Multi-Scale Materials Science for Energy and Environment, 〈MSE〉2, UMI 3466, Joint CNRS-MIT Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Universität Duisburg-Essen, Physik von Transport und Verkehr, 47058 Duisburg, Germany.
Phys Rev E. 2017 Jan;95(1-1):012311. doi: 10.1103/PhysRevE.95.012311. Epub 2017 Jan 12.
We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P(v=0) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P(v∈{0,1}) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.
我们通过模拟和分析技术研究了纳格尔-施雷克伯格元胞自动机交通流模型。为了更好地理解堵塞相变的本质，我们分析了速度为 0 的停车车辆的比例 P(v=0)作为平均车辆密度的函数。我们提出了一个简单的论点，给出了发生堵塞的自由密度的估计值，并与模拟结果吻合得很好。我们证明了堵塞车辆的比例 P(v∈{0,1})可以分解为三个因素（堵塞率、堵塞寿命和堵塞大小），我们从随机游走的角度推导出了这些因素的标度指数，这些指数控制了它们在接近临界密度时的标度。
