道路交通网络建模与仿真的代数方法
An algebraic approach for modeling and simulation of road traffic networks
摘要：
本文提出了一种道路交通网络建模与仿真的代数方法。通过定义一组道路交通系统和适当的连接运营商在该集合中，我们表明，大型规则的道路网络可以很容易地建模和模拟。我们定义了基本的道路交通系统，然后将它们相互连接，得到更大的系统。对于交通建模，我们基于LWR一阶交通模型与分段线性基本交通图。这种选择允许用特定代数结构中的许多矩阵来表示任何交通系统。对于交叉口的交通控制，我们考虑了两种情况：交叉口控制的优先规则，和交叉口控制的交通灯。最后，对封闭规则网络上的交通进行了仿真，得到了两种交叉口控制情况下的宏观基本交通图。
英文摘要：
We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily modeled and simulated. We define elementary road traffic systems which we then connect to each other and obtain larger systems. For the traffic modeling, we base on the LWR first order traffic model with piecewise-linear fundamental traffic diagrams. This choice permits to represent any traffic system with a number of matrices in specific algebraic structures. For the traffic control on intersections, we consider two cases: intersections controlled with a priority rule, and intersections controlled with traffic lights. Finally, we simulate the traffic on closed regular networks, and derive the macroscopic fundamental traffic diagram under the two cases of intersection control.
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