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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
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 12 (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.
Sensitivity analysis of traffic equilibria
 Transportation Science
, 1973
"... informs ® doi 10.1287/trsc.1030.0043 © 2004 INFORMS The contribution of the paper is a complete analysis of the sensitivity of elastic demand traffic (Wardrop) equilibria. The existence of a directional derivative of the equilibrium solution (link flow, least travel cost, demand) in any direction is ..."
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Cited by 8 (3 self)
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informs ® doi 10.1287/trsc.1030.0043 © 2004 INFORMS The contribution of the paper is a complete analysis of the sensitivity of elastic demand traffic (Wardrop) equilibria. The existence of a directional derivative of the equilibrium solution (link flow, least travel cost, demand) in any direction is given a characterization, and the same is done for its gradient. The gradient, if it exists, is further interpreted as a limiting case of the gradient of the logitbased SUE solution, as the dispersion parameter tends to infinity. In the absence of the gradient, we show how to compute a subgradient. All these computations (directional derivative, (sub)gradient) are performed by solving similar traffic equilibrium problems with affine link cost and demand functions, and they can be performed by the same tool as (or one similar to) the one used for the original traffic equilibrium model; this fact is of clear advantage when applying sensitivity analysis within a bilevel (or mathematical program with equilibrium constraints, MPEC) application, such as for congestion pricing, OD estimation, or network design. A small example illustrates the possible nonexistence of a gradient and the computation of a subgradient. Key words: traffic equilibrium; stochastic user equilibrium; sensitivity analysis; directional derivative; bilevel optimization
Efficiency and Braess’ Paradox under Pricing in General Networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATION
, 2002
"... We study the flow control and routing decisions of selfinterested users in a general congested network where a single profitmaximizing service provider sets prices for different paths in the network. We define an equilibrium of the user choices. We then define the monopoly equilibrium (ME) as the ..."
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Cited by 7 (4 self)
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We study the flow control and routing decisions of selfinterested users in a general congested network where a single profitmaximizing service provider sets prices for different paths in the network. We define an equilibrium of the user choices. We then define the monopoly equilibrium (ME) as the equilibrium prices set by the service provider and the corresponding user equilibrium. We analyze the networks containing different types of user utilities: elastic or inelastic. For a network containing inelastic user utilities, we show the flow allocations at the ME and the social optimum are the same. For a network containing elastic user utilities, we explicitly characterize the ME and study its performance relative to the user equilibrium at 0 prices and the social optimum that would result from centrally maximizing the aggregate system utility. We also define Braess’ Paradox for a network involving pricing and show that Braess’ Paradox does not occur under monopoly prices.
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
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 ...
Sensitivity of Wardrop Equilibria ⋆
"... Abstract. We study the sensitivity of equilibria in the wellknown game theoretic traffic model due to Wardrop. We mostly consider singlecommodity networks. Suppose, given a unit demand flow at Wardrop equilibrium, one increases the demand by ε or removes an edge carrying only an εfraction of flow ..."
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Abstract. We study the sensitivity of equilibria in the wellknown game theoretic traffic model due to Wardrop. We mostly consider singlecommodity networks. Suppose, given a unit demand flow at Wardrop equilibrium, one increases the demand by ε or removes an edge carrying only an εfraction of flow. We study how the equilibrium responds to such an εchange. Our first surprising finding is that, even for linear latency functions, for every ε> 0, there are networks in which an εchange causes every agent to change its path in order to recover equilibrium. Nevertheless, we can prove that, for general latency functions, the flow increase or decrease on every edge is at most ε. Examining the latency at equilibrium, we concentrate on polynomial latency functions of degree at most p with nonnegative coefficients. We show that, even though the relative increase in the latency of an edge due to an εchange in the demand can be unbounded, the path latency at equilibrium increases at most by a factor of (1 + ε) p. The increase of the price of anarchy is shown to be upper bounded by the same factor. Both bounds are shown to be tight. Let us remark that all our bounds are tight. For the multicommodity case, we present examples showing that neither the change in edge flows nor the change in the path latency can be bounded. 1
Choice of Routes in Congested . . .
, 2005
"... The Braess paradox (Braess, 1968) consists of showing that, in equilibrium, adding a new link that connects two routes running between a common origin and common destination may raise the travel cost for each network user. We report the results of two experiments designed to study whether the parado ..."
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The Braess paradox (Braess, 1968) consists of showing that, in equilibrium, adding a new link that connects two routes running between a common origin and common destination may raise the travel cost for each network user. We report the results of two experiments designed to study whether the paradox is behaviorally realized in two simulated traffic networks that differ from each other in their topology. Implementing a withinsubjects design, both experiments include finite populations of paid participants in a computercontrolled setup who independently and repeatedly choose travel routes in one of two types of traffic networks, one without the added links and the other with the added links, to minimize their travel costs. Our results reject the hypothesis that the paradox is of marginal value and its force, if at all evident, diminishes with experience. Rather, they strongly support the alternative hypothesis that with experience in traversing the traffic network players converge to choosing the Pareto deficient equilibrium routes despite sustaining a sharp decline in their earnings.
Influence of Beckmann, . . .
 PREPARED FOR THE PANEL: STUDIES IN THE ECONOMICS OF TRANSPORTATION: A RETROSPECTIVE, AT THE 50TH NORTH AMERICAN REGIONAL SCIENCE ASSOCIATION MEETING IN PHILADELPHIA,
, 2003
"... This paper describes the impact and influence of the book, Studies in the Economics of Transportation, by M. J. Beckmann, C. B. McGuire, and C. B. Winsten, published in 1956 by Yale University Press. The focus of this paper is on the book’s impacts on innovations in modeling, methodological developm ..."
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This paper describes the impact and influence of the book, Studies in the Economics of Transportation, by M. J. Beckmann, C. B. McGuire, and C. B. Winsten, published in 1956 by Yale University Press. The focus of this paper is on the book’s impacts on innovations in modeling, methodological developments, and applications in transportation science and in other disciplines as well.
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