A multi-scale multi-lane model for traffic regulation via autonomous vehicles

TL;DR

This paper introduces a multi-scale traffic model incorporating autonomous vehicles as moving bottlenecks, coupling PDEs for lane densities with ODEs for AV trajectories, and analyzes their mathematical properties and limits.

Contribution

It presents a novel coupled PDE-ODE model for multi-lane traffic with AVs, proving existence of solutions and analyzing their limiting behavior.

Findings

Existence of entropy weak solutions for the coupled model

Characterization of the limit as AV influence vanishes

Numerical simulations illustrating the model's behavior

Abstract

We propose a new model for multi-lane traffic with moving bottlenecks, e.g., autonomous vehicles (AV). It consists of a system of balance laws for traffic in each lane, coupled in the source terms for lane changing, and fully coupled to ODEs for the AVs' trajectories.More precisely, each AV solves a controlled equation depending on the traffic density, while the PDE on the corresponding lane has a flux constraint at the AV's location. We prove existence of entropy weak solutions, and we characterize the limiting behavior for the source term converging to zero (without AVs), corresponding to a scalar conservation law for the total density.The convergence in the presence of AVs is more delicate and we show that the limit does not satisfy an entropic equation for the total density as in the original coupled ODE-PDE model. Finally, we illustrate our results via numerical simulations.