Tian, J., Li, G., Treiber, M., Jiang, R., Jia, N. and Ma, S. (2016) Cellular Automaton Model Simulating Spatiotemporal Patterns, Phase Transitions and Concave Growth Pattern of Oscillations in Traffic Flow. Transportation Research Part B-Methodological, 93, 560-575.
https://doi.org/10.1016/j.trb.2016.08.008

has been cited by the following article:

• TITLE: Criterion for the Emergence of Meta-Stable States in Traffic Systems

  AUTHORS: Liuhua Zhu

  KEYWORDS: Traffic Flow, Cellular Automaton, Matthew Effect, Hysteresis Loop Meta-Stable State

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.6, June 1, 2020

  ABSTRACT: The measurements on actual traffic have revealed the existence of meta-stable states with high flow. Such nonlinear phenomena have not been observed in the classic Nagel-Schreckenberg traffic flow model. Here we just add a constraint to the classic model by introducing a velocity-dependent randomization. Two typical randomization strategies are adopted in this paper. It is shown that the Matthew effect is a necessary condition to induce traffic meta-stable states, thus shedding a light on the prerequisites for the emergence of hysteresis loop in the fundamental diagrams.