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 10 years on the aforementioned 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.

Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies

“…Thus, we can deduce the result (2). For the stochasticity, note that Id− h N L k [t] is stochastic for any k = 1, · · · , N G .…”

Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions

“…Some interesting results have been proposed in the literature concerning simulations of kinetic type models [19,20]. Our computational experiments have suggested the use of Monte Carlo particle methods introduced by Bird [21], within the general framework of computational methods for Boltzmann type equations [22], and subsequently extended by various authors by modifying the method depending on the specific system under consideration, for instance [23,24], see also Section 6 of [3] which is specifically focused on crowd and swarm dynamics, while the survey [25] exhaustively covers this challenging field of scientific computing.…”

“…Our paper refers to achievements known in the literature, recently reviewed in [3], to select the model and focuses on the development of simulations to enlighten the following features: the role of obstacles in the generation of overcrowded areas and the dynamics of streams moving towards opposite directions. Both types of simulations are critically analyzed within the general framework of crisis situations.…”

“…Therefore only the essential references are reported in this present paper. The reader interested to a survey, where crowd dynamics, is related to the modeling of vehicles and swarms, is referred to the recent survey [3] which provides and exhaustive report of the bibliography in the field, where all technical details, which are not repeated here, are available.…”

“…A possible derivation rationale has been developed in [7]. Our paper reports, without repeating equations, available in [3,7], the key assumptions that lead to the model recalling that both speed and density have been referred to the highest admissible values so that these quantities take value in [0, 1]. Specifically we look for a minimal model suitable, however, to capture the main features of human crowds.…”