Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles

Abstract

We develop a hierarchical description of traffic flow control by means of driver-assist vehicles aimed at the mitigation of speed-dependent road risk factors. Microscopic feedback control strategies are designed at the level of vehicle-to-vehicle interactions and then upscaled to the global flow via a kinetic approach based on a Boltzmann-type equation. Then first and second order hydrodynamic traffic models, which naturally embed the microscopic control strategies, are consistently derived from the kinetic-controlled framework via suitable closure methods. Several numerical examples illustrate the effectiveness of such a hierarchical approach at the various scales.

arXiv comment30 pages, 12 figures

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Cited by in corpus (14)

• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• Uncertainty damping in kinetic traffic models by driver-assist controls
• Boltzmann-type equations for multi-agent systems with label switching
• The Aw-Rascle traffic model: Enskog-type kinetic derivation and generalisations
• Reconstruction of traffic speed distributions from kinetic models with uncertainties
• Multiscale control of generic second order traffic models by driver-assist vehicles
• Kinetic derivation of Aw-Rascle-Zhang-type traffic models with driver-assist vehicles
• Macroscopic limits of non-local kinetic descriptions of vehicular traffic
• Boltzmann-type description with cutoff of Follow-the-Leader traffic models
• The turnpike property for mean-field optimal control problems
• Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties
• Microscopic and Macroscopic Traffic Flow Models including Random Accidents
• Exponential turnpike property for particle systems and mean-field limit
• Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects