# A multi-lane macroscopic traffic flow model for simple networks

## TL;DR

This paper develops a well-posed macroscopic traffic flow model for multi-lane networks, accommodating real-world complexities like lane changes and speed discontinuities, supported by mathematical proofs and numerical simulations.

## Contribution

It introduces a novel multi-lane traffic model with space discontinuities and proves its well-posedness, extending previous models to more realistic scenarios.

## Key findings

- Existence of solutions established via compactness of Godunov's approximations.
- L^1-stability demonstrated using the doubling of variables technique.
- Numerical simulations illustrate the model's behavior in sample cases.

## Abstract

We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both in the speed law and in the number of lanes. This allows to describe a number of realistic situations. Existence of solutions follows from compactness results on a sequence of Godunov's approximations, while $L^1$-stability is obtained by the doubling of variables technique. Some numerical simulations illustrate the behaviour of solutions in sample cases.