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首页> 外文期刊>Discrete and continuous dynamical systems▼hSeries S >A JUSTIFICATION OF A LWR MODEL BASED ON A FOLLOW THE LEADER DESCRIPTION
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A JUSTIFICATION OF A LWR MODEL BASED ON A FOLLOW THE LEADER DESCRIPTION

机译：基于跟随者描述的LWR模型的证明

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摘要

We investigate the correlations between a macroscopic Lighthill-Whitham and Richards model and a microscopic follow-the-leader model for traffic flow. We prove that the microscopic model tends to the macroscopic one in a sort of kinetic limit, i.e. as the number of individuals tends to infinity, keeping the total mass fixed. Based on this convergence result, we approximately compute the solutions to a conservation law by means of the integration of an ordinary differential system. Prom the numerical point of view, the limiting procedure is then extended to the case of several populations, referring to the macroscopic model in and to the natural multi-population analogue of the microscopic one.
机译：我们研究了宏观的Lighthill-Whitham和Richards模型与微观的跟随领导者流量模型之间的相关性。我们证明微观模型在某种动力学极限中趋向于宏观模型，即随着个体数量趋于无穷大而使总质量固定不变。基于此收敛结果，我们通过整合一个常微分系统来近似计算守恒律的解。从数字的角度出发，然后将限制程序扩展到几个种群的情况，参考微观模型中的宏观模型以及微观种群的自然多种群类似物。

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