1,648 research outputs found
Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
In this paper we develop a framework for parameter estimation in macroscopic
pedestrian models using individual trajectories -- microscopic data. We
consider a unidirectional flow of pedestrians in a corridor and assume that the
velocity decreases with the average density according to the fundamental
diagram. Our model is formed from a coupling between a density dependent
stochastic differential equation and a nonlinear partial differential equation
for the density, and is hence of McKean--Vlasov type. We discuss
identifiability of the parameters appearing in the fundamental diagram from
trajectories of individuals, and we introduce optimization and Bayesian methods
to perform the identification. We analyze the performance of the developed
methodologies in various situations, such as for different in- and outflow
conditions, for varying numbers of individual trajectories and for differing
channel geometries
Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories---microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in- and outflow conditions, for varying numbers of individual trajectories, and for differing channel geometries
From traffic and pedestrian follow-the-leader models with reaction time to first order convection-diffusion flow models
In this work, we derive first order continuum traffic flow models from a
microscopic delayed follow-the-leader model. Those are applicable in the
context of vehicular traffic flow as well as pedestrian traffic flow. The
microscopic model is based on an optimal velocity function and a reaction time
parameter. The corresponding macroscopic formulations in Eulerian or Lagrangian
coordinates result in first order convection-diffusion equations. More
precisely, the convection is described by the optimal velocity while the
diffusion term depends on the reaction time. A linear stability analysis for
homogeneous solutions of both continuous and discrete models are provided. The
conditions match the ones of the car-following model for specific values of the
space discretization. The behavior of the novel model is illustrated thanks to
numerical simulations. Transitions to collision-free self-sustained stop-and-go
dynamics are obtained if the reaction time is sufficiently large. The results
show that the dynamics of the microscopic model can be well captured by the
macroscopic equations. For non--zero reaction times we observe a scattered
fundamental diagram. The scattering width is compared to real pedestrian and
road traffic data
Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method
Focusing on a specific crowd dynamics situation, including real life
experiments and measurements, our paper targets a twofold aim: (1) we present a
Bayesian probabilistic method to estimate the value and the uncertainty (in the
form of a probability density function) of parameters in crowd dynamic models
from the experimental data; and (2) we introduce a fitness measure for the
models to classify a couple of model structures (forces) according to their
fitness to the experimental data, preparing the stage for a more general
model-selection and validation strategy inspired by probabilistic data
analysis. Finally, we review the essential aspects of our experimental setup
and measurement technique.Comment: 20 pages, 9 figure
Quantitative Description of Pedestrian Dynamics with a Force based Model
This paper introduces a space-continuous force-based model for simulating
pedestrian dynamics. The main interest of this work is the quantitative
description of pedestrian movement through a bottleneck. Measurements of flow
and density will be presented and compared with empirical data. The results of
the proposed model show a good agreement with empirical data. Furthermore, we
emphasize the importance of volume exclusion in force-based models.Comment: 4 pages, 7 figures, 2009 IEEE/WIC/ACM International Joint Conferences
on Web Intelligence and Intelligent Agent Technologies (WI-IAT 2009), 15-18
September 2009, in Milano, Italy, 200
Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents
In this paper a comparison between first order microscopic and macroscopic
differential models of crowd dynamics is established for an increasing number
of pedestrians. The novelty is the fact of considering massive agents,
namely particles whose individual mass does not become infinitesimal when
grows. This implies that the total mass of the system is not constant but grows
with . The main result is that the two types of models approach one another
in the limit , provided the strength and/or the domain of
pedestrian interactions are properly modulated by at either scale. This is
consistent with the idea that pedestrians may adapt their interpersonal
attitudes according to the overall level of congestion.Comment: 26 pages, 8 figure
From individual behaviour to an evaluation of the collective evolution of crowds along footbridges
This paper proposes a crowd dynamic macroscopic model grounded on microscopic
phenomenological observations which are upscaled by means of a formal
mathematical procedure. The actual applicability of the model to real world
problems is tested by considering the pedestrian traffic along footbridges, of
interest for Structural and Transportation Engineering. The genuinely
macroscopic quantitative description of the crowd flow directly matches the
engineering need of bulk results. However, three issues beyond the sole
modelling are of primary importance: the pedestrian inflow conditions, the
numerical approximation of the equations for non trivial footbridge geometries,
and the calibration of the free parameters of the model on the basis of in situ
measurements currently available. These issues are discussed and a solution
strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201
Quantitative Verification of a Force-based Model for Pedestrian Dynamics
This paper introduces a spatially continuous force-based model for simulating
pedestrian dynamics. The main intention of this work is the quantitative
description of pedestrian movement through bottlenecks and in corridors.
Measurements of flow and density at bottlenecks will be presented and compared
with empirical data. Furthermore the fundamental diagram for the movement in a
corridor is reproduced. The results of the proposed model show a good agreement
with empirical data.Comment: 8 pages, 7 figures, Proceedings of Traffic and Granular Flow (TGF)
200
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