Uncertainty damping in kinetic traffic models by driver-assist controls

Abstract

In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the vehicles, by which we prove that it is possible to dampen the propagation of such an uncertainty across the scales. Our analytical and numerical results suggest that the aggregate traffic flow may be made more ordered, hence predictable, by implementing such control protocols in driver-assist vehicles. Remarkably, they also provide a precise relationship between a measure of the macroscopic damping of the uncertainty and the penetration rate of the driver-assist technology in the traffic stream.

References in corpus (7)

• Boltzmann type control of opinion consensus through leaders
• Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• Boltzmann-type models with uncertain binary interactions
• Hybrid stochastic kinetic description of two-dimensional traffic dynamics
• Reconstruction of traffic speed distributions from kinetic models with uncertainties
• Control strategies for road risk mitigation in kinetic traffic modelling

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