Bounded-METANET: A new discrete-time second-order macroscopic traffic flow model for bounded speed

Macroscopic traffic flow models are essential for analysing traffic dynamics in highways and urban roads. While second-order models like METANET capture non-equilibrium traffic states, they often produce unrealistic speed predictions, such as negative values or speeds above the free-flow limit, which limits their reliability in traffic management. To overcome these limitations, we introduce Bounded-METANET, a new discrete-time second-order model that refines METANET's speed update equation by removing the convection term and adding a virtual density mechanism to reflect anticipation and merging effects. This ensures that speeds stay bounded between zero and the free-flow speed, simplifying calibration and boosting usability. Validated with SUMO simulations and real-world German highway data, Bounded-METANET accurately captures non-equilibrium flow and the capacity drop phenomenon, and outperforms METANET in estimating the fundamental diagram under congestion. It achieves lower RMSE for speed and density in noise-free simulation data and better flow estimation in real-world data, though METANET edges out in speed RMSE. Unlike METANET, which can produce erratic shockwave speeds and flow errors, Bounded-METANET delivers consistent, realistic predictions. This makes it a promising tool for traffic modelling and control in various scenarios.