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Car-Following Models

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Differential Equation Models

Part of the book series: Modules in Applied Mathematics ((MAM))

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Abstract

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.

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References

  1. S. Bexelius, “An extended model for car-following,” Transportation Res., vol. 2, pp. 13–21, 1968.

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  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.

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  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.

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  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.

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  5. L. C. Edie, “Car-following and steady-state theory for non-congested traffic,” Operations Res., vol. 9, no. 1, pp. 66–76, 1961.

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  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.

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© 1983 Springer-Verlag New York Inc.

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Baker, R.L. (1983). Car-Following Models. In: Braun, M., Coleman, C.S., Drew, D.A. (eds) Differential Equation Models. Modules in Applied Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5427-0_12

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  • DOI: https://doi.org/10.1007/978-1-4612-5427-0_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-5429-4

  • Online ISBN: 978-1-4612-5427-0

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