Abstract
Inspiriting by advantages of continuous and discrete approaches to model pedestrian dynamics a new discrete-continuous model SIgMA.DC. was developed This model is of individual type; people (particles) move in a continuous space - in this sense model is continuous, but number of directions where particles may move is a model parameter (limited and predetermined by a user) - in this sense model is discrete. To find current velocity vector we do not describe forces that act on people. To have a value of velocity we use a fundamental diagram data; and probability approach is used to find a direction. Description of the model and some simulation results are presented.
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Notes
- 1.
A model is of individual type when trajectories of each person are simulated.
- 2.
There is unified coordinate system, and all data are given in this system.
- 3.
- 4.
Mainly with value 0, 8–0, 9.
- 5.
Note function W(⋅) “works” with nonmovable obstacles only.
- 6.
Actually this situation is impossible. Only function W(⋅) may give (mathematical) zero to probability. If Norm = 0 then particle is surrounded by obstacles from all directions.
- 7.
It is motivated by a front line effect in a dense people mass when front line people move with free movement velocity while middle part is waiting a free space available to make a first step. As a result it leads to a diffusion of the flow. Otherwise simulation will be slower then real process.
- 8.
Parallel update scheme is used here.
- 9.
Only here we operate with coordinates obtained during current time step.
- 10.
- 11.
Model parameters were chosen to simulate directed movement only with the shortest path strategy due to shape of the geometry
- 12.
One hundred simulations for each density were made, and average time is considered.
- 13.
Here we use average value over 100 simulations for each density and corridor.
- 14.
Thirty second is minimal time to reach control line in corridor 100 m in length.
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Acknowledgments
This work is supported by the Integration project of SB RAS 2012–2014, contract 49.
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Kirik, E., Malyshev, A., Popel, E. (2014). Fundamental Diagram as a Model Input: Direct Movement Equation of Pedestrian Dynamics. In: Weidmann, U., Kirsch, U., Schreckenberg, M. (eds) Pedestrian and Evacuation Dynamics 2012. Springer, Cham. https://doi.org/10.1007/978-3-319-02447-9_58
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DOI: https://doi.org/10.1007/978-3-319-02447-9_58
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