Braess's Paradox for Flows Over Time

TL;DR

This paper investigates how Braess's paradox manifests in flow over time models, revealing differences from static flow models and identifying network topologies where the paradox occurs.

Contribution

It demonstrates that Braess's paradox can occur in flow over time models even when absent in static models, and explores asymmetries and conditions for its occurrence.

Findings

Braess's paradox can occur in flow over time even if absent in static models.

Certain network topologies exhibit more severe Braess's ratios in flow over time.

Braess's paradox is not symmetric for flows over time, unlike static flow models.

Abstract

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.