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.
翻译:我们在本篇文章中提出了一个模拟和模拟公路交通网络的代数法。我们通过界定一套公路交通系统和适当的搭配运营商,表明大型定期公路网络可以很容易地建模和模拟。我们定义了基本的公路交通系统,然后我们彼此连接并获得更大的系统。关于交通模式,我们以路运模式为基准,首先以小线基本交通图为基础。这种选择允许代表任何交通系统,在特定的代数结构中设置若干矩阵。关于交叉路口的交通控制,我们考虑了两个案例:由优先规则控制的交叉点,与交通灯的交叉点。最后,我们模拟封闭的定期网络上的交通,并在两个交叉控制的情况下得出宏观的基本交通图。