Velocity statistics of the Nagel-Schreckenberg model
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PhysRevE.93.022305.pdf
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533.18 KB
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Author(s)
Bain, Nicolas
Emig, Thorsten
Ulm, Franz-Josef
Schreckenberg, Michael
Date Issued
February 2016
Journal
Physical Review E
Publisher
American Physical Society
Citation
Bain, Nicolas, Thorsten Emig, Franz-Josef Ulm, and Michael Schreckengerg. "Velocity statistics of the Nagel-Schreckenberg model." Phys. Rev. E 93, 022305 (February 2016). © 2016 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
MIT Energy Initiative
MultiScale Materials Science for Energy and Environment, Joint MIT-CNRS Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.93.022305
