual performance objective. The operating points of the network are the Nash equilibria of the underlying ro ..."
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Cited by 67 (13 self)
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The capacity allocation problem in a network that is to be shared by noncooperative users is considered. Each user decides independently upon its routing strategy, so as to optimize its individual performance objective. The operating points of the network are the Nash equilibria of the underlying routing game. The network designer aims to allocate link capacities, so that the resulting Nash equilibria are efficient, according to some systemwide performance criterion. In general, the solution of such design problems is complex and at times counterintuitive, since adding link capacity might lead to degradation of user performance. For systems of parallel links, we show that such paradoxes do not occur and that the capacity allocation problem has a simple and intuitive optimal solution, that coincides with the solution in the singleuser case.
RevenueMaximizing Pricing and Capacity Expansion in a ManyUsers Regime
, 2002
"... In this paper, we consider a network where each user is charged a fixed price per unit of bandwidth used, but where there is no congestiondependent pricing. However, the transmission rate of each user is assumed to be a function of network congestion (like TCP), and the price per unit bandwidth. We ..."
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Cited by 66 (7 self)
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In this paper, we consider a network where each user is charged a fixed price per unit of bandwidth used, but where there is no congestiondependent pricing. However, the transmission rate of each user is assumed to be a function of network congestion (like TCP), and the price per unit bandwidth. We are interested in answering the following question: how should the network choose the price to maximize its overall revenue? To obtain a tractable solution, we consider a single link accessed by many users where the capacity is increased in proportion to the number of users. We show the following result: as the number of users increases, the optimal priceperunitbandwidth charged by the service provider may increase or decrease depending upon the bandwidth of the link. However, for all values of the link capacity, the service provider's revenueperunitbandwidth increases and the overall performance of each user (measured in terms of a function of its throughput, the network congestion and the cost incurred by the user for bandwidth usage) improves. Since the revenue per unit bandwidth increases, it provides an incentive for the service provider to increase the available bandwidth in proportion to the number of users.
Designing networks for selfish users is hard
 In Proceedings of the 42nd Annual Symposium on Foundations of Computer Science
, 2001
"... Abstract We consider a directed network in which every edge possesses a latency function specifying the time needed to traverse the edge given its congestion. Selfish, noncooperative agents constitute the network traffic and wish to travel from a source s to a sink t as quickly as possible. Since th ..."
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Cited by 60 (8 self)
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Abstract We consider a directed network in which every edge possesses a latency function specifying the time needed to traverse the edge given its congestion. Selfish, noncooperative agents constitute the network traffic and wish to travel from a source s to a sink t as quickly as possible. Since the route chosen by one network user affects the congestion (and hence the latency) experienced by others, we model the problem as a noncooperative game. Assuming each agent controls only a negligible portion of the overall traffic, Nash equilibria in this noncooperative game correspond to st flows in which all flow paths have equal latency. A natural measure for the performance of a network used by selfish agents is the common latency experienced by each user in a Nash equilibrium. It is a counterintuitive but wellknown fact that removing edges from a network may improve its performance; the most famous example of this phenomenon is the socalled Braess's Paradox. This fact motivates the following network design problem: given such a network, which edges should be removed to obtain the best possible flow at Nash equilibrium? Equivalently, given a large network of candidate edges to be built, which subnetwork will exhibit the best performance when used selfishly? We give optimal inapproximability results and approximation algorithms for several network design problems of this type. For example, we prove that for networks with n vertices and continuous, nondecreasing latency functions, there is no approximation algorithm for this problem with approximation ratio less than n/2 (unless P = N P). We also prove this hardness result to be best possible by exhibiting an n/2approximation algorithm. For networks in which the latency of each edge is a linear function of the congestion, we prove that there is no ( 43 ffl)approximation algorithm for the problem (for any ffl> 0, unless P = N P); the existence of a 43approximation algorithm follows easily from existing work, proving this hardness result sharp. Moreover, we prove that an optimal approximation algorithm for these problems is what we call the trivial algorithm: given a network of candidate edges, build the entire network. A consequence of this result is that Braess's Paradox (even in its worstpossible manifestation) is impossible to detect efficiently.
Using Collective Intelligence To Route Internet Traffic
 IN ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 1999
"... A COllective INtelligence (COIN) is a set of interacting reinforcement learning (RL) algorithms designed in an automated fashion so that their collective behavior optimizes a global utility function. We summarize the theory of COINs, then present experiments using that theory to design COINs to cont ..."
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Cited by 59 (24 self)
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A COllective INtelligence (COIN) is a set of interacting reinforcement learning (RL) algorithms designed in an automated fashion so that their collective behavior optimizes a global utility function. We summarize the theory of COINs, then present experiments using that theory to design COINs to control internet traffic routing. These experiments indicate that COINs outperform all previously investigated RLbased, shortest path routing algorithms.