Abstract
We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that could explain in a simple way such observed self-organizing phenomena as the sequence of the phase transitions“free flow → synchronized motion → jam” and the hysteresis in them. We introduce a new variable called order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to “many-body” effects in the car interaction in contrast to such variables as the mean car density and velocity being actually the zeroth and first moments of the “one-particle” distribution function. Therefore, we regard the order parameter as an additional independent state variable of traffic flow and formulate the corresponding evolution equation governing the lane changing rate. In this context we analyze the instability of homogeneous traffic flow manifesting itself in both of these phase transitions and endowing them with the hysteresis. Besides, the jam state is characterized by the vehicle flows at different lanes being independent of one another.
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
B.S. Kerner and H. Rehborn, Phys. Rev. E 53, R4275 (1996).
B.S. Kerner, Phys. Rev. Lett. 81, 3797 (1998).
B.S. Kerner and H. Rehborn, Phys. Rev. E 53, R1297 (1996).
B.S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997).
B.S. Kerner, Physics World 12, 25 (1999).
B.S. Kerner, in: Transportation and Traffic Theory, A. Ceder (Ed.), p. 147 (Pergamon, Amsterdam, 1999).
D. Helbing, Verkehrsdynamik, (Springer, Berlin, 1997).
D. Helbing and M. Treiber, Phys. Rev. Lett. 81, 3042 (1998).
M. Treiber, A. Hennecke, and D. Helbing, Phys. Rev. E 59, 239 (1999).
V. Shvetsov and D. Helbing, Phys. Rev. E 59, 6328 (1999).
A. Klar and R. Wegener, SIAM J. Appl. Math. 59, 983, 1002 (1999).
H.Y. Lee, D. Kim, and M.Y. Choi, in: Traffic and Granular Flow’97, M. Schreckenberg and D.E. Wolf, (Eds.), p. 433 (Springer, Singapore, 1998).
T. Nagatani, Physica A 264, 581 (1999).
T. Nagatani, Phys. Rev. E 60, 1535 (1999).
L. Neubert, L. Santen, A. Schadschneider, and M. Schreckenberg, Phys. Rev. E 60, 6480 (1999).
R. Mahnke and N. Pieret, Phys. Rev. E 56, 2666 (1997).
R. Mahnke and J. Kaupužs, Phys. Rev. 59, 117 (1999).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lubashevsky, I.A., Mahnke, R. (2000). Order Parameter as an Additional State Variable of Unstable Traffic Flow. In: Helbing, D., Herrmann, H.J., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’99. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59751-0_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-59751-0_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64109-1
Online ISBN: 978-3-642-59751-0
eBook Packages: Springer Book Archive