Research ArticleOpen AccessGoogle Scholar indexed
Clusters in Macroscopic Traffic Flow Models
Universidad Autónoma Metropolitana, Iztapalapa, México
Universidad Autónoma Metropolitana, Iztapalapa, México
- 1 Universidad Autónoma Metropolitana, Iztapalapa, México
- 2 Universidad Autónoma Metropolitana, Iztapalapa, México
World Journal of Mechanics·Volume 02 (2012)·Pages 51–60·Published 29 February 2012·DOI10.4236/wjm.2012.21007
Copy link · social · email
Abstract
This paper concerns the traveling wave formation in macroscopic traffic flow models. The dynamics involved in this problem is described following a close analogy to compressible fluid dynamics. It is well known that vehicle clusters appear along a highway when the homogenous steady state taken as a reference is linearly unstable. The cluster properties are determined in an approximate way in terms of the parameters proper to each model and are compared between them.
KeywordsTraffic FlowSolitons
- H. X. Ge, R. J. Cheng and S. Q. Dai, “KdV and Kink- Antikinksolitons in Car-Following Models,” Physica A: Statistical Mechanics and Its Applications, Vol. 357, No. 3-4, 2005, pp. 466-476. doi:10.1016/j.physa.2005.03.059
- H. B. Zhu and S. Q. Dai, “Numerical Simulation of Soliton and Kink Density Waves in Traffic Flow with Periodic Boundaries,” Physica A: Statistical Mechanics and Its Applications, Vol. 387, No. 16-17, 2008, pp. 4367- 4375. doi:10.1016/j.physa.2008.01.067
- Z. Z. Liu, X. J. Zhou, X. M. Liu and J. Luo, “Density Waves in Traffic Flow of Two Kinds of Vehicles,” Phy- sical Review E, Vol. 67, No. 1, 2003, pp. 017601-017604. doi:10.1103/PhysRevE.67.017601
- D. Helbing, “Traffic and Related Self-Driven Many-Particle Systems,” Reviews of Modern Physics, Vol. 73, No. 4, 2001, pp. 1067-1139. doi:10.1103/RevModPhys.73.1067
- M. J. Lighthill and G. B. Whitham, “On Kinematic Waves II. A Theory of Traffic Flow on Long Crowded Roads,” Proceedings of the Royal Society of London, Vol. 229, 1955, pp. 317-345.
- H. J. Payne, “Mathematical Models of Public Systems,” Simulation Councils, Inc., 1971.
- R. D. Kühne and R. Beckschulte, “Transportation and Traffic Theory,” Proceedings of 12th International Symposium on Transportation and Traffic Theory, Elsevier, Berkeley, 1993.
- B. S. Kerner and P. Konh?user, “Cluster Effect in Initially Homogenous Traffic Flow,” Physical Review E, Vol. 48, No. 4, 1993, R2335-R2338. doi:10.1103/PhysRevE.48.R2335
- B. S. Kerner and P. Konh?user, “Structure and Parameters of Clusters in Traffic Flow,” Physical Review E, Vol. 50, No. 51, 1994, pp. 54-83. doi:10.1103/PhysRevE.50.54
- A. Aw and M. Rascle, “Resurrection of “Second Order,” Models of Traffic Flow,” SIAM Journal of Applied Mathe- matics, Vol. 60, No. 3, 2000, pp. 916-938. doi:10.1137/S0036139997332099
- A. Aw, A. Klar, T. Materne and M. Rascle, “Derivation of Continuum Traffic Flow Models from Microscopic Follow the Leader Models,” SIAM Journal of Applied Mathematics, Vol. 63, No. 1, 2002, pp. 259-278. doi:10.1137/S0036139900380955
- W. Marques Jr. and R. M. Velasco, “An Improved Second-Order Continuum Traffic Model,” Journal of Statistical Mechanics: Theory and Experiment, Vol. 2010, 2010, P02012. doi:10.1088/1742-5468/2010/02/P02012
- D. Helbing, “Improved Fluid-Dynamic Model for Vehicular Traffic,” Physical Review E, Vol. 51, No. 4, 1995, pp. 3164-3169. doi:10.1103/PhysRevE.51.3164