Macroscopic modeling and simulations of room evacuation

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne-Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in minimization of the travel time and avoidance of congested areas. We apply a mixed finite volume-finite element method to solve the problems and present error analysis for the eikonal solver, gradient computation and the second order model yielding a first order convergence. We show that Hughes' model is incapable of reproducing complex crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally, using the second order model, we study numerically the evacuation of pedestrians from a room through a narrow exit.Comment: 22 page

Crowd dynamics

Crowd dynamics are complex. This thesis examines the nature of the crowd and its dynamics with specific reference to the issues of crowd safety. A model (Legion) was developed that simulates the crowd as an emergent phenomenon using simulated annealing and mobile cellular automata. We outline the elements of that model based on the interaction of four parameters: Objective, Motility, Constraint and Assimilation. The model treats every entity as an individual and it can simulate how people read and react to their environment in a variety of conditions. Which allows the user to study a wide range of crowd dynamics in different geometries and highlights the interactions of the crowd with their environment. We demonstrate that the model runs in polynomial time and can be used to assess the limits of crowd safety during normal and emergency egress. Over the last 10 years there have been many incidents of crowd related disasters. We highlight deficiencies in the existing guidelines relating to crowds. We compare and contrast the model with the safety guidelines and highlight specific areas where the guides may be improved. We demonstrate that the model is capable of reproducing these dynamics without additional parameters, satisfying Occam's Razor. The model is tested against known crowd dynamics from field studies, including Wembley Stadium, Balham Station and the Hong Kong Jockey club. We propose an alternative approach to assessing the dynamics of the crowd through the use of the simulation and analysis of least effort behaviour. Finally we test the model in a variety of applications where crowd related incidents warrant structural alterations at client sites. We demonstrate that the model explains the variance in a variety of field measurements, that it is robust and that it can be applied to future designs where safety and crowd comfort are criteria for design and cost savings

Phase transitions in crowd dynamics of resource allocation

We define and study a class of resources allocation processes where $gN$ agents, by repeatedly visiting $N$ resources, try to converge to optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density $g$ of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents ($g<1$), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a non-trivial faster-is-slower effect.Comment: 7 pages, 7 fig

A simple Monte Carlo model for crowd dynamics

In this paper we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of non-equilibrium hard-disk fluids and discuss general implications of our model.Comment: to be published in Physical Review

Agent Based Modelling and Simulation of Pedestrian Crowds in Panic Situations

The increasing occurrence of panic stampedes during mass events has motivated studying the impact of panic on crowd dynamics. Understanding the collective behaviors of panic stampedes is essential to reducing the risk of deadly crowd disasters. In this work, we use an agent-based formulation to model the collective human behavior in such crowd dynamics. We investigate the impact of panic behavior on crowd dynamics, as a specific form of collective behavior, by introducing a contagious panic parameter. The proposed model describes the intensity and spread of panic through the crowd. The corresponding panic parameter impacts each individual to represent a different variety of behaviors that can be associated with panic situations such as escaping danger, clustering, and pushing. Simulation results show contagious panic and pushing behavior, resulting in a more realistic crowd dynamics model

Non Local Conservation Laws in Bounded Domains

The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to define a non local operator adapted to the presence of a boundary. Numerical integrations show that the resulting model provides qualitatively reasonable solutions