Skip to main content

Influence of Spreading Hazardous Material in Macroscopic Evacuation Dynamics: A Proof of Concept

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

Abstract

In this article, an evacuation model describing the egress in case of danger is considered. The underlying evacuation model is based on continuous network flows, while the spread of some gaseous hazardous material relies on an advection–diffusion equation. A proof of concept shows differences to the usually used macroscopic evacuation models.

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. H. W. Hamacher and S. A. Tjandra, “Mathematical modelling of evacuation problems - a state of the art,” in Pedestrian and Evacuation Dynamics, M. Schreckenberger and S. D. Sharma, Eds., Berlin, Springer, 2002, pp. 227–266.

    Google Scholar 

  2. A. Schadschneider, W. Klingsch, H. Klüpfel, T. Kretz, C. Rogsch and A. Seyfried, “Evacuation dynamics: Empirical results, modeling and applications,” in Encyclopedia of Complexity and System Science, B. Meyers, Ed., New York, Springer, 2009, pp. 3142–3176.

    Chapter  Google Scholar 

  3. D. Helbing, “A mathematical model for the behavior of pedestrians,” Behavioral Science, vol. 36, pp. 298–310, 1991.

    Article  Google Scholar 

  4. G. M. Coclite, M. Garavello and B. Piccoli, “Traffic flow on a road network,” SIAM Journal on Mathematical Analysis, no. 36, pp. 1862–1886, 2005.

    Google Scholar 

  5. M. Herty and A. Klar, “Modeling, simulatoin, and optimization of traffic flow networks,” SIAM Journal on Scientific Computing, vol. 25, pp. 1066–1087, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Göttlich, M. Herty and A. Klar, “Network models for supply chains,” Communications in Mathematical Sciences, vol. 3, pp. 545–559, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Göttlich, S. Kühn, J. P. Ohst, S. Ruzika and M. Thiemann, “Evacuation dynamics influenced by spreading hazardous material,” Networks and Heterogeneous Media, vol. 6, no. 3, p. 443, September 2011.

    Google Scholar 

  8. H. Holden and N. H. Risebro, “A mathematical model of traffic flow on a network of unidirectional roads,” SIAM Journal on Mathematical Analysis, vol. 26, pp. 999–1017, 1995.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

S. Ruzika is partially supported by BMBF, Project REPKA, FKZ 13N9961 (TU KL). S. Kühn and J.P. Ohst are supported by Stiftung Rheinland-Pfalz für Innovation, Project EvaC, FKZ 989.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Simone Göttlich .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Göttlich, S., Kühn, S., Ohst, J.P., Ruzika, S. (2014). Influence of Spreading Hazardous Material in Macroscopic Evacuation Dynamics: A Proof of Concept. 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_22

Download citation

Publish with us

Policies and ethics