The Braess Paradox in a network of totally asymmetric exclusion processes

TL;DR

This paper investigates the Braess paradox within a realistic traffic network model using totally asymmetric exclusion processes, revealing how added links can both improve and worsen travel times depending on network density and fluctuations.

Contribution

It introduces a TASEP-based model to study the Braess paradox, capturing nonlinear effects, jams, and fluctuations, providing a detailed phase diagram of network behavior.

Findings

At low densities, added edges reduce travel times.

Classical Braess paradox occurs at intermediate densities.

High densities also benefit from added links.

Abstract

We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to a road network leads to a user optimum with higher travel times for all network users. Travel times on the TASEPs are nonlinear in the density, and jammed states can occur due to the microscopic exclusion principle, leading to a more realistic description of trafficlike transport on the network than in previously studied linear macroscopic mathematical models. Furthermore, the stochastic dynamics allows us to explore the effects of fluctuations on network performance. We observe that for low densities, the added edge leads to lower travel times. For slightly higher densities, the Braess paradox occurs in its classical sense. At intermediate densities, strong fluctuations in the travel times dominate the system's behavior due to links that are in a domain-wall state. At high densities, the added link leads to lower travel times. We present a phase diagram that predicts the system's state depending on the global density and crucial path-length ratios.