Communications in Mathematical Sciences

Volume 14 (2016)

Number 3

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

Pages: 643 – 669



Gabriella Puppo (Dipartimento di Scienza ed Alta Tecnologia, Università dell’Insubria, Como, Italy)

Matteo Semplice (Dipartimento di Matematica, Università di Torino, Italy)

Andrea Tosin (Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy)

Giuseppe Visconti (Dipartimento di Scienza ed Alta Tecnologia, Università dell’Insubria, Como, Italy)


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.


traffic flow, kinetic models, multispecies kinetic equations, fundamental diagrams

2010 Mathematics Subject Classification

65Z05, 76P05, 90B20

Full Text (PDF format)

Published 26 February 2016