A Space-time Nonlocal Traffic Flow Model: Relaxation Representation and Local 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 $2\times 2$ 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.

32 pages

References in corpus (3)

• Nonlocal traffic models with general kernels: singular limit, entropy admissibility, and convergence rate
• Conservation laws with nonlocal velocity -- the singular limit problem
• A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels