Unveiling traffic capacity in the mixed HV and CAV environment: A theoretical approach with CAV clustering intensity

By integrating advanced communication and autonomous driving technologies, connected and autonomous vehicles (CAVs) are expected to have a shorter reaction time and drive in platoons to achieve a more compact safe time headway, and thus exhibit the great potential to increase road capacity. However, human-driven vehicles (HVs) and CAVs will coexist and share urban traffic infrastructure for a long transitional time, and the platoon size of CAVs is limited by technological constraints and safety concerns. These factors complicate the calculation and theoretical analysis of mixed traffic capacity. Unlike the fixed constant in a pure HV environment, traffic capacity in the mixed HV and CAV environment is a complex stochastic variable influenced by various factors, such as the CAV penetration rate, the maximum platoon size of CAVs, and the spatial distribution of heterogeneous vehicles in the mixed traffic flow. To provide a generalized methodology for calculating and analyzing mixed lane capacity, we propose an index named CAV clustering intensity. This index has a clear physical meaning and explicit expression, allowing for the quantitative characterization of the longitudinal distribution of heterogeneous vehicles without any simplified assumptions regarding car-following patterns and the spatial distribution of mixed traffic flow. Accordingly, a Markov chain model is established to theoretically derive an explicit expression for calculating mixed lane capacity, which is mathematically expressed as a multivariate function of CAV penetration rate, maximum platoon size, and CAV clustering intensity. The effect of all these factors on mixed lane capacity is explored by rigorously theoretical analysis. Then, the problem of calculating the upper and lower bounds of lane capacity in the yet-to-be-realized mixed traffic environment is equivalently transformed into a vehicle arrangement problem. Two linear programming models are established and theoretically derive the explicit mathematical expression of capacity bounds and the corresponding spatial distribution of mixed traffic flow in scenarios with unlimited and limited platoon sizes. Finally, the numerical characteristics (e.g., mean, variance, probability distribution) of stochastic lane capacity are also calculated to provide a more comprehensive understanding of its stochastic properties.