Skip to main content

Macroscopic Simulation of Open Systems and Micro-Macro Link

  • Conference paper
Traffic and Granular Flow ’99

Abstract

We discuss the numerical treatment of boundary conditions for a non-local macroscopic model of uni-directional traffic. Furthermore, we propose a general scheme to derive non-local macroscopic models from given microscopic car-following models. Assuming identical (macroscopic) initial and boundary conditions, we show that there are microscopic models for which the corresponding macroscopic version displays a very similar dynamics. This enables us to combine micro- and macrosimulations of road sections by simple algorithms and even to simulate them simultaneously.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Treiber, A. Hennecke, and D. Helbing, Derivation, properties, and simulation of a gas-kinetic-based, non-local traffic model, Phys. Rev. E 59, 239–253 (1999).

    Article  Google Scholar 

  2. W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Vols. I & II (Academic Press, New York, 1965).

    MATH  Google Scholar 

  3. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, (Cambridge University Press, Cambridge, 1992).

    MATH  Google Scholar 

  4. D. Helbing, From microscopic to macroscopic traffic models, in: A Perspective Look at Nonlinear Media, J. Parisi, S.C. Müller, and W. Zimmermann, (Eds.), pp. 122–139 (Springer, Berlin, 1998).

    Chapter  Google Scholar 

  5. M. Treiber etal.,Micro simulations of congested traffic, in this volume.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hennecke, A., Treiber, M., Helbing, D. (2000). Macroscopic Simulation of Open Systems and Micro-Macro Link. In: Helbing, D., Herrmann, H.J., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’99. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59751-0_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59751-0_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64109-1

  • Online ISBN: 978-3-642-59751-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics