# Limitations and Improvements of the Intelligent Driver Model (IDM)

arXiv: https://arxiv.org/abs/2104.02583 · HTML: https://mlsanity.com/paper/2104.02583/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2021.

## Built on by (most cited first, 17 of 17)

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- [The Integration of Prediction and Planning in Deep Learning Automated Driving Systems: A Review](https://mlsanity.com/paper/2308.05731/) (2023)
- [Machine Learning for Autonomous Vehicle's Trajectory Prediction: A comprehensive survey, Challenges, and Future Research Directions](https://mlsanity.com/paper/2307.07527/) (2023)
- [EnduRL: Enhancing Safety, Stability, and Efficiency of Mixed Traffic Under Real-World Perturbations Via Reinforcement Learning](https://mlsanity.com/paper/2311.12261/) (2023)
- [Car-Following Models: A Multidisciplinary Review](https://mlsanity.com/paper/2304.07143/) (2023)
- [CARL: Congestion-Aware Reinforcement Learning for Imitation-based Perturbations in Mixed Traffic Control](https://mlsanity.com/paper/2404.00796/) (2024)
- [Validity Learning on Failures: Mitigating the Distribution Shift in Autonomous Vehicle Planning](https://mlsanity.com/paper/2406.01544/) (2024)
- [Dynamic High-Order Control Barrier Functions with Diffuser for Safety-Critical Trajectory Planning at Signal-Free Intersections](https://mlsanity.com/paper/2412.00162/) (2024)
- [HAD-Gen: Human-like and Diverse Driving Behavior Modeling for Controllable Scenario Generation](https://mlsanity.com/paper/2503.15049/) (2025)
- [Reinforcement Learning Based Oscillation Dampening: Scaling up Single-Agent RL algorithms to a 100 AV highway field operational test](https://mlsanity.com/paper/2402.17050/) (2024)
- [Enabling the Evaluation of Driver Physiology Via Vehicle Dynamics](https://mlsanity.com/paper/2309.04078/) (2023)
- [PlanScope: Learning to Plan Within Decision Scope for Urban Autonomous Driving](https://mlsanity.com/paper/2411.00476/) (2024)
- [Control Analysis and Design for Autonomous Vehicles Subject to Imperfect AI-Based Perception](https://mlsanity.com/paper/2509.12137/) (2025)
- [Sparse Threats, Focused Defense: Criticality-Aware Robust Reinforcement Learning for Safe Autonomous Driving](https://mlsanity.com/paper/2601.01800/) (2026)
- [Bridging Network Fragmentation: A Semantic-Augmented DRL Framework for UAV-aided VANETs](https://mlsanity.com/paper/2603.18871/) (2026)
- [An Empirical Markov Chain Car-Following (MC-CF) Model](https://mlsanity.com/paper/2603.27909/) (2026)
- [Trust as a Field: A Macroscopic Representation for Vehicular Networks](https://mlsanity.com/paper/2608.18178/) (2026)

## Abstract (arXiv)

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 occur only 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.