Skip to main content

A Macroscopic Multiple Species Pedestrian Flow Model Based on Heuristics Implemented with Finite Volumes

  • Conference paper
  • First Online:
Pedestrian and Evacuation Dynamics 2012

Abstract

We present a macroscopic model for pedestrian movement and its implementation. The focus is on the simulation of multiple interacting pedestrian streams. The number of different species is potentially unrestricted. Tunability is provided by parameters common to all pedestrian species as well as species-specific parameters.

The primary goal of our model is the description of pedestrian motion in non-panic circumstances but we expect that an extension to panic scenarios is feasible.

The implementation uses a finite volume method in order to enforce mass conservation, and method-specific optimizations model certain aspects of pedestrian behavior. Furthermore, we apply a set of heuristics to obtain a particularly simple model.

The intent to simulate human crowds in realistic environments implies the need to manage arbitrary domain and cell shapes. Development flexibility suggests to use open source code. These requirements, and its code maturity, made OpenFOAM our choice to base the implementation on.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Huth, F., Bärwolff, G., Schwandt, H.: Some fundamental considerations for the application of macroscopic models in the field of pedestrian crowd simulation. Preprint ID 2012/16 at http://www.math.tu-berlin.de/menue/forschung/veroeffentlichungen/preprints_2012 (2012)

  2. Cristiani, E., Piccoli, B., Tosin, A.: Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints. In Bellomo, N., Naldi, G., Pareschi, L., Toscani, G., eds.: Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston (2010) 337–364

    Google Scholar 

  3. Moussaïd, M., Helbing, D., Theraulaz, G.: How simple rules determine pedestrian behavior and crowd disasters. PNAS 108 (2011) 6884–6888

    Article  Google Scholar 

  4. Bierlaire, M., Antonini, G., Weber, M.: Behavioral dynamics for pedestrians. In Axhausen, K.W., ed.: Moving Through Nets: The Physical and Social Dimensions of Travel. Elsevier (2003) 81–106

    Google Scholar 

  5. Gigerenzer, G.: Why heuristics work. Perspectives on Psychological Science 3 (2008) 20–29

    Article  Google Scholar 

  6. Predtechenskii, V.M., Milinskii, A.I.: Planning for Foot Traffic Flow in Buildings. Amerind Publishing, New Delhi (1978) translation of Proekttirovanie Zhdanii s. Uchetom Organizatsii Dvizheniya Lyuddskikh Potokov (Moscow: Stroiizdat, 1969).

    Google Scholar 

  7. Weidmann, U.: Transporttechnik der Fußgänger – transporttechnische Eigenschaften des Fußgängerverkehrs (Literaturstudie). Schriftenreihe der IVT 90 (1993) in German.

    Google Scholar 

  8. Schadschneider, A., Klingsch, W., Kluepfel, H., Kretz, T., Rogsch, C., Seyfried, A.: Evacuation dynamics: Empirical results, modeling and applications. Encyclopedia of Complexity and Systems Science (2009) 3142–3176

    Google Scholar 

  9. Berres, S., Ruiz-Baier, R., Schwandt, H., Tory, E.M.: An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks and Heterogeneous Media (NHM) 6 (2011)

    Google Scholar 

  10. Hughes, R.L.: A continuum theory for the flow of pedestrians. Transportation Research Part B 36 (2002) 507–535

    Article  Google Scholar 

  11. Piccoli, B., Tosin, A.: Pedestrian flows in bounded domains with obstacles. Continuum Mechanics and Thermodynamics 21 (2009) 85–107

    Article  MATH  MathSciNet  Google Scholar 

  12. Huth, F., Bärwolff, G., Schwandt, H.: Fundamental diagrams and multiple pedestrian streams. Preprint ID 2012/17 at http://www.math.tu-berlin.de/menue/forschung/veroeffentlichungen/preprints_2012/ (2012)

  13. Helbing, D., Farkas, I.J., Vicsek, T.: Freezing by heating in a driven mesoscopic system. Phys. Rev. Lett. 84 (2000) 1240–1243

    Article  Google Scholar 

  14. Radzihovsky, L., Clark, N.A.: Comment on “Freezing by heating in a driven mesoscopic system”. Phys. Rev. Lett. 90 (2003) 189603

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of Deutsche Forschungsgemeinschaft (German Research Foundation) for the project SCHW548/5-1 + BA1189/4-1.

An invaluable contribution to this research has been committed by the open source software community. Notably, we used OpenFOAM by the OpenFOAM Team at Silicon Graphics International Corp. for the simulations and ParaView, supported by Kitware and several collaborators, octave and gnuplot for the processing and visualization of the results.

Finally, we would like to thank the organizers of the 6th International Conference on Pedestrian and Evacuation Dynamics 2012, ETH Zurich, Switzerland.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Frank Huth .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Huth, F., Bärwolff, G., Schwandt, H. (2014). A Macroscopic Multiple Species Pedestrian Flow Model Based on Heuristics Implemented with Finite Volumes. 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_49

Download citation

Publish with us

Policies and ethics