Management strategy for the maximum platoon size of connected automated vehicles in a freeway lane: A mixed traffic capacity modeling approach

Platoon size of connected automated vehicles (CAVs) is crucial for influencing road traffic capacity. However, the maximum platoon size has dynamic feature under varying CAV penetration rates, rather than a fixed value adopted in previous studies. Additionally, connected vehicles (CVs), which are upgraded from human-driven vehicles (HVs) by installing vehicle-to-vehicle devices, have distinct capacity capability characteristic compared to CAVs and have received limited attention in the literature. By modeling capacity of mixed traffic including both CAV platoons and CVs, this paper presents a strategy for managing maximum CAV platoon size, providing insights to collaborative development of CAV platoons and CV upgrades to improve mixed traffic capacity. First, we define ten general spacing patterns in such a mixed traffic environment and analytically derive their probabilities using Markov chain model. Stochastic distribution of CAV platooning is considered in the derivation of pattern probabilities. We then develop an analytical model for exploring mixed traffic capacity by deriving the fundamental diagram. This capacity model allows us to numerically examine impact of various system factors and present the management strategy mentioned. Our results indicate that dynamically optimizing CAV maximum platoon size is primarily influenced by CAV penetration rate and stochastic platooning intensity, with only a weak correlation to CV proportion among all HVs. However, increasing CV proportion is beneficial for enhancing mixed traffic capacity under the management strategy of CAV platoons, particularly in scenarios with low CAV penetration rates. Thus, a collaborative approach to upgrading CVs and developing CAV platoons is essential for significantly improving mixed traffic capacity.