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.

Economic Segregation Under the Action of Trading Uncertainties

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“…This results in a substantial difference between the present approach and the previous ones, in which the propensity factor has been treated as a random parameter [5,[56][57][58][59]. In a different context, we mention also the approach proposed in [30,32,78,79] based on the methods of uncertainty quantification.…”

“…A significant part of this research activity applied the methodology of statistical mechanics to build kinetic-type equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] able to reproduce at best the typical features of economies, including the formation of fat-tailed distributions observed by Pareto in capitalistic societies [19]. The modeling of the economic aspects of multi-agent systems has benefited greatly from related research in which statistical physics has been applied to interdisciplinary fields ranging from the classical biological context [20][21][22][23][24], to the new aspects of socio-economic [25][26][27][28][29] and traffic dynamics [30][31][32][33].…”

Uncertainty quantification and control of kinetic models of tumour growth under clinical uncertainties

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Boltzmann-type equations for multi-agent systems with label switching

“…Boltzmann-type kinetic equations are a valuable tool to model multi-agent systems, their success being confirmed by a great variety of modern applications which take advantage of the formalism of the collisional kinetic theory. The literature in the field is constantly growing as witnessed by very recent contributions to econophysics [9], human ecology [27], vehicular traffic with autonomous vehicles [23,28,29], opinion formation [22], biology [14,15,24]. Kinetic models of multi-agent systems are based on a revisitation of the methods of the classical kinetic theory, however with remarkable differences due to the different nature of the physical systems at hand.…”