2,678 research outputs found
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
agents, by repeatedly visiting 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 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 (), 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
- …