随机元胞自动机中道路交通动力学与宏观一阶模型的关系
Relating the dynamics of road traffic in a stochastic cellular automaton to a macroscopic first-order model
摘要：
在本文中，我们描述了微观交通元胞自动机（TCA）模型（即，Nagel和Schreckenberg的随机TCA模型）和Lighthill、Whitham和Richards（LWR）的宏观一阶流体动力学模型。我们的方法的创新方面，是我们明确地得出LWR的基本图直接从STCA的规则集，通过假设一个平稳性条件，转换成一组线性不等式的STCA的规则。反过来，这些约束定义了基本图的形状，然后将其指定给LWR模型。应用我们的方法模拟案例研究，使我们能够比较这两种模式的时空行为。我们的研究结果表明，在噪声的存在下，在推导出的基本图的容量流是高估的STCA模型。直接指定STCA的能力流的LWR基本图，有效地补救了两种方法之间的大部分不匹配。我们的方法认为STCA补充LWR模型，反之亦然，所以结果可以很大的帮助时，解释两个模型中的交通动态。特别吸引人的是，STCA可以可视化交通流动态的高阶特征，例如，稀疏波的爱好者。
英文摘要：
In this paper, we describe a relation between a microscopic traffic cellular automaton (TCA) model (i.e., the stochastic TCA model of Nagel and Schreckenberg) and the macroscopic first-order hydrodynamic model of Lighthill, Whitham, and Richards (LWR). The innovative aspect of our approach, is that we explicitly derive the LWR's fundamental diagram directly from the STCA's rule set, by assuming a stationarity condition that converts the STCA's rules into a set of linear inequalities. In turn, these constraints define the shape of the fundamental diagram, which is then specified to the LWR model. Application of our methodology to a simulation case study, allows us to compare the tempo-spatial behavior of both models. Our results indicate that, in the presence of noise, the capacity flows in the derived fundamental diagram are overestimations of those of the STCA model. Directly specifying the STCA's capacity flows to the LWR fundamental diagram, effectively remedies most of the mismatches between both approaches. Our methodology sees the STCA complementary to the LWR model and vice versa, so the results can be of great assistance when interpreting the traffic dynamics in both models. Especially appealing, is the fact that the STCA can visualize the higher-order characteristics of traffic stream dynamics, e.g., the fans of rarefaction waves.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
