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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 620 (28 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
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 68 (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.
On the interaction between overlay routing and underlay routing
 in Proc. of IEEE INFOCOM ’05
, 2005
"... Abstract — In this paper, we study the interaction between ..."
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Cited by 35 (1 self)
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Abstract — In this paper, we study the interaction between
Network Topology and the Efficiency of Equilibrium
, 2002
"... Different kinds of networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities make each user's cost depend on the other users' choices of routes. If each user chooses the leas ..."
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Cited by 24 (4 self)
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Different kinds of networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities make each user's cost depend on the other users' choices of routes. If each user chooses the least expensive (e.g., fastest) route from the users' common point of origin to the common destination, the result may be inefficient in the sense that there is an alternative assignment of routes to users that reduces the costs of all users. However, this may happen only for certain kinds of network topologies. This paper gives several alternative characterizations of networks in which inefficiencies may occur. In particular, a necessary and sufficient condition for inefficiency is that one of several specific, simple networks is embedded in the network. Keywords: Congestion, network topology, Braess's paradox, transportation networks, Wardrop equilibrium. 2 1.
Counterintuitive throughput behaviors in networks under endtoend control
 IEEE/ACM Transactions on Networking
, 2006
"... Abstract — It has been shown that as long as traffic sources adapt their rates to aggregate congestion measure in their paths, they implicitly maximize certain utility. In this paper we study some counterintuitive throughput behaviors in such networks, pertaining to whether a fair allocation is alw ..."
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Cited by 23 (10 self)
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Abstract — It has been shown that as long as traffic sources adapt their rates to aggregate congestion measure in their paths, they implicitly maximize certain utility. In this paper we study some counterintuitive throughput behaviors in such networks, pertaining to whether a fair allocation is always inefficient and whether increasing capacity always raises aggregate throughput. A bandwidth allocation policy can be defined in terms of a class of utility functions parameterized by a scalar α that can be interpreted as a quantitative measure of fairness. An allocation is fair if α is large and efficient if aggregate throughput is large. All examples in the literature suggest that a fair allocation is necessarily inefficient. We characterize exactly the tradeoff between fairness and throughput in general networks. The characterization allows us both to produce the first counterexample and trivially explain all the previous supporting examples. Surprisingly, our counterexample has the property that a fairer allocation is always more efficient. In particular it implies that maxmin fairness can achieve a higher throughput than proportional fairness. Intuitively, we might expect that increasing link capacities always raises aggregate throughput. We show that not only can throughput be reduced when some link increases its capacity, more strikingly, it can also be reduced when all links increase their capacities by the same amount. If all links increase their capacities proportionally, however, throughput will indeed increase. These examples demonstrate the intricate interactions among sources in a network setting that are missing in a singlelink topology.
On the Interaction Between Overlay Routing and Traffic Engineering
 in Proceedings of IEEE INFOCOM
, 2005
"... Abstract — In this paper, we study the interaction between ..."
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Cited by 20 (1 self)
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Abstract — In this paper, we study the interaction between
Paradoxes in distributed decisions on optimal load balancing for networks of homogeneous computers
 J. ACM
"... In completely symmetric systems that have homogeneous nodes (hosts, computers, or processors) with identical arrival processes, an optimal static load balancing scheme does not involve the forwarding of jobs among nodes. Using an appropriate analytic model of a distributed computer system, we examin ..."
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Cited by 19 (10 self)
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In completely symmetric systems that have homogeneous nodes (hosts, computers, or processors) with identical arrival processes, an optimal static load balancing scheme does not involve the forwarding of jobs among nodes. Using an appropriate analytic model of a distributed computer system, we examine the following three decision schemes for load balancing: completely distributed, intermediately distributed, and completely centralized. We show that there is no forwarding of jobs in the completely centralized and completely distributed schemes, but that in an intermediately distributed decision scheme, mutual forwarding of jobs among nodes is possible, leading to degradation in system performance for every decision maker. This result appears paradoxical, because by adding communication capacity to the system for the sharing of jobs between nodes, the overall system performance is degraded. We characterize conditions under which such paradoxical behavior occurs, and we give examples in which the degradation of performance may increase without bound. We show that the degradation reduces and finally disappears in the limit as the intermediately distributed decision scheme tends to a completely distributed one.
Braess' Paradox in a Loss Network
, 1995
"... Braess' paradox is said to occur in a network if the addition of an extra link leads to worse performance. It has been shown to occur in transportation networks (such as road networks) and also in queueing networks. Here, we show that it can occur in loss networks. ..."
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Cited by 17 (0 self)
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Braess' paradox is said to occur in a network if the addition of an extra link leads to worse performance. It has been shown to occur in transportation networks (such as road networks) and also in queueing networks. Here, we show that it can occur in loss networks.
The Roads Taken: Theory and Evidence on Route Choice in the wake of the I35W Mississippi River Bridge Collapse and Reconstruction
, 2010
"... Route choice analysis investigates the path travelers follow to implement their travel plan. It is the most frequent, and thus arguably the most important decision travelers make on a daily basis. Long established efforts have been dedicated to a normative model of the route choice decision, while i ..."
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Cited by 7 (0 self)
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Route choice analysis investigates the path travelers follow to implement their travel plan. It is the most frequent, and thus arguably the most important decision travelers make on a daily basis. Long established efforts have been dedicated to a normative model of the route choice decision, while investigations of route choice from a descriptive perspective have been limited. Wardrop’s first principle, or the shortest path assumption, is still widely used in route choice models. Most recent route choice models, following either the random utility maximization or rulebased paradigm, require explicit enumeration of feasible routes. The quality of model estimation and prediction is sensitive to the appropriateness of the consideration set. However, few empirical studies of revealed route characteristics have been reported in the literature. Moreover, factors beyond travel time, such as preferences for travel time reliability, inertia in changing routes, and travel experience that could also have significant impacts on route choice, have not been fully explored and incorporated in route choice modeling. The phenomenon that people use more than one route between the same origin and destination during a period
Identifying Winners and Losers in Transportation
 In Press) Transportation Research Record
, 2002
"... The issues surrounding transportation equity, both external and internal to transportation, are explored. Several examples are provided of transportation improvements that impose transportation costs on more individuals than those who are benefited. Beyond counting the number of winners and losers, ..."
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Cited by 6 (2 self)
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The issues surrounding transportation equity, both external and internal to transportation, are explored. Several examples are provided of transportation improvements that impose transportation costs on more individuals than those who are benefited. Beyond counting the number of winners and losers, several quantitative measures of equity are suggested and applied to a test case: ramp meters in the Twin Cities, Minneapolis–St. Paul, in Minnesota. It is recommended that transportation benefitcost analyses include an “equity impact statement,” which would consider the distribution of opportunities to participate in decisions and the outcomes of those decisions (in terms of mobility, economic, environmental, and health effects) that different strata (spatial, temporal, modal, generational, gender, racial, cultural, and income) of the population receive. Policy makers would then have additional information on which to base decisions. Social welfare includes both efficiency and equity. Transportation