# Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives

@article{Albi2019VehicularTC, title={Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives}, author={G. Albi and N. Bellomo and Luisa Fermo and Seung-Yeal Ha and Jeongho Kim and L. Pareschi and David Poyato and J. Soler}, journal={Mathematical Models and Methods in Applied Sciences}, year={2019}, volume={29}, pages={1901-2005} }

This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of ...

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#### References

SHOWING 1-10 OF 190 REFERENCES

Influence of drivers ability in a discrete vehicular traffic model

- Computer Science
- 2017

A vehicular traffic model is presented, based on the so-called Kinetic Theory of Active Particles. Vehicles are characterized by a lattice of discrete speeds and by the driving ability of the… Expand

Toward a Mathematical Theory of Behavioral-Social Dynamics for Pedestrian Crowds

- Computer Science, Physics
- 2014

It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. Expand

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

- Computer Science
- SIAM Rev.
- 2011

A review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena and a critical analysis focused on research perspectives that consider the development of a unified modeling strategy are presented. Expand

On the Interplay between Behavioral Dynamics and Social Interactions in Human Crowds

- Mathematics, Physics
- 2017

This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral… Expand

On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics

- Mathematics
- 2014

This paper deals with the multiscale modeling of vehicular traffic according to a kinetic
theory approach, where the microscopic state of vehicles is described by position, velocity
and activity,… Expand

Multiscale Modeling of Granular Flows with Application to Crowd Dynamics

- Physics, Mathematics
- Multiscale Model. Simul.
- 2011

A new multiscale modeling technique relies on a recently introduced measure-theoretic approach, which allows one to manage the microscopic and the macroscopic scale under a unique framework and in the resulting coupled model the two scales coexist and share information. Expand

Behavioral crowds: Modeling and Monte Carlo simulations toward validation

- Physics
- 2016

Abstract A mesoscopic model of behavioral crowds is developed within the framework of the kinetic theory for active particles. An analytic long-time equilibrium solution is obtained which gives a… Expand

COUPLING TRAFFIC FLOW NETWORKS TO PEDESTRIAN MOTION

- Computer Science
- 2014

Scalar macroscopic models for traffic and pedestrian flows are coupled and the resulting system is investigated numerically, investigating several physical situations, where pedestrians and cars interact. Expand

Hybrid Stochastic Kinetic Description of Two-Dimensional Traffic Dynamics

- Computer Science, Mathematics
- SIAM J. Appl. Math.
- 2018

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane...

Pedestrian Dynamics: From Empirical Results to Modeling

- Computer Science
- 2018

The state of the art of the interplay between empirical and theoretical studies of pedestrian dynamics, including the properties of microscopic pedestrian models, is reviewed. Expand