Modelling traffic flow: Solving and interpreting differential equations

M McCartney, Malachy Carey

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)115-121
JournalTeaching Mathematics and its Applications
Issue number3
Publication statusPublished (in print/issue) - Sept 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:
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.
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