Modelling traffic flow: Solving and interpreting differential equations

M McCartney; Malachy Carey

doi:10.1093/teamat/18.3.115

Modelling traffic flow: Solving and interpreting differential equations

M McCartney, Malachy Carey

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

A simple mathematical model for how traffic flows along a road is introduced. The resulting first-order ordinary differential equations can be used as an application of solution techniques taught at A-level and first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the equation produces.

Original language	English
Pages (from-to)	115-121
Journal	Teaching Mathematics and its Applications
Volume	18
Issue number	3
DOIs	https://doi.org/10.1093/teamat/18.3.115
Publication status	Published - Sep 1999

Bibliographical note

Reference text: 1. Wan, F. Y. M., "Mathematical Models and Their Analysis."
Harper and Row, 1989.
2. Prigogine, I. and Herman, R., "Kinetic Theory of Vehicular
Traffic." American Elsevier, 1971.
3. Low, D. J. and Addison, P. S., A nonlinear temporal headway
model of traffic dynamics, Nonlinear Dynamics, 1998,
16, 127-151.
4. Resnick, M., "Turtles, Termites and Traffic Jams." MIT
Press, 1995.
5. Paramics web site: http:Hwww.paramics.com/
6. Tallarida, R. I., "Pocket Book of Integrals and
Mathematical Formulas." 2/e, CRC Press, 1992.
7. Daganzo, C. F., "Fundamentals of Transportation and
Traffic Operations." Pergamon, 1999.
Downloaded from http://teamat.oxfordjournals.org/ at university of ulster on December 10, 2013

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title = "Modelling traffic flow: Solving and interpreting differential equations",

abstract = "A simple mathematical model for how traffic flows along a road is introduced. The resulting first-order ordinary differential equations can be used as an application of solution techniques taught at A-level and first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the equation produces.",

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note = "Reference text: 1. Wan, F. Y. M., {"}Mathematical Models and Their Analysis.{"} Harper and Row, 1989. 2. Prigogine, I. and Herman, R., {"}Kinetic Theory of Vehicular Traffic.{"} American Elsevier, 1971. 3. Low, D. J. and Addison, P. S., A nonlinear temporal headway model of traffic dynamics, Nonlinear Dynamics, 1998, 16, 127-151. 4. Resnick, M., {"}Turtles, Termites and Traffic Jams.{"} MIT Press, 1995. 5. Paramics web site: http:Hwww.paramics.com/ 6. Tallarida, R. I., {"}Pocket Book of Integrals and Mathematical Formulas.{"} 2/e, CRC Press, 1992. 7. Daganzo, C. F., {"}Fundamentals of Transportation and Traffic Operations.{"} Pergamon, 1999. Downloaded from http://teamat.oxfordjournals.org/ at university of ulster on December 10, 2013",

year = "1999",

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doi = "10.1093/teamat/18.3.115",

language = "English",

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AB - A simple mathematical model for how traffic flows along a road is introduced. The resulting first-order ordinary differential equations can be used as an application of solution techniques taught at A-level and first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the equation produces.

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JO - Teaching Mathematics and its Applications

JF - Teaching Mathematics and its Applications

SN - 0268-3679

IS - 3

ER -

Modelling traffic flow: Solving and interpreting differential equations

Abstract

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