一个简单的确定性交通流模型的遍历性
Ergodic properties of a simple deterministic traffic flow model re(al)visited
摘要：
我们研究了一类作用于整数序列空间的映射的统计性质，它模拟了简单确定性交通流的动力学。我们根据各种模式的密度统计，得到了这些映射对应于任意初始组态的轨迹的渐近性质（当时间趋于无穷大时），并描述了这些系统的弱吸引子及其收敛速率.以前只有所谓的规则的初始配置（具有密度，只有有限的波动的部分和它周围）的情况下，一个慢粒子模型（最大速度为1）已被严格研究。应用从替代动力学中借用的思想，我们能够将对应于多车道交通和具有快粒子（速度大于1）的流的交通流模型的分析减少到具有单车道交通和慢粒子的流的最简单的情况，其中关键的技术步骤是导出给定粒子簇的精确寿命。最后讨论了该方法在多车道交通流优化重定向中的应用。
英文摘要：
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of those maps corresponding to arbitrary initial configurations in terms of statistics of densities of various patterns and describe weak attractors of these systems and the rate of convergence to them. Previously only the so called regular initial configurations (having a density with only finite fluctuations of partial sums around it) in the case of a slow particles model (with the maximal velocity 1) have been studied rigorously. Applying ideas borrowed from substitution dynamics we are able to reduce the analysis of the traffic flow models corresponding to the multi-lane traffic and to the flow with fast particles (with velocities greater than 1) to the simplest case of the flow with the one-lane traffic and slow particles, where the crucial technical step is the derivation of the exact life-time for a given cluster of particles. Applications to the optimal redirection of the multi-lane traffic flow are discussed as well.
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