Selforganization and a dynamical transition in traffic flow models

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.

References(16)

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[1]

Introduction to the Theory of Traffic Flow

N.H. Gartner
,
N.H.M. Wilson
,
W. Leutzbach

[1]

Traffic Flow Theory (National Research Council

D.L. Gerlough
,
M.J. Huber

[1]

1975)

Washington D.C.

[2]

Theory and Applications of Cellular Automata ( , Singapore, 1986)

S. Wolfram

[3]

See e.g., Lattice Gas Methods for PDE’s, Proceedings of the NATO Advanced Research Workshop

G.D. Doolen

- Physica D 47 1

[4]

B. Schnittman

- Int.J.Mod.Phys.B 4 2269

[5]

P. Bak
,
C. Tang
,
K. Wisenfeld

- Phys.Rev.Lett. 57 1111

[6]

M. Gerhardt
,
H. Schuster

- Physica D 36 209

[7]

Note that the fact that we find static behavior above pc and dynamic behavior below does not mean that there are no static configurations with p < pc or dynamic configurations with p > pc. What it means is that these cases are atypical and have very small basins of attraction in the ensemble of random initial conditions. In fact the static configuration with smallest possible p > 0 has p = 2/N → 0 as N → ∞, and the dynamic configuration with v = 1 and largest possible p has p = 2/3

[8]

Introduction to Percolation Theory

D. Stauffer

[9]

The dynamics of charge-density waves

G. Gruner
(
- UCLA
)

- Rev.Mod.Phys. 60 (1988) 1129-1181
•
DOI:
- 10.1103/RevModPhys.60.1129

[9]

Charge Density Waves in Solids, ( , 1989)

L.P. Gorkov
,
G. Grüner

[10]

Note that a similar situation occurs in lattice gas cellular automata on the triangular lattice, where some states can have several different outcomes. In this case one can use either a deterministic approach such as using different outcomes in even and odd time steps or the non-deterministic approach. The deterministic approach is more efficient in numerical simulations, while there seems to be no significant difference in the results between the two approaches

[11]

This one dimensional model is identical to Wolfram’s CA rule no. 184, which is asymmetric and thus does not belong to the set of 32 legal rules with a three site neighborhood. This model was previously studied in the context of surface growth through ballistic deposition ). Related stochastic models in two dimensions with one type of arrow have also been studied

J. Krug
,
H. Spohn

- Phys.Rev.A 38 4271

[11]

Finite-size effects and shock fluctuations in the asymmetric simple-exclusion process

- Phys.Rev.A 45 (1992) 618-625
•
DOI:
- 10.1103/PhysRevA.45.618

[12]

This result is obtained analytically by considering the vacant sites as left moving arrows, with an exchange dynamics such that the numbers of right arrows and left arrows moving in each time step are the same