We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P(v=0) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P(v\∈{0,1}) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.

}, issn = {2470-0045}, doi = {10.1103/PhysRevE.95.012311}, url = {https://link.aps.org/doi/10.1103/PhysRevE.95.012311}, author = {Bette, Henrik M. and Habel, Lars and Emig, Thorsten and Schreckenberg, Michael} } @article {326, title = {Velocity statistics of the Nagel-Schreckenberg model}, journal = {Physical Review E}, volume = {93}, year = {2016}, month = {Feb-18-2016}, pages = {Article Number: 022305}, 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) correlation 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 sufficiently large number of velocity states. Our results for the vv correlation 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.

}, issn = {2470-0045}, doi = {10.1103/PhysRevE.93.022305}, author = {Bain, Nicolas and Emig, Thorsten and Franz-Josef Ulm and Schreckenberg, Michael} }