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 - Funding Information:
∗Received by the editors March 22, 2021; accepted for publication (in revised form) by L. Billings October 1, 2021; published electronically July 21, 2022. https://doi.org/10.1137/21M1406477 Funding: This research was based on work supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under Vehicle Technologies Office award number CID DE-EE0008872. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the U.S. government. The work of the second author was supported by the National Science Foundation under grant CNS-1837244. The work of the ninth author was supported by the National Science Foundation under grant CNS-1837481. †Department of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, CA 94720 USA (albeaik@berkeley.edu). ‡Institute for Transportation Studies (ITS), University of California, Berkeley, Berkeley, CA 94720 USA (bayen@ berkeley.edu, keimer@berkeley.edu). §Department of Mathematics, Penn State University, University Park, PA 16802 USA (mxc6028@psu.edu). ¶School of Mathematical and Statistical Science, Arizona State University, Tempe, AZ 85281 USA (xiaoqian. gong@asu.edu). ∥Centre d’Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), Ecole des Ponts, 77455 Marne-la-Vallée, France (amaury.hayat@enpc.fr). #Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA 94720 USA (nicolas.kardous@berkeley.edu). ††Department of Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University, Camden, NJ 08103 USA (sean.mcquade@rutgers.edu, piccoli@camden.rutgers.edu). ‡‡Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720 USA (yiling.you@ berkeley.edu).
Funding Information:
This research was based on work supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under Vehicle Technologies Office award number CID DE-EE0008872. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the U.S. government. The work of the second author was supported by the National Science Foundation under grant CNS-1837244. The work of the ninth author was supported by the National Science Foundation under grant CNS-1837481.
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 -