# On the Braess Paradox with Nonlinear Dynamics and Control Theory

## TL;DR

This paper demonstrates the occurrence of the Braess paradox in nonlinear traffic flow models and proposes control strategies to mitigate it, providing a general framework for uncongested network flows.

## Contribution

It introduces a control-theoretic approach to prevent the Braess paradox in nonlinear traffic networks, expanding understanding of network flow management.

## Key findings

- Braess paradox exists in nonlinear traffic models
- Control methods can prevent the paradox
- Framework applies to uncongested network flows

## Abstract

We show the existence of the Braess paradox for a traffic network with nonlinear dynamics described by the Lighthill-Whitham-Richards model for traffic flow. Furthermore, we show how one can employ control theory to avoid the paradox. The paper offers a general framework applicable to time-independent, uncongested flow on networks. These ideas are illustrated through examples.