Investigating Braess' Paradox with Time-Dependent Queues
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
Braess's paradox for flows over time
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
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Creation of a new link or increase in capacity of an existing link can reduce the efficiency of a congested network as measured by the total travel cost. This phenomenon, of which an extreme example is given by Braess paradox, has been examined in conventional studies within the framework of static assignment. For dynamic traffic assignment, which makes account of the effect of congestion through explicit representation of queues, Akamatsu (2000) gave a simple example of the occurrence of this paradox. The present paper extends that result to a more general network. We first present a necessary and sufficient condition for the paradox to occur in a general network in which there is a queue on each link. We then give a graph-theoretic interpretation of the condition, which gives us a convenient method to test whether or not the paradox will occur by performing certain tests on information that describes the network structure. Finally, as an application of this theory, we examine several example networks and queueing patterns where occurrence of this paradox is inevitable.