Skip to main content

Linking of Three-Phase Traffic Theory and Fundamental Diagram Approach to Traffic Flow Modeling

  • Chapter
  • First Online:
Introduction to Modern Traffic Flow Theory and Control
  • 2524 Accesses

Abstract

A link between three-phase traffic theory and the fundamental diagram approach to traffic flow modeling can be created through the use of the averaging of an infinite number of steady states of synchronized flow shown in Figs.11.1 and 11.5 to one synchronized flow speed for each density. In this case, we should find rules for vehicle motion in a traffic flow model whose steady states are associated with a fundamental diagram, however, the model should show the free flow, synchronized flow, and wide moving jam phases as well as the F→S→J transitions.

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
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.S. Kerner, S.L. Klenov, J. Phys. A: Math. Gen. 39, 1775–1809 (2006); 7605

    Article  MATH  MathSciNet  Google Scholar 

  2. B.S. Kerner, The Physics of Traffic, (Springer, Berlin, New York, 2004)

    Google Scholar 

  3. A.D. May, Traffic Flow Fundamentals, (Prentice-Hall, Inc., New Jersey, 1990)

    Google Scholar 

  4. F.A. Haight, Mathematical Theories of Traffic Flow,(Academic Press, New York, 1963)

    MATH  Google Scholar 

  5. W. Leutzbach Introduction to the Theory of Traffic Flow, (Springer, Berlin, 1988)

    Google Scholar 

  6. Highway Capacity Manual 2000, (National Research Council, Transportation Research Boad, Washington, D.C., 2000)

    Google Scholar 

  7. C.F. Daganzo, Fundamentals of Transportation and Traffic Operations, (Elsevier Science Inc., New York, 1997)

    Google Scholar 

  8. R. Wiedemann, Simulation des Verkehrsflusses, (University of Karlsruhe, Karlsruhe, 1974)

    Google Scholar 

  9. I. Prigogine, R. Herman, Kinetic Theory of Vehicular Traffic, (American Elsevier, New York, 1971)

    MATH  Google Scholar 

  10. G.B. Whitham, Linear and Nonlinear Waves, (Wiley, New York, 1974)

    MATH  Google Scholar 

  11. M. Cremer, Der Verkehrsfluss auf Schnellstrassen, (Springer, Berlin, 1979)

    Google Scholar 

  12. N.H. Gartner, C.J. Messer, A.K. Rathi (editors), Traffic Flow Theory: A State-of-the-Art Report, (Transportation Research Board, Washington DC, 2001)

    Google Scholar 

  13. D.C. Gazis, Traffic Theory, (Springer, Berlin, 2002)

    MATH  Google Scholar 

  14. G.F. Newell, Applications of Queuing Theory, (Chapman Hall, London, 1982)

    Google Scholar 

  15. M. Papageorgiou, Application of Automatic Control Concepts in Traffic Flow Modeling and Control, (Springer, Berlin, New York, 1983)

    Book  Google Scholar 

  16. D.E. Wolf, Physica A 263, 438–451 (1999)

    Article  MathSciNet  Google Scholar 

  17. D. Chowdhury, L. Santen, A. Schadschneider, Physics Reports 329, 199 (2000)

    Article  MathSciNet  Google Scholar 

  18. D. Helbing, Rev. Mod. Phys. 73, 1067–1141 (2001)

    Article  Google Scholar 

  19. T. Nagatani, Rep. Prog. Phys. 65, 1331–1386 (2002)

    Article  Google Scholar 

  20. K. Nagel, P. Wagner, R. Woesler, Oper. Res. 51, 681–716 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. R. Mahnke, J. Kaupužs, I. Lubashevsky, Phys. Rep. 408, 1–130 (2005)

    Article  Google Scholar 

  22. N. Bellomo, V. Coscia, M. Delitala, Math. Mod. Meth. App. Sc. 12, 1801–1843 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  23. B. Piccoli, A. Tosin, in Encyclopedia of Complexity and System Science, ed. by R.A. Meyers. (Springer, Berlin, 2009), pp. 9727–9749

    Google Scholar 

  24. H. Rakha, P. Pasumarthy, S. Adjerid, Transportation Letters, 1, 95–110 (2009)

    Article  Google Scholar 

  25. B.S. Kerner, Trans. Res. Rec. 1678, 160–167 (1999)

    Article  Google Scholar 

  26. B.S. Kerner, Physics World 12, 25–30 (August 1999)

    Google Scholar 

  27. S. Krauß, P. Wagner, C. Gawron, Phys. Rev. E 55, 5597–5602 (1997)

    Article  Google Scholar 

  28. K. Nagel, M. Schreckenberg, J. Phys. (France) I 2, 2221–2229 (1992); R. Barlović, L. Santen, A. Schadschneider, M. Schreckenberg, Eur. Phys. J. B 5, 793–800 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Boris S. Kerner .

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kerner, B.S. (2009). Linking of Three-Phase Traffic Theory and Fundamental Diagram Approach to Traffic Flow Modeling. In: Introduction to Modern Traffic Flow Theory and Control. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02605-8_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02605-8_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02604-1

  • Online ISBN: 978-3-642-02605-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics