# Braess paradox in a network with stochastic dynamics and fixed strategies

## TL;DR

This paper investigates the Braess paradox in a stochastic traffic network with fixed driver strategies, revealing that adding a new road often worsens travel times except at very low densities, and that gridlock states are common.

## Contribution

It introduces a microscopic particle dynamics model with fixed route choices to analyze the Braess paradox, extending previous random-route studies and highlighting the impact of fixed strategies.

## Key findings

- Travel time reduction occurs only at very low densities.
- Braess' paradox dominates most of the phase diagram.
- Gridlock states are prevalent in the model.

## Abstract

The Braess paradox can be observed in road networks used by selfish users. It describes the counterintuitive situation in which adding a new, per se faster, origin-destination connection to a road network results in increased travel times for all network users. We study the network as originally proposed by Braess but introduce microscopic particle dynamics based on the totally asymmetric exclusion processes. In contrast to our previous work [10.1103/PhysRevE.94.062312], where routes were chosen randomly according to turning rates, here we study the case of drivers with fixed route choices. We find that travel time reduction due to the new road only happens at really low densities and Braess' paradox dominates the largest part of the phase diagram. Furthermore, the domain wall phase observed in [10.1103/PhysRevE.94.062312] vanishes. In the present model gridlock states are observed in a large part of phase space. We conclude that the construcion of a new road can often be very critical and should be considered carefully.