Second-order multilane traffic flow models: from the microscopic to the macroscopic scale

Abstract

This study addresses multilane vehicular traffic modelling, focusing on the transition between microscopic (individual vehicle-based) to macroscopic (aggregate flow-based) descriptions. While previous research on multilane traffic has largely focused on first-order models, we derive two new multilane second-order macroscopic models by applying a microscopic-to-macroscopic limit to the multilane Bando-Follow-the-Leader model. The resulting models incorporate lane-changing through source terms in a hyperbolic system of balance laws. We propose several numerical experiments showing that the models can reproduce complex traffic phenomena, including congestion propagation, non-equilibrium effects, and asymmetric lane usage. Leveraging experimental datasets from real-world highways, we further construct lane-specific empirical fundamental diagrams and compare them with their simulated counterparts, showing that our models can faithfully capture critical density values and characteristic lane-dependent patterns, thus offering a robust and generalizable tool for realistic traffic flow analysis