851 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
Modeling rationality to control self-organization of crowds: An environmental approach
In this paper we propose a classification of crowd models in built
environments based on the assumed pedestrian ability to foresee the movements
of other walkers. At the same time, we introduce a new family of macroscopic
models, which make it possible to tune the degree of predictiveness (i.e.,
rationality) of the individuals. By means of these models we describe both the
natural behavior of pedestrians, i.e., their expected behavior according to
their real limited predictive ability, and a target behavior, i.e., a
particularly efficient behavior one would like them to assume (for, e.g.,
logistic or safety reasons). Then we tackle a challenging shape optimization
problem, which consists in controlling the environment in such a way that the
natural behavior is as close as possible to the target one, thereby inducing
pedestrians to behave more rationally than what they would naturally do. We
present numerical tests which elucidate the role of rational/predictive
abilities and show some promising results about the shape optimization problem
Quickest Paths in Simulations of Pedestrians
This contribution proposes a method to make agents in a microscopic
simulation of pedestrian traffic walk approximately along a path of estimated
minimal remaining travel time to their destination. Usually models of
pedestrian dynamics are (implicitly) built on the assumption that pedestrians
walk along the shortest path. Model elements formulated to make pedestrians
locally avoid collisions and intrusion into personal space do not produce
motion on quickest paths. Therefore a special model element is needed, if one
wants to model and simulate pedestrians for whom travel time matters most (e.g.
travelers in a station hall who are late for a train). Here such a model
element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte
Pedestrian flows in bounded domains with obstacles
In this paper we systematically apply the mathematical structures by
time-evolving measures developed in a previous work to the macroscopic modeling
of pedestrian flows. We propose a discrete-time Eulerian model, in which the
space occupancy by pedestrians is described via a sequence of Radon positive
measures generated by a push-forward recursive relation. We assume that two
fundamental aspects of pedestrian behavior rule the dynamics of the system: On
the one hand, the will to reach specific targets, which determines the main
direction of motion of the walkers; on the other hand, the tendency to avoid
crowding, which introduces interactions among the individuals. The resulting
model is able to reproduce several experimental evidences of pedestrian flows
pointed out in the specialized literature, being at the same time much easier
to handle, from both the analytical and the numerical point of view, than other
models relying on nonlinear hyperbolic conservation laws. This makes it
suitable to address two-dimensional applications of practical interest, chiefly
the motion of pedestrians in complex domains scattered with obstacles.Comment: 25 pages, 9 figure
The Effect of Integrating Travel Time
This contribution demonstrates the potential gain for the quality of results
in a simulation of pedestrians when estimated remaining travel time is
considered as a determining factor for the movement of simulated pedestrians.
This is done twice: once for a force-based model and once for a cellular
automata-based model. The results show that for the (degree of realism of)
simulation results it is more relevant if estimated remaining travel time is
considered or not than which modeling technique is chosen -- here force-based
vs. cellular automata -- which normally is considered to be the most basic
choice of modeling approach.Comment: preprint of Pedestrian and Evacuation 2012 conference (PED2012)
contributio
Multiscale modeling of granular flows with application to crowd dynamics
In this paper a new multiscale modeling technique is proposed. It relies on a
recently introduced measure-theoretic approach, which allows to manage the
microscopic and the macroscopic scale under a unique framework. In the
resulting coupled model the two scales coexist and share information. This
allows to perform numerical simulations in which the trajectories and the
density of the particles affect each other. Crowd dynamics is the motivating
application throughout the paper.Comment: 30 pages, 9 figure
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