Limitations and Improvements of the Intelligent Driver Model (IDM)

Saleh Albeaik, Alexandre Bayen, Maria Teresa Chiri, Xiaoqian Gong, Amaury Hayat, Nicolas Kardous, Alexander Keimer, Sean T. McQuade, Benedetto Piccoli, Yiling You

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1862-1892
Number of pages31
JournalSIAM Journal on Applied Dynamical Systems
Issue number3
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation


  • IDM
  • car-following model
  • discontinuous ODEs
  • existence and uniqueness of solutions of ODE
  • intelligent driver model
  • microscopic traffic modeling
  • system of ODEs
  • traffic modeling
  • well-posedness of ODEs


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