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International Journal of Mathematical Research

June 2014, Volume 3, 3, pp 25-36

On Mathematical Model for the Study of Traffic Flow on the High Ways

Sunday Emmanuel Fadugba

,

Joseph Temitayo Okunlola

,

Adedoyin Olayinka Ajayi

,

Olaronke Helen Edogbanya

Sunday Emmanuel Fadugba 1 Joseph Temitayo Okunlola 2
Adedoyin Olayinka Ajayi 1 Olaronke Helen Edogbanya 4

  1. Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria 1

  2. Department of Mathematical and Physical sciences, Afe Babalola University, Ado Ekiti, Nigeria 2

  3. Department of Mathematics, Federal University of Lokoja, Kogi State, Nigeria 4


Abstract:

This paper presents mathematical model for the study of traffic flow on the highways.  The effect of the density of cars on the overall interactions of the vehicles along a given distance of the road was investigated. We also observed that the density of cars per mile affects the net rate of interaction between them.
Contribution/ Originality
This study uses new estimation methodology to determine the effect of the density of cars on the overall inSteractions of the vehicles along a given distance of the road.

Keywords:


Reference:

  1. O. G. Omogunloye and O. O. Ayeni, "An application of the average delay model to traffic congestion at a multi road junction point," Research Journal in Engineering and Applied Sciences, vol. 1, pp. 342-350, 2012.
  2. E. A. Akinrelere and R. O. Ayeni, "Shockwaves in arterial blood flow," Journal of Nigerian Mathematical Society, vol. 2, pp. 91 - 98, 1983.
  3. B. D. Greenshields, J. R. Bibbins, W. S. Channing, and H. H. Miller, "A study of traffic capacity," Highway Research Board Proceedings, vol. 14, pp. 448-477, 1935.
  4. R. Herman, E. W. Montroll, R. Potts, and R. W. Rothery, "Traffic dynamics: Analysis of stability in car-following," Operations Research, vol. 1, pp. 86-106, 1959.
  5. L. D. Landau and E. M. Lifshitz, Fluid mechanics, 2nd ed. vol. 6: Butterworth-Heinemann, 1987.
  6. H. L. Liu and Z. Wang, "The discontinuous finite element method for red-and- green light models for the traffic flow," Mathematics and Computers in Simulation, vol. 2009, pp. 07-16, 2001.
  7. R. E. Mickens, Non-standard finite-difference models of differential equations. Singapore: World Scientific, 1994.
  8. J. H. Olseen and A. Sharpiro, "Large amplitude unsteady flow in liquid filled elastic tubes," J. Fluid Mechanics, vol. 29, pp. 513-538, 1967.
  9. P. I. Richards, "Shock waves on the highway," Operations Research, vol. 4, pp. 42-51, 1956.
  10. H. G. Nathan, J. M. Carroll, and K. R. Ajay, Monograph on traffic flow theory; US department of transportation vol. 62: Federal Highway Administration Pub, 1997.
  11. W. R. Reilly, C. C. Gardner, and J. H. Kell, "A technique for measurement of delay at intersections," FHWA Report RD-76-135/137, FHWA, U.S. Department of Transportation, Washington, D.C.1976.
  12. Transportation Research Board, "Providing a highway system with reliable travel times," Future Strategic Highway Research Plan Area 3. Available http://wwwcf.fhwa.dot.gov/exit.cfm?link=http://www4.trb.org/trb/newshrp.nsf/web/progress_reports?OpenDocument, 2003.

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Funding:

Competing Interests:

Acknowledgement:


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