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Article Dans Une Revue SIAM Journal on Applied Dynamical Systems Année : 2022

Limitations and Improvements of the Intelligent Driver Model (IDM)

Saleh Albeaik
  • Fonction : Auteur
Alexandre Bayen
  • Fonction : Auteur
Maria Teresa Chiri
  • Fonction : Auteur
Xiaoqian Gong
  • Fonction : Auteur
Nicolas Kardous
  • Fonction : Auteur
Alexander Keimer
Sean Mcquade
  • Fonction : Auteur
Benedetto Piccoli
Yiling You
  • Fonction : Auteur

Résumé

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 \(-\infty\) 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 \textit{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 straight-forward improvements, such as those obtained by slightly changing the acceleration to prevent the velocity from becoming negative.

Dates et versions

hal-04360444 , version 1 (21-12-2023)

Identifiants

Citer

Saleh Albeaik, Alexandre Bayen, Maria Teresa Chiri, Xiaoqian Gong, Amaury Hayat, et al.. Limitations and Improvements of the Intelligent Driver Model (IDM). SIAM Journal on Applied Dynamical Systems, 2022, 21 (3), pp.1862-1892. ⟨10.1137/21M1406477⟩. ⟨hal-04360444⟩
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