Crowd Dynamics, Volume 2

This chapter provides an introduction to the contents of Gibelli (in Crowd Dynamics, Volume 2—Theory, Models, and Safety Problems. Modeling and Simulation in Science, Engineering, and Technology, Birkhäuser, New York, 2020) and a general critical analysis on modeling, simulation, and control of human crowds with emphasis on research perspectives. The contents are organized in three parts: firstly, three key topics are stated which will be probably the focus of future research; Subsequently, the contents of Chaps. “Artificial Neural Networks for the Estimation of Pedestrian Interaction Forces–Mixed Traffic Simulation of Cars and Pedestrians for Transportation Policy Assessment” are summarized by setting them in the context of the aforementioned key research topics; finally, some promising research directions are presented and discussed.

We present a data fitting approach for the social force model by Helbing and Molnár using artificial neural networks. The latter are used as a universal approximation for the unknown interaction forces between pedestrians. We train the artificial neural network simultaneously with other parameters arising in the model by utilizing a tailored cost function and stochastic gradient techniques. We test our approach using real data sets for the unidirectional and bidirectional flow in corridors and point out the advantages and drawbacks of the proposed approach.

Modeling the behavior of pedestrians walking in crowds is an outstanding fundamental challenge, deeply connected with the physics of flowing active matter. The strong societal relevance of the topic, for its relations with individual safety and comfort, sparked vast modeling efforts from multiple scientific communities. Yet, likely because of the technical difficulties in acquiring experimental data, models quantitatively reproducing (statistical) features of pedestrian flows are scarce. This contribution has a twofold aim. First, we consider a pedestrian dynamics modeling approach previously proposed by some of the authors and based on Langevin equations. We review the approach and show that in the undisturbed and in the pair-wise avoidance regimes (i.e., in absence of interactions between pedestrians and in case of avoidance of a single individual walking in the opposite direction) the model is in quantitative agreement with real-life high-statistics measurements. Second, moving towards the final goal of quantitative and generic crowd dynamics models, we consider the more complex case of a single individual walking through a dense crowd advancing in the opposite direction. We analyze the challenges connected to treating such dynamics and extend the Langevin model to reproduce quantitatively selected observed features.

Research from crowd psychology and pedestrian dynamics can inform one another to improve understandings and predictions of collective behaviour. In this chapter, we provide an overview of theoretical insights from crowd psychology on intragroup and intergroup behaviour and discuss possible avenues for implementing principles of the social identity approach into pedestrian models. Specifically, we debate the use of outdated assumptions of crowd behaviour, discuss how the core tenets of social identity theory and self-categorisation theory are central to understanding collective behaviour, showcase how perceptions and experiences of crowd members can be dynamic and influence their perceived safety and behaviour, and then point to recent trends in using crowd psychology to inform models of pedestrian movement and behaviour in emergencies. Finally, we examine barriers to incorporating social psychological theory into models, and look ahead to potential collaborative projects to improve crowd safety and experiences.

We consider several macroscopic models, based on systems of conservation laws, for the study of crowd dynamics. All the systems considered here contain nonlocal terms, usually obtained through convolutions with smooth functions, used to reproduce the visual horizon of each individual. We classify the various models according to the physical domain (the whole space \({\mathbb {R}}^N\) or a bounded subset), to the terms affected by the nonlocal operators, and to the number of different populations we aim to describe. For all these systems, we present the basic well posedness and stability results.

Stochastic drift-diffusion processes and the related Fokker–Planck equations appear to be adequate for modeling the motion of pedestrians in different circumstances, and for the design of control strategies for different purposes. In this paper, some mathematical contribution in this field are reviewed that include different modeling issues concerning the control of a single pedestrian subject to perturbation and the development of a framework for pedestrian’s avoidance dynamics based on the formulation of a Fokker–Planck Nash game. This review also includes a discussion on the mean-field approach to crowd motion and provides pointers to related models.

We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the aspects are highlighted in a detailed discussion of a particular controlled particle dynamics. The applied techniques are shown on this simple problem to illustrate the basic methods. Computational results confirming the theoretical findings are presented and further particle models are discussed.

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: the first one consists in using special agents, called leaders, to steer the crowd towards the desired direction. Leaders can be either hidden in the crowd or recognizable as such. This strategy heavily relies on the power of the social influence (herding effect), namely the natural tendency of people to follow group mates in situations of emergency or doubt. The second one consists in modify the surrounding environment by adding in the walking area multiple obstacles optimally placed and shaped. The aim of the obstacles is to naturally force people to behave as desired. Both control strategies discussed in this paper aim at reducing as much as possible the intervention on the crowd. Ideally the natural behavior of people is kept, and people do not even realize they are being led by an external intelligence. Mathematical models are discussed at different scales of observation, showing how macroscopic (fluid-dynamic) models can be derived by mesoscopic (kinetic) models which, in turn, can be derived by microscopic (agent-based) models.

In this chapter, the authors report on the construction of a new framework for simulating mixed traffic consisting of cars, trams, and pedestrians that can be used to support road management, signal control, and public transit. More specifically, a layered road structure, originally designed for car traffic simulations, was extended to interact with a one-dimensional tram model and one-/two-dimensional pedestrian models. The newly implemented pedestrian models and interaction rules were verified through simulations involving simple road environments, and the resulting simulated values were found to be in near agreement with the empirical data. The proposed framework is then used to assess the impact of a tramway extension plan for a real city. Those simulation results showed that the impact of the proposed tramway on existing car traffic would not be severe, and by extension, implied that the proposed framework could help stakeholders decide on expansion scenarios that would be agreeable to both tram users and private car owners.