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

Abstract

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 the kinetic models developed in the last ten years on the afore-mentioned topics so that overlapping with previous reviews can be avoided. Although the main focus of this paper lies on the mesoscopic models for collective dynamics, we provide a brief overview on the corresponding micro and macroscopic models, and discuss intermediate role of mesoscopic model between them. Moreover, we provide a number of selected challenging research perspectives for readers' attention.