A Simple Analytical Model for Predicting Cooperative Ratio in Agreement-Seeking Cooperative Driving Automation with C-V2X Communication

Cooperative Driving Automation (CDA) has emerged as an active research area in recent years, categorized into four classes of operations with varying levels of cooperation as defined in the SAE J3216 standard. Among these, Class C CDA, referred to as Agreement-Seeking Cooperation (ASC), has received limited attention in literature. Unlike Cooperative Adaptive Cruise Control (CACC), which typically engages when lead vehicles are identified as cooperative and disagree under manual override or safety-critical conditions, ASC requires agents to exchange messages interactively to reach consensus on a proposed plan and its implementation. This necessitates more sophisticated communication and control designs, which in turn influences customized ASC efficiency. Previous work has examined, through simulation, the impact of three key parameters on ASC system performance: CDA message transmission frequency, Packet Drop Ratio (PDR), and Cooperation Duration Length (CDL). In this paper, we extend that investigation by conducting Hardwarein-the-Loop (HIL) experiments in a scenario-based simulation environment, integrating the ASC controller with vehicle-to-vehicle (V2V) communication enabled by PC5-based Cellular Vehicle-toEverything (C-V2X) radios. Using HIL test data, we derived a simple analytical model based on Pascal Distribution to predict the Cooperative Ratio (CR), which is a key index defined by cooperative time over the total scenario time. The model explores the fundamental mechanism of how transmission frequency, total trip time, instance CDA engagement probability and CDL collaboratively impact Cooperative Ratio. The validation of model with experimental data reports the relative error is less than 5% for scenarios with CDA message transmission frequency higher than 5 HZ. Furthermore, because the model is independent of specific control logic assumptions, it provides a practical tool for guiding the design of ASC communication protocols and control strategies.