Mixed connected autonomous and human-driven vehicular traffic: Single-lane stochastic capacity modeling by incorporating heterogeneous and random headways

Capacity improvement has been widely recognized as one of the major benefits brought by the emerging connected and autonomous vehicle (CAV) technology, as CAVs are able to maintain shorter headways in the traffic stream. Nevertheless, the penetration of CAVs also increases the heterogeneity of headway configuration and raises additional challenges in modeling the traffic capacity. This study aims to model the stochasticity of the single-lane highway capacity for the mixed traffic consisting of both CAVs and human-driven vehicles (HVs), with consideration of heterogeneity (i.e., distinctness of headway types) and randomness (i.e., variability within each type of headway) of headways in the mixed traffic. To this end, we propose a unified analytical approach based on the phase-type distributions, considering the effects of CAV platooning and two kinds of conservative driving modes. Concretely, we model the mixed traffic fleet as a platooned arrival process, featured by three components including the vehicular platoon size distribution, the intra-platoon headway distribution, and the inter-platoon headway distribution. These types of distributions are formulated in phase-type form (PH-distribution), and then coupled together to develop a Markovian arrival process. Upon exploiting the statistical properties of the developed Markovian arrival process, we analytically derive the mean and variance of single-lane capacity under mixed traffic conditions. The PH-distributions of headways are calibrated using real-world vehicle trajectory data, and Monte Carlo simulations are performed to validate the proposed approach. Numerical analyses are carried out to examine the impact of traffic conditions on the stochasticity. To demonstrate the applicability of the proposed methodology, we extend the scenario to a two-lane road and conduct reliability-based lane policy analysis under different CAV penetration rates and risk-averse attitudes of the road manager. Numerical results indicate that optimal lane policies with reliability considered differ substantially from those in the risk-neutral case.