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Article
Towards an Analytical Theory for the Solution of the Nagel-Schreckenberg Model with vmax > 1
This version is not peer-reviewed.
Submitted:
28 February 2023
Posted:
28 February 2023
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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
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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