A Space-time Nonlocal Traffic Flow Model: Relaxation Representation and Local Limit

TL;DR

This paper introduces a space-time nonlocal traffic flow model incorporating inter-vehicle communication, establishes its well-posedness, and demonstrates its relation to classical models through relaxation limits.

Contribution

It develops a novel nonlocal conservation law with a finite-speed information travel assumption and connects it to established traffic flow models via relaxation representation.

Findings

Model well-posedness under certain conditions

Reformulation as a hyperbolic system with relaxation

Recovery of classical traffic model in equilibrium limit

Abstract

We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal integral of weighted traffic density. The well-posedness of the model is established under suitable conditions on the model parameters and by a suitably-defined initial condition. In a special case where the weight kernel in the nonlocal integral is an exponential function, the nonlocal model can be reformulated as a $2\times2$ hyperbolic system with relaxation. With the help of this relaxation representation, we show that the Lighthill-Whitham-Richards model is recovered in the equilibrium approximation limit.