Modeling and analysis of the platoon size of Connected Autonomous Vehicles in a mixed traffic environment

In a mixed traffic environment that consists of both Connected Autonomous Vehicles (CAVs) and Human-driven Vehicles (HVs), the platoon sizes of CAVs play a significant role in traffic flow analysis. However, the statistical properties of these platoon sizes have not been thoroughly addressed in existing research. This study aims to fill this critical gap by modeling CAV platoon sizes as a random variable, analyzing scenarios both with and without a Maximum Platoon Size (MPS) constraint. Specifically, the frequencies and corresponding probability distributions of CAV platoon sizes under these conditions are derived. Furthermore, the distribution derivations are extended by incorporating platooning willingness. Through numerical analysis, the results reveal that the proposed probability distributions align closely with numerical observations, demonstrating the consistency and reliability of the model. The study also explores the characteristics of these distributions, as well as the effects of the MPS constraint and platooning willingness. By examining the platooning behaviors in mixed traffic and providing analytical derivations for CAV platoon size probability distributions, this research lays a robust mathematical foundation for further analysis of mixed traffic dynamics, enhancing traffic management and efficiency in increasingly automated traffic environments.