Delay-aware information flow topology design for mixed traffic stability: A unified analysis framework with communication constraints

The stability of mixed traffic composed of connected and automated vehicles (CAVs) and human-driven vehicles (HDVs) is fundamentally limited by communication imperfections such as delay and packet loss. Although various aspects of mixed traffic control have been studied, prior work typically considers information flow topology, platoon organization, and communication delay in isolation, leaving their combined effects insufficiently understood. To address this gap, we propose a unified analytical framework that explicitly links these factors to mixed traffic string stability. The framework decomposes traffic flow into three probabilistic subsystems: independent HDVs, independent CAVs, and mixed platoons. The interactions are governed by three representative information flow topologies: Predecessor Following (PF), Multi-Predecessor Following (MPF), and Multi-Successor Leading (MSL). Closed-form transfer functions are derived to quantify head-to-tail stability margins under heterogeneous vehicle dynamics and finite communication delays. Analytical derivations and large-scale simulations reveal distinct performance regimes: (i) Under low delay conditions, MSL achieves superior stability relative to PF; (ii) Beyond this threshold, MSL experiences abrupt performance collapse due to actuator saturation and backward information amplification; and (iii) MPF maintains smoother degradation, offering better robustness at moderate and high delays. Additional analyses on non-uniform CAV distributions, platoon size, and stochastic link failures confirm the generality of these trade offs. The results establish fundamental delay-dependent boundaries for mixed traffic control and provide actionable design guidelines for topology selection and platoon management under realistic communication constraints.