A non-local traffic flow model for 1-to-1 junctions with buffer

TL;DR

This paper introduces a novel non-local PDE-ODE traffic flow model for 1-to-1 junctions with buffers, providing existence results, numerical methods, and analysis of limit behaviors, advancing understanding of complex traffic dynamics.

Contribution

It develops a new non-local traffic model for junctions with buffers, including existence proofs, numerical schemes, and limit analysis, which were not previously addressed.

Findings

Existence of solutions in free flow case

Numerical approximation methods for the model

Limit behavior analysis as kernel support varies

Abstract

Inthispaper,weintroduceanon-localPDE-ODEtrafficmodeldevotedtothedescriptionof a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general case. In addition, we show a maximum principle which is uniform in the non-local interaction range. Further, we exploit the limit models as the support of the kernel tends to zero and to infinity. We compare them with other already existing models for traffic and production flow and present numerical examples.