Stability of a Nonlocal Traffic Flow Model for Connected Vehicles

TL;DR

This paper analyzes the stability of a nonlocal traffic flow model for connected vehicles, showing conditions under which traffic remains stable or develops persistent waves, informing future vehicle control algorithms.

Contribution

It provides a stability analysis of a nonlocal LWR traffic model, highlighting how proper use of nonlocal information ensures stability and wave dissipation.

Findings

Nonlocal traffic flow can be stable with proper information utilization.

Improper use of nonlocal data can cause persistent traffic waves.

Exponential decay of traffic waves under certain conditions.

Abstract

The emerging connected and automated vehicle technologies allow vehicles to perceive and process traffic information in a wide spatial range. Modeling nonlocal interactions between connected vehicles and analyzing their impact on traffic flows become important research questions to traffic planners. This paper considers a particular nonlocal LWR model that has been studied in the literature. The model assumes that vehicle velocities are controlled by the traffic density distribution in a nonlocal spatial neighborhood. By conducting stability analysis of the model, we obtain that, under suitable assumptions on how the nonlocal information is utilized, the nonlocal traffic flow is stable around the uniform equilibrium flow and all traffic waves dissipate exponentially. Meanwhile, improper use of the nonlocal information in the vehicle velocity selection could result in persistent traffic waves. Such results can shed light to the future design of driving algorithms for connected and automated vehicles.