Creation and annihilation of traffic jams in a stochastic asymmetric exclusion model with open boundaries: a computer simulation
Creation and annihilation of traffic jams in a stochastic asymmetric exclusion model with open boundaries: a computer simulation
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具有开放边界的随机不对称排除模型中交通拥堵的产生和消除：计算机模拟
DOI：
10.1088/0305-4470/28/24/008
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
T. Nagatani
中科院分区：
文献类型：
--
作者：
T. Nagatani
通过计算机模拟研究了交通堵塞的产生和消除。扩展了一维完全非对称排斥模型，考虑了粒子（汽车）的随机跃迁，如果前向最近邻粒子未被占据，则粒子以跃迁概率pt向前移动.接近pt = 1时，系统渐近地进入一个稳定状态，表现出自组织临界性。在自组织临界状态下，当汽车临时停车时，同时产生交通堵塞（启停波）和空波。交通堵塞通过与空波碰撞而消失。交通堵塞和空波之间的合并过程描述的弹道湮灭过程与对创建。在pt = 1附近产生的问题与Krug和Spohn（1988）研究的一维晶体生长中的弹道过程一致。起止波的典型寿命的比例约为Δ pt = 0.54+或-0.04，其中Δ pt = 1-pt。结果表明，寿命的累积分布Nm（Delta pt）近似满足标度形式Nm（Delta pt）= Delta pt 1.1f（m Delta pt 0.54）.此外，连续交通堵塞之间的典型间隔近似为Δ pt-0.5+或-0.04。交通堵塞的累积间隔分布Ns（Delta pt）近似满足标度形式Ns（Delta pt）= Delta pt 0.50g（s Delta pt 0.50）。对于pt <1，没有缩放保持。
The creation and annihilation of traffic jams are studied by a computer simulation. The one-dimensional (1D) fully-asymmetric exclusion model with open boundaries for parallel update is extended to take into account stochastic transition of particles (cars) where a particle moves ahead with transition probability pt if the forward nearest neighbour is not occupied. Near pt=1, the system is derived asymptotically into a steady state exhibiting a self-organized criticality. In the self-organized critical state, a traffic jam (start-stop wave) and an empty wave are created at the same time when a car stops temporarily. The traffic jam disappears by colliding with the empty wave. The coalescence process between traffic jams and empty waves is described by the ballistic annihilation process with pair creation. The resulting problem near pt=1 is consistent with the ballistic process in the context of 1D crystal growth studied by Krug and Spohn (1988). The typical lifetime of start-stop waves scales as approximately= Delta pt-0.54+or-0.04 where Delta pt=1-pt. It is shown that the cumulative distribution Nm( Delta pt) of lifetimes satisfies the scaling form Nm( Delta pt) approximately= Delta pt1.1f(m Delta pt0.54). Also, the typical interval between consecutive traffic jams scales as approximately= Delta pt-0.5+or-0.04. The cumulative interval distribution Ns( Delta pt) of traffic jams satisfies the scaling form Ns( Delta pt) approximately= Delta pt0.50g(s Delta pt0.50). For pt<1, no scaling holds.