SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1377-1391, January 2020.
We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is unidirectional, and the dynamics of each vehicle is described by a follow-the-leader model. From a mathematical point of view, this amounts to defining a system of ODEs on an arbitrary network. A general existence and uniqueness result is provided, while priorities at junctions are shown to hinder the stability of solutions. We investigate the occurrence of the Braess paradox in a time-dependent setting within this model. The emergence of Nash equilibria in a nonstationary situation results in the appearance of Braess-type paradoxes, and this is supported by numerical simulations.

中文翻译：

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通用网络上车辆交通的微观建模

SIAM应用数学杂志，第80卷，第3期，第1377-1391页，2020年1月。
我们引入形式主义来处理道路网络上车辆交通的微观建模。每条道路上的交通都是单向的，每辆车的动态性由跟随者模型来描述。从数学角度来看，这相当于在任意网络上定义ODE系统。提供了一个普遍存在和唯一性的结果，而结点处的优先级却显示出会妨碍解决方案的稳定性。我们调查了Braess悖论在此模型中随时间变化的情况下的发生。非平稳状态下纳什均衡的出现导致Braess型悖论的出现，这得到了数值模拟的支持。