A Comparative Study of Oscillatory Perturbations in Car-Following Models

TL;DR

The paper tackles platoon stability under oscillatory disturbances by benchmarking four car-following models—OVM, IDM, GMM, and CACC—under Type I lead-vehicle perturbations and varying communication delays up to $\tau = 1.5$ s. It develops a unified mathematical and experimental framework, deriving string-stability conditions for each model and validating them with continuous perturbations (and additional discrete perturbations in the appendix). Key findings show CACC generally provides the strongest disturbance attenuation, IDM offers robust performance without V2V, while OVM and GMM are more sensitive to delays and require careful parameterization. The results offer actionable guidance for designing resilient platooning systems in mixed-traffic scenarios and set a benchmark for cross-model evaluations in future work.

Abstract

As connected and autonomous vehicles become more widespread, platooning has emerged as a key strategy to improve road capacity, reduce fuel consumption, and enhance traffic flow. However, the benefits of platoons strongly depend on their ability to maintain stability. Instability can lead to unsafe spacing and increased energy usage. In this work, we study platoon instability and analyze the root cause of its occurrence, as well as its impacts on the following vehicle. To achieve this, we propose a comparative study between different car-following models such as the Intelligent Driver Model (IDM), the Optimal Velocity Model (OVM), the General Motors Model (GMM), and the Cooperative Adaptive Cruise Control (CACC). In our approach, we introduce a disruption in the model by varying the velocity of the leading vehicle to visualize the behavior of the following vehicles. To evaluate the dynamic response of each model, we introduce controlled perturbations in the velocity of the leading vehicle, specifically, sinusoidal oscillations and discrete velocity changes. The resulting vehicle trajectories and variations in inter-vehicle spacing are analyzed to assess the robustness of each model to disturbance propagation. The findings offer insight into model sensitivity, stability characteristics, and implications for designing resilient platooning control strategies.

Figures (28)

• Figure 1: Response of the car-following model for different damping ratios $\xi_n$.
• Figure 2: Stability Map of IDM-based Platoon Dynamics in $(\Delta v, T)$ Space
• Figure 3: Stability Map of OVM-based Platoon Dynamics in $(\Delta x^*, \alpha)$ Space
• Figure 4: Stability Map of GMM-based Platoon Dynamics in $(\Delta x^*, \alpha)$ Space
• Figure 5: Stability Map of CACC-based Platoon Dynamics in $(k_v, k_a)$ Space