Modeling the clustering strength of connected autonomous vehicles and its impact on mixed traffic capacity

In a mixed traffic environment consisting of connected autonomous vehicles (CAVs) and human-driven vehicles (HVs), platooning intensity serves as a critical metric, quantifying the strength of CAV clustering, with inherent ramifications for traffic flow efficiency. While various definitions of platooning intensity are found in existing literature, many fall short in effectively capturing the strength of CAV clustering in mixed traffic. To address the gap, this study models the vehicle stream of mixed traffic on the single-lane road as a binary sequence and proposes the autocorrelation-based platooning intensity (API) metric. Through theoretical analysis, the proposed API is shown to be an effective indicator for measuring the clustering strength of CAVs. The probability distribution of API through fisher transformation is also derived. This study then moves on to formulate the capacity of mixed traffic, taking into account CAV penetration rate, API, and stochastic headway. Numerical verification of the estimated mixed traffic capacity reveals a negligible error (less than 1%) compared to simulated capacity. Marginal analysis confirms the validity of related propositions, notably that stronger CAV clustering does not always improve traffic capacity due to headway stochasticity. The outcome of this study contributes to the understanding of CAV platooning intensity and offers valuable insights for advancing mixed traffic modeling and management.