The Riemann Solver for Traffic Flow at an Intersection with Buffer of Vanishing Size

TL;DR

This paper investigates the behavior of traffic flow models at intersections with diminishing buffer sizes, proving convergence to a new self-similar solution characterized by a Lipschitz continuous Riemann solver.

Contribution

It introduces a novel Limit Riemann Solver for traffic flow at intersections with vanishing buffers, demonstrating its convergence and continuous dependence on parameters.

Findings

Convergence of buffer-based solutions to a Limit Riemann Solver as buffer size approaches zero

The Limit Riemann Solver depends Lipschitz continuously on all parameters

The model provides a rigorous mathematical framework for traffic flow at intersections with minimal buffer capacity

Abstract

The paper examines the model of traffic flow at an intersection introduced in [2], containing a buffer with limited size. As the size of the buffer approach zero, it is proved that the solution of the Riemann problem with buffer converges to a self-similar solution described by a specific Limit Riemann Solver (LRS). Remarkably, this new Riemann Solver depends Lipschitz continuously on all parameters.