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. Preprints2023, 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.
Cite as:
Laval, J. Towards an Analytical Theory for the Solution of the Nagel-Schreckenberg Model with vmax > 1. Preprints2023, 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 forvmax= 1is known since the 90s, yet forvmax>1it remains an open question. It isconjectured here that this general solution can be generated from the basic solution (forvmax= 1) by a linear coordinate transformation, theshear mapping, which requires no additional parameters in the deterministic case, and two additional parameters otherwise. The proposedsolutions show remarkable agreement with existing numerical solutions, except in the congested regime where the Monte Carlo data showsmore concavity than the more linear congested branches predicted by the theory. More research is needed to investigate this bias.
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.
