Analysis of a heterogeneous kinetic model for traffic flow

In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model based on a lattice of speeds because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic.Comment: 31 page

Derivation and Empirical Validation of a Refined Traffic Flow Model

The gas-kinetic foundation of fluid-dynamic traffic equations suggested in previous papers [Physica A 219, 375 and 391 (1995)] is further refined by applying the theory of dense gases and granular materials to the Boltzmann-like traffic model by Paveri-Fontana. It is shown that, despite the phenomenologically similar behavior of ordinary and granular fluids, the relations for these cannot directly be transferred to vehicular traffic. The dissipative and anisotropic interactions of vehicles as well as their velocity-dependent space requirements lead to a considerably different structure of the macroscopic traffic equations, also in comparison with the previously suggested traffic flow models. As a consequence, the instability mechanisms of emergent density waves are different. Crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Analysis of a multi-population kinetic model for traffic flow

In this work we extend a recent kinetic traffic model [G. Puppo, M. Semplice, A. Tosin, G. Visconti, Kinet. Relat. Models, in press, 2016] to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model proposed in [G. Puppo, M. Semplice, A. Tosin, G. Visconti, Commun. Math. Sci., 14:643-669, 2016] because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic

Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet fully reproduced nor explained by mathematical models. In this paper, resting on the methods of kinetic theory, we introduce a new traffic model which takes into account the heterogeneous nature of the flow of vehicles along a road. In more detail, the model considers traffic as a mixture of two or more populations of vehicles (e.g., cars and trucks) with different microscopic characteristics, in particular different lengths and/or maximum speeds. With this approach we gain some insights into the scattering of the data in the regime of congested traffic clearly shown by actual measurements