TY - JOUR
T1 - Limitations and Improvements of the Intelligent Driver Model (IDM)
AU - Albeaik, Saleh
AU - Bayen, Alexandre
AU - Chiri, Maria Teresa
AU - Gong, Xiaoqian
AU - Hayat, Amaury
AU - Kardous, Nicolas
AU - Keimer, Alexander
AU - McQuade, Sean T.
AU - Piccoli, Benedetto
AU - You, Yiling
N1 - Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics
PY - 2022
Y1 - 2022
N2 - 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 the presence of lane changing, on-ramps, and other network components, as it is the case for most commonly used microsimulators. 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.
AB - 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 the presence of lane changing, on-ramps, and other network components, as it is the case for most commonly used microsimulators. 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.
KW - IDM
KW - car-following model
KW - discontinuous ODEs
KW - existence and uniqueness of solutions of ODE
KW - intelligent driver model
KW - microscopic traffic modeling
KW - system of ODEs
KW - traffic modeling
KW - well-posedness of ODEs
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U2 - 10.1137/21M1406477
DO - 10.1137/21M1406477
M3 - Article
AN - SCOPUS:85134881091
SN - 1536-0040
VL - 21
SP - 1862
EP - 1892
JO - SIAM Journal on Applied Dynamical Systems
JF - SIAM Journal on Applied Dynamical Systems
IS - 3
ER -