论文标题
规则184模糊的蜂窝自动机作为交通流量的数学模型
Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow
论文作者
论文摘要
规则184模糊蜂窝自动机被视为交通流的数学模型，因为它包含两个基本的交通流模型，即规则184蜂窝自动机和汉堡方程，是特殊情况。我们表明，该模型的基本图（通量密度图）由三个部分组成：自由流部分，拥塞部分和两个周期性部分。可能对应于同步模式区域的两个周期部分是图中的二维区域，其边界由自由流和拥塞部分组成。我们证明，拥塞和两个周期性部分的任何状态都是稳定的，但在自由流部分中的任何状态都不稳定，而在自由流部分中的任何状态都是不稳定的。该模型和瓶颈效应的瞬态行为也通过数值模拟检查。此外，为了研究低密度或高密度极限，我们考虑了模型的超级物质极限，并表明任何超级交流状态都会在有限的时间步骤中转向速度的波动波状态，以实现通用初始条件。
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.
