Summary
From probabilistic point of view we investigate a quite classical dynamical system given by stochastic differential equations, i. e. ordinary differential equations driven by multiplicative noise. Based on this Langevin approach the probability density distributions of vehicular velocities as well as headway distances are calculated and discussed.
Our work is a continuation of a stochastic theory of freeway traffic based on a Master equation approach presented first at Traffic and Granular Flow '97 as the one—cluster model. The extension to our multi—cluster model can be found at Traffic and Granular Flow ’99.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Schmelzer, G. Röpke, R. Mahnke: Aggregation Phenomena in Complex Systems, Wiley—VCH, Weinheim, 1999.
I. Prigogine, R. Herman: Kinematic Theory of Vehicular Traffic, Elsevier, New York, 1971.
D. Helbing: Rev. Mod. Phys. 73, 1067–1141, 2001.
D. E. Wolf, M. Schreckenberg, A. Bachem (Eds.): Traffic and Granular Flow, World Scientific Publ., Singapore, 1996.
M. Schreckenberg, D. E. Wolf (Eds.): Traffic and Granular Flow '97, Springer, Singapore, 1998.
M. Bando, K. Hasebe, A. Nakayama, A. Shibata, Y. Sugiyama: Japan J. Indust. and Appl. Math. 11, 203, 1994; Phys. Rev. E 51, 1035, 1995.
M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, A. Shibata, Y. Sugiyama: J. Phys. I France 5, 1389, 1995.
L. Arnold: Random Dynamical Systems, Springer, Berlin, 1998.
R. Mahnke, J. Kaupužs: Presentation at second workshop on Traffic and Granular Flow, Duisburg, October 1997, see D. E. Wolf (Eds.): Traffic and Granular Flow '97, Springer, Singapore, 1998 [5]}, p. 439; 447.
R. Mahnke, N. Pieret: Phys. Rev. E 56, 2666, 1997.
R. Mahnke, J. Kaupužs: Phys. Rev. E 59, 117, 1999.
R. Mahnke, and J. Kaupužs: Networks and Spatial Economics 1, 103–136, 2001.
R. Mahnke, J. Kaupžs, V. Frishfelds: Atmospheric Research 65, 261–284, 2003.
P. E. Kloeden, E. Platen: Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mahnke, R., Kaupužs, J., Tolmacheva, J. (2005). Stochastic Description of Traffic Breakdown: Langevin Approach. In: Hoogendoorn, S.P., Luding, S., Bovy, P.H.L., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’03. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28091-X_17
Download citation
DOI: https://doi.org/10.1007/3-540-28091-X_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25814-8
Online ISBN: 978-3-540-28091-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)