Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T17:11:23.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Traffic Lights or Roundabout? Analysis using the Modified Kinematic LWR Model

Part of: Basic methods in fluid mechanics Hyperbolic equations and systems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 January 2016

S. R. Pudjaprasetya ,
J. Bunawan  and
C. Novtiar
S. R. Pudjaprasetya*
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
J. Bunawan
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
C. Novtiar
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*
*Corresponding author. Email address:sr_pudjap@math.itb.ac.id (S.R. Pudjaprasetya)
Get access

Abstract

Traffic flow is treated as a continuum governed by the kinematic LWR model and the Greenshield flux function. The model is modified to describe traffic flow on a road with traffic lights or a roundabout. Parameters introduced determine the traffic flow behaviour and queue formation, and numerical simulations based on the Godunov method are carried out. The numerical procedure is shown to converge, and produces results consistent with previous analytic results.

Keywords

Kinematic LWR modelRiemann solutionsGodunov method

MSC classification

Secondary: 65M08: Finite volume methods 76M12: Finite volume methods 35L65: Conservation laws
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 1 , February 2016 , pp. 80 - 88
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bagnerini, P., Colombo, R.M., Corli, A. and Pedretti, S., Conservation versus balance laws in traffic flow, Traffic and Granular Flow ’03, pp. 235–240 (2005).Google Scholar
[2]Chimdessa, Y., Kassa, S.M. and Lemecha, L., Efficiency of roundabouts as compared to traffic light controlled intersections in urban road networks, Momona Ethiopian J. Sc. (MEJS) 5, 81–100 (2013).Google Scholar
[3]Daganzo, C.F., The cell transmission model: A dynamic representation of highway traffic consistent with hydrodynamic theory, Transportation Res. B 28, 269–287 (1994).Google Scholar
[4]Daganzo, C.F., The cell transmission model II: Network traffic, Transportation Res. B 29, 79–93 (1995).CrossRefGoogle Scholar
[5]Daganzo, C.F., A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections. II: Merges and the onset of congestion, Transportation Res. B 36, 131–169 (2002).CrossRefGoogle Scholar
[6]Ni, D., Lecture Notes in Traffic Flow Theory, A Unified Perspective, Elsevier (2013).Google Scholar
[7]Fowkes, N.D. and Mahony, J.J., An Introduction to Mathematical Modelling, Wiley (1994).Google Scholar
[8]Haberman, R., Mathematical Models, Prentice-Hall (1977).Google Scholar
[9]Herty, M. and Klar, A., modelling, simulation, and optimization of traffic flow networks, SIAM J. Sci. Comput. 25, 1066–1087 (2003).Google Scholar
[10]Holden, H. and Risebro, N.H., A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Analysis 26, 999–1017 (1995).CrossRefGoogle Scholar
[11]Lebacque, J.P., The Godunov scheme and what it means for first order traffic flow models, in the International Symposium on Transportation and Traffic Theory, Lyon, France (1996).Google Scholar
[12]Mattheij, R.M.M., Rienstra, S.W. and ten Thije Boonkkamp, J.H.M., Partial Differential Equation: Modelling, Analysis, Computation, The Netherlands Society for Industrial and Applied Mathematics, Philadelphia (2005).Google Scholar
[13]Orosz, G., Wilson, R.E. and Stépána, G., Traffic jams: Dynamics and control, Phil. Trans. R. Soc. A 368, 4455–4479 (2010).Google Scholar
[14]Papageorgiou, M., Dynamic modelling, assignment and route guidance in traffic networks, Transportation Res. B 24, 471–495 (1990).Google Scholar
[15]Rodegerdts, L.A.et al., NCHRP Report 572: Applying roundabouts in the United States, Washington, D.C., Transportation Research Board, National Research Council (2007).Google Scholar
[16]Zhou, W., Xie, J. and Deng, L., Study of one-lane roundabout traffic flow characteristic based on computer simulation, Adv. information Sc. Service Sc. (AISS) 4, No. 17, (2012).Google Scholar
[17]Wang, R. and Ruskin, H.J., modelling traffic flow at a single-lane urban roundabout, Comp. Phys. Comm. 147, 570–576 (2002).CrossRefGoogle Scholar