title: Velocity statistics of the Nagel-Schreckenberg model.
abstract: The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) covariance function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for a sufficiently large number of velocity states. Our results for the vv covariance function resemble features of a second-order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.
authors.affiliation: Multi-Scale Materials Science for Energy and Environment, 〈MSE〉2, UMI 3466, The Joint CNRS-MIT Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bain
authors.affiliation: Multi-Scale Materials Science for Energy and Environment, 〈MSE〉2, UMI 3466, The Joint CNRS-MIT Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors.forename: Thorsten
authors.initials: T
authors.lastname: Emig
authors.affiliation: Multi-Scale Materials Science for Energy and Environment, 〈MSE〉2, UMI 3466, The Joint CNRS-MIT Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors.forename: Franz-Josef
authors.initials: FJ
authors.lastname: Ulm
authors.affiliation: Physik von Transport und Verkehr, Universität Duisburg-Essen, 47048 Duisburg, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Schreckenberg
mesh_terms: D008962:Models, Theoretical; D018986:Motor Vehicles; D011336:Probability