Freeway traffic management via kinetic compartmental models

Other conference contribution, 2025

In this study, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ordinary differential equations (ODEs) that are formally equivalent to the kinetic systems used to model chemical reaction networks. An in-depth numerical analysis of the TRM is performed. The paper assesses incremental asymptotic stability for TRM discretized systems of ordinary differential equations (ODEs), hinting a new freeway traffic state estimation concept: open-loop stable state estimators. Finally, it proposes a unified freeway dynamic speed and ramp metering control approach via the modification of the reaction dynamics.