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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 516 (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
Selfish Traffic Allocation for Server Farms
, 2003
"... We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price... ..."
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Cited by 77 (5 self)
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We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price...
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 59 (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.
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 least expensiv ..."
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Cited by 17 (3 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.
Measuring Winners and Losers from the new I35W Mississippi River Bridge
, 2009
"... The opening of the replacement for the I35W Mississippi River Bridge bridge on September 18th, 2008 provides a unique opportunity to evaluate the impacts generated by this additional link on network performance, and thus empirically test whether a Braess Paradox occurred. Using detailed GPS data to ..."
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Cited by 4 (4 self)
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The opening of the replacement for the I35W Mississippi River Bridge bridge on September 18th, 2008 provides a unique opportunity to evaluate the impacts generated by this additional link on network performance, and thus empirically test whether a Braess Paradox occurred. Using detailed GPS data to estimate travel times on links and for origindestination pairs, this research finds that while on average travel time improved with the reopening of the bridge, the subsequent restoration of parts of the rest of the network to their precollapse configuration worsened travel times significantly on average. In all cases, the distribution of winners and losers indicates clear spatial patterns associated with these network changes. While no Braess paradox was found in this case, the research provides a method for measuring such phenomena. 1
Braess’s Paradox in Large Random Graphs
, 2008
"... Braess’s Paradox is the counterintuitive but wellknown fact that removing edges from a network with “selfish routing” can decrease the latency incurred by traffic in an equilibrium flow. Despite the large amount of research motivated by Braess’s Paradox since its discovery in 1968, little is known ..."
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Cited by 1 (0 self)
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Braess’s Paradox is the counterintuitive but wellknown fact that removing edges from a network with “selfish routing” can decrease the latency incurred by traffic in an equilibrium flow. Despite the large amount of research motivated by Braess’s Paradox since its discovery in 1968, little is known about whether it is a common realworld phenomenon, or a mere theoretical curiosity. We prove that Braess’s Paradox is likely to occur in a natural random network model: with high probability, there is a traffic rate and a set of edges whose removal improves the latency of traffic in an equilibrium flow by a constant factor. Our proof approach is robust and shows that the global behavior of an equilibrium flow in a large random network is similar to that in Braess’s original fournode example.
ATIS at Rush Hour: Adaptation and Departure Time Coordination in Iterated Commuting
, 1997
"... Morning commuters adjust their departure times in response to daytoday changes in congestion. Advanced Traveler Information Systems (ATIS) may enable motorists to employ fundamentally new strategies when adapting their departure times to fluctuations in congestion. At the same time, new driver ..."
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Morning commuters adjust their departure times in response to daytoday changes in congestion. Advanced Traveler Information Systems (ATIS) may enable motorists to employ fundamentally new strategies when adapting their departure times to fluctuations in congestion. At the same time, new driver strategies will likely give rise to different road network behaviors. This paper explores the mutual feedback between driver strategy and traffic system performance through a simulation model of rush hour commuting. Motorists in this model choose departure times according to three adaptive strategies. When commuters apply adaptive strategies that require ATIS in the present model, outcomes for both individual motorists and the system as a whole are by several measures worse than when drivers use a simple strategy that does not require ATIS. These results largely agree with an earlier study of a nearly identical model of rushhour commuting. This document is available in HTML on the ...
Metropolitan Consortium. We would also like to thank John Bloomfield, Carlos Carrion, Randy
, 2010
"... This report represents the results of research conducted by the authors and does not necessarily represent the views ..."
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This report represents the results of research conducted by the authors and does not necessarily represent the views
Planned Versus Unplanned: Travel Impacts and Adjustment Strategies of the Collapse and the Reopening of I35W Bridge
, 2009
"... Task 3: Following collection of the various aggregate and disaggregate data sets, analysis of the travel behavior and traffic flow elements of the bridge collapse will be carried out. As outlined in the Summary of Research Methodology section, this generally involves summarizing the travel behavior ..."
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Task 3: Following collection of the various aggregate and disaggregate data sets, analysis of the travel behavior and traffic flow elements of the bridge collapse will be carried out. As outlined in the Summary of Research Methodology section, this generally involves summarizing the travel behavior impacts of the bridge closure and its eventual reconstruction, modeling flows on the transportation network with and without the I35W Bridge link and determining the amount of diversion in terms of road and use costs. This document contains three reports constituting the Data Analysis task: