Stability Analysis of Mixed-Autonomy Traffic with CAV Platoons using Two-class Aw-Rascle Model
DOI: 10.1109/cdc42340.2020.9304438
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Summary
This paper investigates the deterministic and stochastic stability of mixed-autonomy traffic comprising connected and autonomous vehicle (CAV) platoons and conventional human-driven vehicles on a freeway segment. Motivated by the need to understand how CAV platoons affect traffic congestion, stability, and throughput, the authors address the limitations of existing macroscopic models that fail to capture heterogeneous vehicle classes and stochastic arrival patterns. The study specifically examines the trade-offs between traffic stability and maximum flow rate under varying ratios of CAV penetration. The methodology employs a two-class Aw-Rascle (AR) partial differential equation (PDE) model to describe the evolution of densities and velocities for both vehicle classes. Class 1 represents regular vehicles, while Class 2 represents CAV platoons, characterized by larger occupied surface areas but slower equilibrium speeds. The authors linearize the 4×4 hyperbolic PDE model around spatially uniform steady states, identifying four characteristic speeds. Three speeds are always positive (downstream propagation), while the fourth can be negative in congested regimes, representing upstream propagation of velocity perturbations. To capture randomness in CAV arrival rates, the deterministic model is extended into a stochastic framework using a two-mode continuous-time Markov process. This process switches between two operational modes representing qualitatively distinct traffic dynamics: free flow and congestion. Stability analysis is conducted using Lyapunov approaches for both deterministic regimes and the Markov-switching system. The results demonstrate that traffic stability is heavily dependent on the regime defined by the fourth characteristic speed. In the free regime, where all characteristic speeds are positive, the system is always exponentially stable. In the congested regime, where the fourth speed is negative, stability is conditional and requires satisfying specific linear matrix inequalities (LMIs). The analysis reveals a fundamental trade-off: increasing the density of CAV platoons can shift the traffic state from an unstable congested regime to a stable free regime while maintaining the maximum equilibrium flow rate. However, if the system remains in the free regime but moves away from the maximum flow line, increasing CAV penetration reduces the total equilibrium flow rate. For the stochastic model, sufficient conditions for stochastic exponential stability are derived, ensuring that traffic densities and velocities remain bounded in the spatial L2 norm despite random switching between free and congested modes. The significance of this work lies in providing a rigorous PDE-based framework for analyzing mixed-autonomy traffic stability. It highlights that CAV platoons can act as stabilizing agents by mitigating the upstream propagation of disturbances that cause stop-and-go waves, albeit with potential throughput costs. The findings offer theoretical guidance for CAV platooning operations, suggesting that managing the ratio of CAVs can limit the negative effects of randomness and improve overall traffic stability. This contributes to the broader field of traffic control by integrating stochastic modeling with macroscopic PDEs to address the complexities of heterogeneous, mixed-autonomy environments.
Key finding
Increasing the penetration rate of slower CAV platoons can stabilize mixed-autonomy traffic by shifting it from a congested to a free-flow regime, but this stability improvement results in a reduction of the maximum equilibrium flow rate.
Methodology
modeling
Provenance
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|---|---|---|---|---|---|---|
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| verify | success | — | — | — | 2 | 2026-06-10 |
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