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In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation…

We analyze numerically some macroscopic models of pedestrian motion such as Hughes model [1] and mean field game with nonlinear mobilities [2] modeling fast exit scenarios in pedestrian crowds. A model introduced by Hughes consisting of a…

Roger Hughes proposed a macroscopic model for pedestrian dynamics, in which individuals seek to minimize their travel time but try to avoid regions of high density. One of the basic assumptions is that the overall density of the crowd is…

In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…

A series of accidents caused by crowd within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on discrete element method, a granular dynamic model, in which human body is simplified…

We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction.", arXiv…

In the framework inspired by R. L. Hughes model (Transp. Res. B, 2002) for pedestrian evacuation in a corridor, we establish existence of a solution by a topological fixed point argument. This argument applies to a class of models where the…

We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes' model, cf. Hughes: A continuum theory for the flow of pedestrians. Transportation research part B: methodological, 36 (2002). We assume…

We consider a kinetic theory approach to model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools…

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to…

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…

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,…

We present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux…

Inspired by the works of Hughes [17, 18], we formalize and prove the well posedness of a hyperbolic--elliptic system whose solutions describe the dynamics of a moving crowd. The resulting model is here shown to be well posed and the time of…

The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model…

We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Moussaid et al, PNAS 2011, where the pedestrians are supposed to have constant speeds. This IBM supposes that…

We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…

In this paper we present numerical simulations of a macroscopic vision-based model [1] derived from microscopic situation rules described in [2]. This model describes an approach to collision avoidance between pedestrians by taking…

In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd - usually a fixed…