Modelling traffic flow: Solving and interpreting differential equations

M McCartney, Malachy Carey

Research output: Contribution to journal › Article

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.
LanguageEnglish
Pages115-121
JournalTeaching Mathematics and its Applications
Volume18
Issue number3
DOIs
Publication statusPublished - Sep 1999

Fingerprint

traffic
differential equations
roads
students
mathematical models

Cite this

McCartney, M ; Carey, Malachy. / Modelling traffic flow: Solving and interpreting differential equations. In: Teaching Mathematics and its Applications. 1999 ; Vol. 18, No. 3. pp. 115-121.
@article{8131600149ef44ed803faf8a680c23b0,
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.",
author = "M McCartney and Malachy Carey",
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",
month = "9",
doi = "10.1093/teamat/18.3.115",
language = "English",
volume = "18",
pages = "115--121",
journal = "Teaching Mathematics and its Applications",
issn = "0268-3679",
number = "3",

}

McCartney, M & Carey, M 1999, 'Modelling traffic flow: Solving and interpreting differential equations', Teaching Mathematics and its Applications, vol. 18, no. 3, pp. 115-121. https://doi.org/10.1093/teamat/18.3.115

Modelling traffic flow: Solving and interpreting differential equations. / McCartney, M; Carey, Malachy.

In: Teaching Mathematics and its Applications, Vol. 18, No. 3, 09.1999, p. 115-121.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Modelling traffic flow: Solving and interpreting differential equations

AU - McCartney, M

AU - Carey, Malachy

N1 - 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

PY - 1999/9

Y1 - 1999/9

N2 - 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.

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.

U2 - 10.1093/teamat/18.3.115

DO - 10.1093/teamat/18.3.115

M3 - Article

VL - 18

SP - 115

EP - 121

JO - Teaching Mathematics and its Applications

T2 - Teaching Mathematics and its Applications

JF - Teaching Mathematics and its Applications

SN - 0268-3679

IS - 3

ER -

McCartney M, Carey M. Modelling traffic flow: Solving and interpreting differential equations. Teaching Mathematics and its Applications. 1999 Sep;18(3):115-121. https://doi.org/10.1093/teamat/18.3.115

Access to Document