Nonlocal reaction traffic flow model with on-off ramps

TL;DR

This paper introduces a non-local scalar balance law model for traffic flow with on-ramps and off-ramps, using numerical schemes to analyze solution behavior and establish well-posedness.

Contribution

It develops a novel non-local traffic flow model with ramps and proves well-posedness using numerical and analytical methods.

Findings

Numerical simulations demonstrate solution behavior.

The model maintains bounded variation and L^ estimates.

Well-posedness of the non-local traffic flow model is established.

Abstract

We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the traffic flow over the on-ramp and off-ramps. We approximate the problem using an upwind-type numerical scheme and we provide L^\infty and BV estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.