元胞自动机模型中能量耗散的边界效应
Boundary effects on energy dissipation in a cellular automaton model
摘要：
本文数值研究了具有开边界条件（OBC）的Nagel-Schreckenberg（NaSch）模型中由交通引起的能量耗散.数值结果表明，在确定性和非确定性NaSch模型中，存在非零的能量耗散率Ed，不存在真正的自由流动相.在确定性的情况下，存在消光率$β{cd}$的临界值，低于该临界值，Ed随着$β$的增加而增加，但是高于该临界值，Ed在速度极限Vmax>2的情况下突然减小。然而，当vmax<3时，Ed不发生不连续的变化。在非确定性情况下，耗散能量有两种不同的贡献：一种来自随机化，另一种来自相互作用，这是确定性情况下耗散能量的唯一原因。两种耗散机制的相对贡献在随机NaSch模型与OBC。能量耗散率Ed与业务相位直接相关。在Vmax=1的情况下，理论分析与数值计算结果在三个阶段（低密度，高密度和最大电流阶段）的协议。
英文摘要：
In this paper, we numerically study energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Numerical results show that there is a nonvanishing energy dissipation rate Ed, and no true free-flow phase exists in the deterministic and nondeterministic NaSch models with OBC. In the deterministic case, there is a critical value of the extinction rate $β{cd}$ below which Ed increases with increasing $β$, but above which Ed abruptly decreases in the case of the speed limit vmax>2. However, when vmax<3, no discontiguous change in Ed occurs. In the nondeterministic case, the dissipated energy has two different contributions: one coming from the randomization, and one from the interactions, which is the only reason for dissipating energy in the deterministic case. The relative contributions of the two dissipation mechanisms are presented in the stochastic NaSch model with OBC. Energy dissipation rate Ed is directly related to traffic phase. Theoretical analyses give an agreement with numerical results in three phases (low-density, high-density and maximum current phase) for the case vmax=1.
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