Stochastic capacity analysis for a distributed connected automated vehicle virtual car-following control strategy

Capacity analysis of the pure connected automated vehicle (CAV) traffic remains a challenging problem due to the high-dimensional factors involved in the control design. Especially, the communication loss and communication topology greatly impact the headway variation of CAVs and hence capacity with stochastic properties. This study provides a stochastic framework to mathematically derive multiple factors' impact including free-flow speed, control gains, communication loss, and traffic arrival pattern on the pure CAV traffic capacity based on a virtual car-following control strategy targeting a single-lane highway and merging section. To begin with, we first mathematically derive the stochastic capacity for a single-lane highway based on a multi-predecessor-based linear feedback and feedforward car-following model for generic stochastic communication loss models. For a further illustration, a detailed analysis is conducted based on a well-known Signal-to-Interference-plus-Noise Ratio (SINR) communication loss model. We then extend the derivation to a merging section by a virtual car-following concept considering traffic arrival pattern's stochasticity. Numerical sensitivity analyses have been conducted to systematically evaluate the impact of multiple factors mentioned. As the result indicated, the stochastic communication loss and traffic arrival pattern do have a significant impact on the pure CAV traffic capacity of the above scenarios.