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Towards an Analytical Theory for the Solution of the Nagel-Schreckenberg Model with vmax > 1
Version 1
: Received: 28 February 2023 / Approved: 28 February 2023 / Online: 28 February 2023 (09:10:18 CET)
How to cite: Laval, J. Towards an Analytical Theory for the Solution of the Nagel-Schreckenberg Model with vmax > 1. Preprints 2023, 2023020514. https://doi.org/10.20944/preprints202302.0514.v1 Laval, J. Towards an Analytical Theory for the Solution of the Nagel-Schreckenberg Model with vmax > 1. Preprints 2023, 2023020514. https://doi.org/10.20944/preprints202302.0514.v1
Abstract
An exact solution for the Nagel-Schreckenberg model for vmax = 1 is known since the 90s, yet for vmax > 1 it remains an open question. It is conjectured here that this general solution can be generated from the basic solution (for vmax = 1) by a linear coordinate transformation, the shear mapping, which requires no additional parameters in the deterministic case, and two additional parameters otherwise. The proposed solutions show remarkable agreement with existing numerical solutions, except in the congested regime where the Monte Carlo data shows more concavity than the more linear congested branches predicted by the theory. More research is needed to investigate this bias.
Keywords
urban congestion; traffic flow theory; transportation; phase transitions; surface growth; Nonequilibrium physics; criticality
Subject
Physical Sciences, Applied Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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