Uncertainty modeling of connected and automated vehicle penetration rate under mixed traffic environment

Accurate knowledge of the penetration rate of connected and automated vehicles (CAVs) is crucial for effective control applications during the transition from mixed traffic to full CAV deployment. Previous studies have focused on characterizing or controlling mixed traffic with a fixed CAV penetration rate. However, in reality, the on-road penetration rate of CAVs varies, even if their market share remains constant. This study presents a mathematical model that estimates the CAV penetration rate while considering this variability. We propose an uncertainty-based penetration rate estimation model to assess the variability of CAV numbers on the road. This model utilizes a probabilistic modified random walk approach to estimate the distribution. To enhance the realism of mixed traffic flow, we incorporate realistic vehicle braking and starting behaviors using an improved cellular automata-based mixed traffic flow model. Simulation results demonstrate that our uncertainty-based penetration rate estimation model accurately describes CAV numbers and estimates the variability in mixed traffic flow, specifically within opened circular boundaries and on-ramps. Moreover, we demonstrate the practical applicability of the uncertainty models in real-world situations, showcasing their potential to enhance system optimizations.