Journal of the ACM (JACM)
Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks
Transportation Science
A stronger bound on Braess's Paradox
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On the severity of Braess's paradox: designing networks for selfish users is hard
Journal of Computer and System Sciences - Special issue on FOCS 2001
On a Paradox of Traffic Planning
Transportation Science
Nash Equilibria and the Price of Anarchy for Flows over Time
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
A competitive strategy for routing flow over time
ACM SIGecom Exchanges
Existence and uniqueness of equilibria for flows over time
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
A Stackelberg strategy for routing flow over time
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Contention issues in congestion games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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We study the properties of Braess's paradox in the context of the model of congestion games with flow over time introduced by Koch and Skutella. We compare them to the well known properties of Braess's paradox for Wardrop's model of games with static flows. We show that there are networks which do not admit Braess's paradox in Wardrop's model, but which admit it in the model with flow over time. Moreover, there is a topology that admits a much more severe Braess's ratio for this model. Further, despite its symmetry for games with static flow, we show that Braess's paradox is not symmetric for flows over time. We illustrate that there are network topologies which exhibit Braess's paradox, but for which the transpose does not. Finally, we conjecture a necessary and sufficient condition of existence of Braess's paradox in a network, and prove the condition of existence of the paradox either in the network or in its transpose.