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.

中文翻译：

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混合交通环境下联网和自动驾驶车辆渗透率的不确定性建模

准确了解联网和自动驾驶车辆 (CAV) 的渗透率对于从混合交通向全面 CAV 部署过渡期间的有效控制应用至关重要。之前的研究主要集中在表征或控制具有固定 CAV 渗透率的混合流量。然而，实际上，即使 CAV 的市场份额保持不变，其在道路上的渗透率也有所不同。本研究提出了一个数学模型，在考虑这种可变性的同时估计 CAV 渗透率。我们提出了一种基于不确定性的渗透率估计模型来评估道路上 CAV 数量的变化。该模型利用概率修正随机游走方法来估计分布。为了增强混合交通流的真实感，我们使用改进的基于元胞自动机的混合交通流模型结合了真实的车辆制动和启动行为。仿真结果表明，我们基于不确定性的渗透率估计模型准确地描述了 CAV 数量并估计了混合交通流的变化，特别是在开放的圆形边界和入口匝道内。此外，我们展示了不确定性模型在现实世界中的实际适用性，展示了它们增强系统优化的潜力。