Analysis of a multi-population kinetic model for traffic flow
Analysis of a multi-population kinetic model for traffic flow
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交通流多群体动力学模型分析
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
G. Visconti
中科院分区：
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作者：
G. Puppo;M. Semplice;A. Tosin;G. Visconti
在这项工作中，我们扩展了最近的一个动态交通模型[G.Puppo，M.Semplice，A.Tosin，和G.Visconi，Kine.雷拉特。模型，在出版社，2016]到一个以上的车辆类别的情况，每一种都有几个不同的微观特征。我们考虑了一个只有二元相互作用的类玻尔兹曼框架，这些相互作用发生在属于不同类别的车辆之间。我们的方法不同于[G.Puppo，M.Semplice，A.Tosin，和G.Visconi，Commun]中提出的多粒子动力学模型。数学课。科学，14：643-669,2016]因为这里我们假设速度空间是连续的，并且我们引入一个参数来描述车辆在相互作用后提高其速度所执行的物理速度跳跃。模型被离散化，以便从数值上研究得到的基本图的结构，并通过研究适定性来分析方程组。此外，我们还计算了离散化模型的平衡点，结果表明，当网格中的速度较小时，可以得到精确的渐近动力学分布。最后，我们引入了一种新的概率律来减弱交通流图中出现的容量急剧下降。
In this work we extend a recent kinetic traffic model [G. Puppo, M. Semplice, A. Tosin, and G. Visconti, Kinet. Relat. Models, in press, 2016] to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model proposed in [G. Puppo, M. Semplice, A. Tosin, and G. Visconti, Commun. Math. Sci., 14:643-669, 2016] because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic.