On the stability of a heterogeneous platoon-based traffic system with multiple anticipations in the presence of connected and automated vehicles

Connected and automated vehicles (CAVs) have attracted substantial research attention in heterogeneous traffic settings due to their inherent traffic-stabilizing characteristics. However, insufficient focus has been directed towards the heterogeneity in communication topologies of CAVs, particularly in the presence of human-driven vehicles (HDVs). Consequently, our comprehension of traffic stability in such heterogeneous environments remains constrained, overlooking crucial aspects such as CAV platooning and multi-anticipation controls. To address these gaps, this study presents a first attempt to extend the frequency-based characterizations of string stability, i.e., L_p norms, to the heterogeneous traffic of CAVs and HDVs operating in a multi-anticipation multi-platoon system. The proposed adaptive mode conversions and platooning under incomplete communication environments are also incorporated into research scenarios. Our contribution involves establishing a comprehensive modeling framework for analyzing the propagation of deviations within platoons amidst heterogeneous traffic. Particularly, we developed quantitative stability metrics for systems based on platooning dynamics by characterizing their transfer functions. Additionally, a comprehensive comparison was conducted among different stability characterizations and various multi-anticipation topologies of CAVs, with the commonly researched single-anticipation topology (predecessor-following) used as a baseline. The numerical results, utilizing specific models and calibrated parameters, demonstrated the significant superiority of multi-anticipation topologies over the single-anticipation one in ensuring head-to-tail stability. Moreover, the stricter condition of L_∞ stability compared to the L₂ stability was further refined with quantitative analysis in this study. As a result, this work expands the connotation of heterogeneity in the presence of CAVs and strengthens the comprehension of stability conditions in the heterogeneous traffic domain.