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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 678 (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 80 (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 72 (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 leas ..."
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Cited by 28 (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.
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 8 (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
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 7 (7 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 5 (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.
Network economics
 HANDBOOK OF COMPUTATIONAL ECONOMETRICS
, 2009
"... Networks throughout history have provided the foundations by which humans conduct their economic activities. Transportation networks and logistical networks make possible the movement of individuals, goods, and services, whereas communication networks enable the exchange of messages and information ..."
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Cited by 4 (0 self)
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Networks throughout history have provided the foundations by which humans conduct their economic activities. Transportation networks and logistical networks make possible the movement of individuals, goods, and services, whereas communication networks enable the exchange of messages and information. Energy networks provide the fuel to support economic activities.
Traffic flow and road user impacts of the collapse of the I35W Bridge over the Mississippi River.” Report no
, 2010
"... Major network disruptions have significant impacts on local travelers. A good understanding of behavioral reactions to such incidents is crucial for traffic mitigation, management, and planning. Existing research on such topics is limited. The collapse of the I35W Mississippi River Bridge (August 1 ..."
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Cited by 3 (3 self)
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Major network disruptions have significant impacts on local travelers. A good understanding of behavioral reactions to such incidents is crucial for traffic mitigation, management, and planning. Existing research on such topics is limited. The collapse of the I35W Mississippi River Bridge (August 1, 2007) abruptly disrupted habitual routes of about 14,000 daily trips and forced even more travelers to adapt their travel pattern to evolving network conditions. The opening of the replacement bridge on November 18, 2008 generated another disturbance (this time predictable) on the network. Such “natural ” experiments provide unique opportunities for behavioral studies. This study focuses on the traffic and behavioral reactions to both bridge collapse and bridge reopening and contributes to general knowledge by identifying unique patterns following different events. Three types of data collection efforts have been conducted during the appropriate frame of reference (i.e. before vs. after bridge reconstruction): 1) GPS tracking data and associated user surveys, 2) paper and internetbased survey data gauging travel behavior in the postbridge reconstruction phase, and 3) aggregate data relating to freeway and arterial traffic flows, traffic control, and transit ridership. Differences in reactions to planned versus unplanned events were revealed. Changes in travel cost were evaluated and their temporal and spatial patterns were analyzed. This report