非线性动力学、涌现行为与可控扩张：拥挤交通的有效建模
Non-linear Dynamics, Emergent Behaviors and Controlled Expansions: Towards Effective Modeling of the Congested Traffic
摘要：
我们提出了一个框架，从微观加速度模式，原则上可以实验测量和适当的平均构建微观交通模型。由此得到的精确模型可以用来证明文献中各种流行模型的一致性。假设精确模型的解析性，我们建议围绕恒定速度、均匀车头时距“基态“的受控展开是构建各种不同有效模型的适当方式。假设对于任何固定的平均密度都有唯一的基态，我们讨论了由此产生的有效模型的普适性质，重点讨论了耦合非线性常微分方程的涌现量。这些包括最大和最小的进展，使相图中的共存曲线，以及新兴的内在规模，集群之间的相互作用的强度为特征，导致非平凡的集群统计时，不稳定的基态随机扰动。利用突现量的普适性质，给出了一种构造有效流量模型的简单算法。该算法利用从流量密度图中提取的统计定义良好的量来调整模型，由此产生的有效模型自然地捕获和预测了高速公路交通的许多定量和定性经验特征，特别是在存在入口匝道瓶颈的情况下。有效的模型的简单性提供了强有力的证据，随机性，多样性的车辆类型和复杂的个人驾驶行为的建模是\emph{not}基本的许多观察复杂的时空模式在现实的交通动力学。我们还提出了拥塞阶段的性质可以很好地表征有效模型的长期瞬态，从广泛的移动堵塞演变。
英文摘要：
We propose a framework for constructing microscopic traffic models from microscopic acceleration patterns that can in principle be experimental measured and proper averaged. The exact model thus obtained can be used to justify the consistency of various popular models in the literature. Assuming analyticity of the exact model, we suggest that a controlled expansion around the constant velocity, uniform headway "ground state" is the proper way of constructing various different effective models. Assuming a unique ground state for any fixed average density, we discuss the universal properties of the resulting effective model, focusing on the emergent quantities of the coupled non-linear ODEs. These include the maximum and minimum headway that give the coexistence curve in the phase diagram, as well as an emergent intrinsic scale that characterizes the strength of interaction between clusters, leading to non-trivial cluster statistics when the unstable ground state is randomly perturbed. Utilizing the universal properties of the emergent quantities, a simple algorithm for constructing an effective traffic model is also presented. The algorithm tunes the model with statistically well-defined quantities extracted from the flow-density plot, and the resulting effective model naturally captures and predicts many quantitative and qualitative empirical features of the highway traffic, especially in the presence of an on-ramp bottleneck. The simplicity of the effective model provides strong evidence that stochasticity, diversity of vehicle types and modeling of complicated individual driving behaviors are \emph{not} fundamental to many observations of the complex spatiotemporal patterns in the real traffic dynamics. We also propose the nature of the congested phase can be well characterized by the long lasting transient states of the effective model, from which the wide moving jams evolve.
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