Car-Following Models

  • Robert L. BakerJr.
Part of the Modules in Applied Mathematics book series


The automobile is a pervasive feature of modern technological societies despite its accompanying problems of pollution, accidents, and congestion. In the last 25 years a vast amount of literature has been published which we might classify as “traffic science.” This science has attempted to understand through modeling and data gathering the traffic processes and how to modify, optimize, and control them.


Traffic Flow Oscillatory Response Lead Vehicle Instantaneous Acceleration Front Bumper 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Bexelius, “An extended model for car-following,” Transportation Res., vol. 2, pp. 13–21, 1968.CrossRefGoogle Scholar
  2. [2]
    E. A. Bender and L. P. Neuwirth, “Traffic flow: Laplace transforms,” Amer.Math. Monthly, vol. 80., pp. 417–423, 1973. Readable by students; develops some details of stability theory.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    R. E. Chandler, R. Herman, and E. W. Montroll, “Traffic dynamics: Studies in car-following,” Operations Res., vol. 6, pp. 165–184, 1958. First paper on stability theory; develops asymptotic stability for a number of models; higher level than present module, but accessible to better students with some complex variable background.MathSciNetCrossRefGoogle Scholar
  4. [4]
    D. R. Drew, Traffic Flow Theory and Control. New York: McGraw-Hill, 1968. A book on many aspects of traffic science besides car-following; lots of practical examples, many topics accessible to undergraduates.Google Scholar
  5. [5]
    L. C. Edie, “Car-following and steady-state theory for non-congested traffic,” Operations Res., vol. 9, no. 1, pp. 66–76, 1961.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Denos C. Gazis, “Traffic flow and control: Theory and applications,” Amer.Scientist, vol. 60, no. 4, pp. 415–424, 1972. A survey article on traffic science, like a Scientific American article.Google Scholar
  7. [7]
    D. C. Gazis, R. Herman, and R. B. Potts, “Car-following theory of steady state traffic flow,” Operations Res., vol. 7, no. 4, pp. 499–505, 1959. Very readable; uses only algebra and simple integration.MathSciNetCrossRefGoogle Scholar
  8. [8]
    D. C. Gazis, R. Herman and R. W. Rothery, “Nonlinear follow-the-leader models of traffic flow,” Operations Res., vol. 9, no. 4, pp. 545–567, 1961.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    H. Greenberg, “An analysis of traffic flow,” Operations Res., vol. 7, no. 1, pp. 79–85, 1959.MathSciNetCrossRefGoogle Scholar
  10. [10]
    R. Herman, et al., “Traffic dynamics: Analysis of stability in car-following,” Operations Res., vol. 7, pp. 86–106, 1959. The definitive article on stability theory: not accessible to average undergraduates.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Robert Herman and R. B. Potts, Single-Lane Traffic Theory and Experiment, Theory of Traffic Flow. Amsterdam: Elsevier, 1961, pp. 120–146. Very readable summary of car-following without too many technical details; good source of experimental results.Google Scholar
  12. [12]
    G. Lee, “A generalization of linear car-following,” Operations Res., vol. 14, no. 4, pp. 595–606, 1966.CrossRefGoogle Scholar
  13. [13]
    G. F. Newell, “Theories of instability in dense highway traffic,” J. Operations Res. of Japan, vol. 5, pp. 9–54, 1962.MathSciNetGoogle Scholar
  14. [14]
    L. A. Pipes, “An operational analysis of traffic dynamics,” J. Appl. Phys. vol. 24, no. 3, pp. 274–281, 1953. The original paper on car-following; easily read by those with background to read this module.MathSciNetCrossRefGoogle Scholar
  15. [15]
    E. Tuck, “Stability of following in two dimensions,” Operations Res., vol. 9, no. 4, pp. 479–495, 1961.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    W. E. Wilhelm and J. W. Schmidt, “Review of car-following theory,” Transportation Engineering J. of ASCE, vol. 99, no. TE4, pp. 923–931, 1973. A bibliographic survey; easily read by students.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • Robert L. BakerJr.
    • 1
  1. 1.IIT Research InstituteAnnapolisUSA

Personalised recommendations