A microscopic derivation of a traffic flow model on a junction with two entry lines

TL;DR

This paper derives a continuous traffic flow model on a junction from a discrete follow-the-leader model, incorporating traffic lights and priority rules, providing a rigorous link between microscopic and macroscopic descriptions.

Contribution

It introduces a novel derivation of a macroscopic conservation law on a traffic network from a microscopic follow-the-leader model with traffic lights.

Findings

The continuous model is L1 contractive.

The model accounts for traffic light timing and priority rules.

A germ depending on flux and green time describes the junction behavior.

Abstract

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity and after scaling. In the discrete model, the vehicles solve a follow-the-leader model on each branch. The priority rule at the junction is given by a timeperiodic traffic light (with a period tending to infinity with the scaling for technical reasons). The conservation law at the limit is L 1 contractive and described in terms of a germ depending on the flux and on the average amount of time the traffic light is ''green'' on a branch.