Abstract
We propose a new optimization strategy based on inducing stop-and-go waves on the main road and controlling their wavelength. Using numerical simulations of a recent stochastic car-following model [11] we show that this strategy yields optimization of traffic flow in systems with a localized periodic inhomogeneity, such as signalized intersections and entry ramps. The optimization process is explained by our finding of a generalized fundamental diagram (GFD) for traffic, namely a fluxdensity-wavelength relation. Projecting the GFD on the density-flux plane yields a two-dimensional region of stable states, qualitatively similar to that found empirically [7] in synchronized traffic. The empirical finding of the dependence of the wavelength on the average velocity can also be explained using the same approach.
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
D. Chowdhury, L. Santen, and A. Schadschneider: Phys. Rep. 329, 199 (2000).
D. Helbing: Rev. Mod. Phys. (in the press) (2001); cond-mat/0012229 (2000).
D.E. Wolf: Physica A 263, 438 (1999).
A.D. May: Traffic Flow Fundamentals, (Prentice Hall, Englewood Cliffs, N.J. 1990 ).
B.D. Greenshields: High. Res. Rec. 14 468 (1934).
M.J. Lighthill and G.B. Whitham: Proc. R. Soc. London Ser. A 229, 317, (1955).
B.S. Kerner: Phys. Rev. Lett. 81, 3797 (1998).
B.S. Kerner: Physics World 12 (8), 25 (1999).
B.S. Kerner and H. Rehborn: Phys. Rev. Lett. 79, 4030 (1997).
L. Neubert, L. Santen, A. Schadschneider, and M. Schreckenberg: Phys. Rev. E 60, 6480 (1999).
E. Tomer, L. Safonov, and S. Havlin: Phys. Rev. Lett. 84, 382 (2000).
L.A. Safonov, E. Tomer, V.V. Strygin, and S. Havlin: Physica A 285, 147 (2000).
L.A. Safonov, E. Tomer, V.V. Strygin, Y. Ashkenazy, and S. Havlin: Europhys. Lett. 57, 151 (2002).
M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama: Phys. Rev. E 51, 1035 (1995).
Y. Sugiyama: ‘Dynamical Model for Congestion of Freeway Traffic and its Stractural Stability’. In: Traffic and Granular Flow, ed. by D.E. Wolf, M. Schreckenberg, and A. Bachem ( World Scientific, Singapore 1996 ) pp 137–149.
K. Nagel and M. Schreckenberg, J. Phys. I (France) 2, 2221 (1992).
K. Nagel and H.J. Herrmann: Physica A 199, 254 (1993).
K. Nagel and M. Paczuski: Phys. Rev. E 51, 2909 (1995).
O. Biham, A.A. Middleton and D. Levine: Phys. Rev. A. 46, R6124 - R6127 (1992).
R. Herman and R.W. Rothery: ‘Car Following and Steady State Flow’. In: Proceedings of the 2ns International Symposium on the Theory of Road Traffic Flow, London, 1963, ed. by J. Almond, ( Organization for Economic Cooperation and Development, Paris 1965 ) pp 1–11.
D. Helbing and B. Tilch: Phys. Rev. E 58, 133 (1998).
N. Mitarai and H. Nakanishi: Phys. Rev. Lett. 85, 1766 (2000).
M. Treiber, A. Hennecke, and D. Helbing: Phys. Rev. E 62, 1805 (2000).
S. Cheybani, J. Kertesz, and M. Schreckenberg: Phys. Rev. E. 63, 016108 (2001).
H.Y. Lee, H.W. Lee, and D. Kim: Phys. Rev. Lett. 81, 1130 (1998).
D. Helbing and M. Treiber: Science 282, 2001 (1998).
D. Helbing, A. Hennecke, and M. Treiber: Phys. Rev. Lett. 82, 4360 (1999).
Interactive simulations of the deterministic model with and without traffic lights can be found at http://ory.ph.biu.ac.i1/2000/traffic.
D.C. Gazis and R.B. Potts: ‘The Over-Saturated Intersection’. In: Proceedings of the 2ns International Symposium on the Theory of Road Traffic Flow, London, 1963, ed. by J. Almond, ( Organization for Economic Cooperation and Development, Paris 1965 ) pp 221–237.
W.B. Cronje: Transport. Res. Rec. 905, 80 (1983).
D. Chowdhury and A. Schadschneider: Phys. Rev. E. 59, R1311 (1999).
N. H. Gartner, C. Stamatiadis, and P. J. Tarnoff, Transport. Res. Rec. 1494, 98 (1995).
T.H. Chang and J.T. Lin, Transport. Res. B 34, 471 (2000).
H. Zhang, S.G. Ritchie, and W.W. Recker: Transport. Res. C 4, 51 (1996).
M. Treiber and D. Helbing, preprint (2001).
R. Sollacher and H. Lenz: ‘Nonlinear Control of Stop-and-Go Traffic’. In: Tra f fic and Granular Flow ‘89, ed. by D. Helbing, H.J. Herrmann, M. Schreckenberg, and D.E. Wolf, ( Springer, Berlin 2000 ) pp 315–320.
Decreasing a and T would not yield the same result due to relatively large values of T_/r. in Eq. (12).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tomer, E., Safonov, L.A., Havlin, S. (2003). The Generalized Fundamental Diagram of Traffic and Possible Applications. In: Fukui, M., Sugiyama, Y., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow’01. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10583-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-662-10583-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07304-5
Online ISBN: 978-3-662-10583-2
eBook Packages: Springer Book Archive