On the micro-to-macro limit for first-order traffic flow models on networks
On the micro-to-macro limit for first-order traffic flow models on networks
复制标题
网络一阶交通流模型的微观到宏观极限
DOI：
10.3934/nhm.2016002
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Smita Sahu
中科院分区：
文献类型：
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作者：
E. Cristiani;Smita Sahu
在车辆在单一道路上行驶的情况下，微观跟随领导者和宏观流体动力学交通流模型之间的联系已经得到很好的理解。相反，缺乏道路网络中的类似连接。这可能是由于网络上的宏观交通模型通常不适定，因为仅靠质量守恒不足以表征路口处的独特解决方案。这种模糊性使得找到微观模型的正确极限变得更加困难，而微观模型又可以在连接点附近以不同的方式定义。
在本文中，我们表明，随着车辆数量趋于无穷大，网络上一阶跟随领导者模型的自然扩展对应于[4,5]中引入的基于 LWR 的多路径模型。
Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic flow models are already well understood in the case of vehicles moving on a single road. Analogous connections in the case of road networks are instead lacking. This is probably due to the fact that macroscopic traffic models on networks are in general ill-posed, since the conservation of the mass is not sufficient alone to characterize a unique solution at junctions. This ambiguity makes more difficult to find the right limit of the microscopic model, which, in turn, can be defined in different ways near the junctions.
In this paper we show that a natural extension of the first-order follow-the-leader model on networks corresponds, as the number of vehicles tends to infinity, to the LWR-based multi-path model introduced in [4,5].