Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow
Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow
复制标题
规则 184 模糊元胞自动机作为交通流数学模型
DOI：
10.1007/s13160-021-00461-3
复制
发表时间：
2020
影响因子：
0.9
通讯作者：
T. Tokihiro
中科院分区：
文献类型：
--
作者：
K. Higashi;J. Satsuma;T. Tokihiro
规则184模糊元胞自动机被视为交通流的数学模型，因为它包含两个基本交通流模型：规则184元胞自动机和Burgers方程作为特例。我们表明该模型的基本图（通量-密度图）由三部分组成：自由流部分、拥塞部分和两周期部分。二周期部分可以对应于同步模式区域，是图中的二维区域，其边界由自由流部分和拥塞部分组成。我们证明任何状态在拥塞和二周期部分都是稳定的，但不是渐近稳定的，而在自由流部分是不稳定的。模型的瞬态行为和瓶颈效应也通过数值模拟进行了检验。此外，为了研究低或高密度极限，我们考虑了模型的超离散极限，并表明对于一般初始条件，任何超离散状态都会在有限时间步长内转变为速度为 1 的行波状态。
The rule 184 fuzzy cellular automaton is regarded as a mathematical model of traffic flow because it contains the two fundamental traffic flow models, the rule 184 cellular automaton and the Burgers equation, as special cases. We show that the fundamental diagram (flux–density diagram) of this model consists of three parts: a free-flow part, a congestion part and a two-periodic part. The two-periodic part, which may correspond to the synchronized mode region, is a two-dimensional area in the diagram, the boundary of which consists of the free-flow and the congestion parts. We prove that any state in both the congestion and the two-periodic parts is stable, but is not asymptotically stable, while that in the free-flow part is unstable. Transient behaviour of the model and bottle-neck effects are also examined by numerical simulations. Furthermore, to investigate low or high density limit, we consider ultradiscrete limit of the model and show that any ultradiscrete state turns to a travelling wave state of velocity one in finite time steps for generic initial conditions.
影响因子：
2.4
作者：
BANDO, M;HASEBE, K;SUGIYAMA, Y
通讯作者：
SUGIYAMA, Y