1997/08/15 by Marton Sasvari, Janos Kertesz · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.56.4104
17 pages LaTeX, 14 PostScript figures, To appear in Phys. Rev. E
arxiv created 1997/08/15 · arxiv updated 2009/11/30
The jamming transition in the stochastic cellular automaton model (Nagel-Schreckenberg model) of highway traffic is analyzed in detail, by studying the relaxation time, a mapping to surface growth problems and the investigation of correlation functions. Three different classes of behavior can be distinguished depending on the speed limit vmax. For vmax = 1 the model is closely related to KPZ class of surface growth. For 1<vmax < ∞ the relaxation time has a well defined peak at a density of cars ρ somewhat lower than position of the maximum in the fundamental diagram: This density can be identified with the jamming point. At the jamming point the properties of the correlations also change significantly. In the vmax=∞ limit the model undergoes a first order transition at ρ→ 0. It seems that in the relevant cases 1<vmax < ∞ the jamming transition is under the influence of second order phase transition in the deterministic model and of the first order transition at vmax=∞ .