Handling congestion in crowd motion modeling

@article{Maury2011HandlingCI,
  title={Handling congestion in crowd motion modeling},
  author={Bertrand Maury and Aude Roudneff-Chupin and Filippo Santambrogio and Juliette Venel},
  journal={Networks Heterog. Media},
  year={2011},
  volume={6},
  pages={485-519}
}
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We limit our approach to very basic principles in terms of behavior, to focus on the particular problems raised by the non-smooth character of the models. We consider that individuals tend to move according to a desired, or spontaneous, velocity. We account… 

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References

SHOWING 1-10 OF 69 REFERENCES

A discrete contact model for crowd motion

TLDR
A numerical scheme for this contact dynamics model, based on a prediction-correction algorithm, is proposed, which aims to develop a crowd motion model designed to handle highly packed situations.

A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE

A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the

Integrating Strategies in Numerical Modelling of Crowd Motion

TLDR
In this paper, several strategies to define the spontaneous velocity are proposed: follow the shortest path, adapt its own velocity to the one of his neighbors, or avoid jams.

The flow of human crowds

▪ Abstract The modern study of a crowd as a flowing continuum is a recent development. Distinct from a classical fluid because of the property that a crowd has the capacity to think, interesting new

Pedestrian flows in bounded domains with obstacles

TLDR
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, which is suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles.

A congestion model for cell migration

This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and

Social force model for pedestrian dynamics.

  • HelbingMolnár
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
It is suggested that the motion of pedestrians can be described as if they would be subject to ``social forces.'' These ``forces'' are not directly exerted by the pedestrians' personal environment,

Numerical Approximation of a Macroscopic Model of Pedestrian Flows

TLDR
This study proposes to extend the transport‐equilibrium strategy proposed in Chalons and Chalons for computing the nonclassical solutions of scalar conservation laws with either a concave‐convex or a convex‐concave flux function and supplemented with an invertible kinetic function.

Computer Simulations of Pedestrian Dynamics and Trail Formation

A simulation model for the dynamic behaviour of pedestrian crowds is mathematically formulated in terms of a social force model, that means, pedestrians behave in a way as if they would be subject to
...