1997
DOI: 10.1016/s0191-2615(96)00024-0
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Braess' paradox: Some new insights

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Cited by 156 publications
(109 citation statements)
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“…Researchers have proposed classification of networks in which the addition of one or more links could degrade performance (Frank 1981;Steinberg and Zangwill 1983), discovered new paradoxes (Arnott et al 1993;Cohen and Kelly 1990;Dafermos and Nagurney 1984;Pas and Principio 1997;Smith 1978;Steinberg and Stone 1988), proved that detecting the BP in networks is algorithmically hard (Roughgarden 2006), and quantified the degree of degradation in network performance from unregulated traffic (Koutsoupias and Papadimitriou 1999;Roughgarden and Tardos 2002). Almost all the existing theoretical work on the problem of detecting and illustrating the BP has considered networks similar to the one presented in Fig.…”
Section: Theoreticalmentioning
confidence: 99%
“…Researchers have proposed classification of networks in which the addition of one or more links could degrade performance (Frank 1981;Steinberg and Zangwill 1983), discovered new paradoxes (Arnott et al 1993;Cohen and Kelly 1990;Dafermos and Nagurney 1984;Pas and Principio 1997;Smith 1978;Steinberg and Stone 1988), proved that detecting the BP in networks is algorithmically hard (Roughgarden 2006), and quantified the degree of degradation in network performance from unregulated traffic (Koutsoupias and Papadimitriou 1999;Roughgarden and Tardos 2002). Almost all the existing theoretical work on the problem of detecting and illustrating the BP has considered networks similar to the one presented in Fig.…”
Section: Theoreticalmentioning
confidence: 99%
“…Roughgarden and Tardos (2002) proved that in traffic networks in which the cost associated with each edge is an affine function of this edge congestion, the flow at the Nash equilibrium has total cost of at most 4/3 times that of the optimal flow. For further extensions, discussions, and examples of the BP and related problems in route choice, see Catoni and Pallottino (1991), Fisk (1979), Penchina (1997), Roughgarden (2005), and Pas and Principio (1997).…”
Section: Previous Theoretical Researchmentioning
confidence: 99%
“…However, as we can see in Figure 1(b), by removing the central zero latency edge, the selfish routing will spread the flow uniformly over the paths between s and t, resulting in an overall latency of 3 2 . Since its discovery Braess's paradox has spawned a significant amount of work aimed at understanding the full implications of the paradox, both theoretically [3,5,11,12] and via anecdotal observations [2,7]. In many ways the recent trend towards studying the "Price of Anarchy" [8,10] has its roots in the discovery of Braess's paradox.…”
Section: Introductionmentioning
confidence: 99%