{
  "id": "cond-mat/9708114",
  "version": "v1",
  "published": "1997-08-15T12:36:34.000Z",
  "updated": "1997-08-15T12:36:34.000Z",
  "title": "On Cellular Automata Models of Single Lane Traffic",
  "authors": [
    "Marton Sasvari",
    "Janos Kertesz"
  ],
  "comment": "17 pages LaTeX, 14 PostScript figures, To appear in Phys. Rev. E",
  "doi": "10.1103/PhysRevE.56.4104",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "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 $v_{max}$. For $v_{max} = 1$ the model is closely related to KPZ class of surface growth. For $1<v_{max} < \\infty$ the relaxation time has a well defined peak at a density of cars $\\rho$ 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 $v_{max}=\\infty $ limit the model undergoes a first order transition at $\\rho \\to 0$. It seems that in the relevant cases $1<v_{max} < \\infty$ the jamming transition is under the influence of second order phase transition in the deterministic model and of the first order transition at $v_{max}=\\infty $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-08-15T12:36:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cellular automata models",
      "single lane traffic",
      "first order transition",
      "second order phase transition",
      "relaxation time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}