Limitations and Improvements of the Intelligent Driver Model (IDM)
Limitations and Improvements of the Intelligent Driver Model (IDM)
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DOI：
10.1137/21m1406477
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Saleh Albeaik;A. Bayen;M. Chiri;Xiaoqian Gong;Amaury Hayat;N. Kardous;Alexander Keimer;Sean T. McQuade
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作者：
Saleh Albeaik;A. Bayen;M. Chiri;Xiaoqian Gong;Amaury Hayat;N. Kardous;Alexander Keimer;Sean T. McQuade
.这篇文章分析了广泛使用的和著名的"智能驾驶员模型"（布里伊IDM），这是一个二阶车辆跟驰模型由一个系统的普通微分方程。虽然近年来对该模型进行了深入的研究，以正确地捕捉交通现象和驾驶员制动行为，但据我们所知，从未进行过严格的适定性研究。首先，它表明，对于一个特定类别的初始数据，车辆的速度成为负的，甚至发散到− ∞在有限的时间，这两个不可取的性质的汽车跟驰模型。然后提出了IDM的各种修改，以避免这种不适定性。模型的理论修正，而不是事后通过对代码实现的特别修改，允许更合理的数值实现和模型功能的保留。事实上，为了避免不一致并确保动态接近原始模型的动态，可能需要检查和清理大量输入数据，这可能会导致大规模模拟实际上不可能出现的情况。虽然适定性问题可能只发生在特定的初始数据中，但当分析不同的交通场景时，这可能会经常发生，特别是在存在车道变换、坡道和其他网络组件的情况下，因为这是最常用的微模拟器的情况。另一方面，它表明，适定性可以保证直接的改进，如通过稍微改变加速度，以防止速度成为负值。
. This contribution analyzes the widely used and well-known “intelligent driver model” (briefly IDM), which is a second order car-following model governed by a system of ordinary differential equations. Although this model was intensively studied in recent years for properly capturing traffic phenomena and driver braking behavior, a rigorous study of the well-posedness has, to our knowledge, never been performed. First it is shown that, for a specific class of initial data, the vehicles’ velocities become negative or even diverge to −∞ in finite time, both undesirable properties for a car-following model. Various modifications of the IDM are then proposed in order to avoid such ill-posedness. The theoretical remediation of the model, rather than post facto by ad-hoc modification of code implementations, allows a more sound numerical implementation and preservation of the model features. Indeed, to avoid inconsistencies and ensure dynamics close to the one of the original model, one may need to inspect and clean large input data, which may result in practically impossible scenarios for large-scale simulations. Although well-posedness issues might only occur for specific initial data, this may happen frequently when different traffic scenarios are analyzed, and especially in presence of lane-changing, on ramps and other network components as it is the case for most commonly used micro-simulators. On the other side, it is shown that well-posedness can be guaranteed by straightforward improvements, such as those obtained by slightly changing the acceleration to prevent the velocity from becoming negative.