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Qian, W., Wang, B., Lin, K., Machado, R.F. and Hama, Y. (2017) A Mesoscopic Approach on Stability and Phase Transition between Different Traffic Flow States. International Journal of Non-Linear Mechanics, 89, 59-68.
https://doi.org/10.1016/j.ijnonlinmec.2016.11.010

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.