Skip to main content

A Microscopic Model of Redistribution of Individuals Inside an ‘Elevator’

  • Conference paper
  • First Online:
Modern Problems in Applied Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

We present and qualitatively analyze a stochastic microscopic model of redistribution of individuals inside a domain which can be thought as representing an elevator. The corresponding mesoscopic model is also derived.

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 74.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. I. Altman, The Environment and Social Behavior: Privacy, Personal Space, Territory, Crowding (Brooks/Cole, Monterey, CA, 1975)

    Google Scholar 

  2. J. Banasiak, M. Lachowicz, Methods of Small Parameter in Mathematical Biology (Birkhäuser, Basel, 2014)

    Book  MATH  Google Scholar 

  3. N. Bellomo, A. Bellouquid, D. Knopoff, From the microscale to collective crowd dynamics. Multiscale Model. Simul. 11, 943–963 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. E. Cristiani, B. Piccoli, A. Tosin (eds.), Multiscale Modeling of Pedestrian Dynamics (Springer, Berlin, 2014)

    MATH  Google Scholar 

  5. M. Dolfin, D. Knopoff, M. Lachowicz, A. Schadschneider, Monte Carlo simulation of space redistribution in an inflow process of individuals, in preparation

    Google Scholar 

  6. M. Dolfin, M. Lachowicz, Z. Szymańska, A General Framework for Multiscale Modeling of Tumor – Immune System Interactions, In Mathematical Oncology, ed. by A. d’Onofrio, A. Gandolfi (Birkhäuser, Basel, 2014), pp. 151–180

    Google Scholar 

  7. S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence (Wiley, New York, 1986)

    Book  MATH  Google Scholar 

  8. T. Ezaki, D. Yanagisawa, K. Ohtsuka, K. Nishinari, Simulation of space acquisition process of pedestrians using proxemic floor field model. Physica A 391, 291–299 (2012)

    Article  Google Scholar 

  9. T. Ezaki, K. Ohtsuka, D. Yanagisawa, K. Nishinari, Inflow process: a counterpart of evacuation, in Traffic and Granular Flow 2013, ed. by M. Chraibi, M. Boltes, A. Schadschneider, A., Seyfried (Springer, Berlin, 2015), pp. 227–231

    Google Scholar 

  10. T. Ezaki, K. Ohtsuka, M. Chraibi, M. Boltes, D. Yanagisawa, A. Seyfried, A. Schadschneider, K. Nishinari, Inflow process of pedestrians to a confined space. Collective Dyn. 1(A:4), 1–18 (2016)

    Google Scholar 

  11. K.A. Forche, Stochastic model of pedestrian inflow to a confined space, Mater’s thesis, University of Cologne

    Google Scholar 

  12. E.T. Hall, The Hidden Dimension (Anchor Books, New York, 1966)

    Google Scholar 

  13. W. Klingsch, C. Rogsch, A. Schadschneider, M. Schreckenberg (eds.), Pedestrian and Evacuation Dynamics 2008 (Springer, Berlin, 2010)

    MATH  Google Scholar 

  14. M. Lachowicz, Individually-based Markov processes modeling nonlinear systems in mathematical biology. Nonlinear Anal. Real World Appl. 12, 2396–2407 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Lasota, J.A. Yorke, Exact dynamical systems and the Frobenius–Perron operator. Trans. Am. Math. Soc. 273, 375–384 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  16. X. Liu, W. Song, L. Fu, Z. Fang, Experimental study of pedestrian inflow in a room with a separate entrance and exit. Physica A 442, 224–238 (2016)

    Article  Google Scholar 

  17. X. Liu, W. Song, L. Fu, W. Lv, Z. Fang, Typical features of pedestrian spatial distribution in the inflow process. Phys. Lett. A 380, 1526–1534 (2016)

    Article  Google Scholar 

  18. M.D. Rosini, Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications. Springer Understanding Complex Systems (Springer, Heidelberg, 2013)

    Book  MATH  Google Scholar 

  19. R. Rudnicki, Models of population dynamics and their applications in genetics, ed. by M. Lachowicz, J. Miȩkisz. From Genetics to Mathematics (World Scientific, Singapore, 2009), pp. 103–147

    Google Scholar 

  20. R. Sommer, Studies in personal space. Sociometry 22, 247–260 (1959)

    Article  Google Scholar 

Download references

Acknowledgements

This work was completed with the support of the university of Messina through the grant Visiting Professor 2016.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mirosław Lachowicz .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dolfin, M., Lachowicz, M., Schadschneider, A. (2018). A Microscopic Model of Redistribution of Individuals Inside an ‘Elevator’. In: Drygaś, P., Rogosin, S. (eds) Modern Problems in Applied Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-72640-3_6

Download citation

Publish with us

Policies and ethics