Journal
MATHEMATICAL CONTROL AND RELATED FIELDS
Volume 11, Issue 3, Pages 681-713Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mcrf.2021018
Keywords
Kinetic traffic models; Boltzmann-type equations; Fokker-Planck equations; uncertainty quantification
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Funding
- Italian Ministry for Education, University and Research (MIUR) through the Dipartimenti di EccellenzaProgramme (2018-2022), Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino [CUP: E11G18000350001]
- Italian Ministry for Education, University and Research (MIUR) through the Dipartimenti di EccellenzaProgramme (2018-2022), Department of Mathematics F. Casorati, University of Pavia
- Italian Ministry for Education, University and Research (MIUR) through PRIN 2017 project [2017KKJP4X]
- Compagnia di San Paolo (Torino)
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The paper proposed a kinetic model of traffic flow with uncertain binary interactions and showed that the uncertainty can be dampened by controlling the microscopic interactions among vehicles, resulting in more ordered and predictable traffic flow. The study also indicated a precise relationship between the penetration rate of driver-assist technology and the macroscopic damping of uncertainty.
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.
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