# Enhancing Freeway Traffic Capacity: The Impact of Autonomous Vehicle Platooning Intensity
## 1 Introduction
How road traffic capacity will be improved with the maturity of CAV technology and the gradual increase in penetration rate represent the most important issues when discussing autonomous vehicles. The introduction of information derived or processed by emerging technologies like CAV implies new specifications and the calibration of classical transport user's behavioral models [25]. A few analytical models and formulations have been developed to study the impacts of the rise in the penetration rate of CAVs on the performance of traffic flow [9; 13; 23; 26; 27]. For example, Ref. [13] provides a general theoretical framework to show how traffic operational capacity will change with the introduction of CAVs, where the CAV penetration rate is taken into account as a major factor. The majority of those studies believe that a growth in MPR is beneficial. The longitudinal control models for CAVs have frequently been examined by researchers [8; 17; 21; 24; 28; 29; 30; 31; 32; 33]. The modeling of CAV behaviors often relies on the Intelligent Driver Model (IDM) and its variations. In a study by [8], a modeling framework was proposed that integrates three different car-following models to simulate interactions between vehicles, with the IDM specifically used for CAVs. Furthermore, [PERSON]. [28] utilized the IDM and its modified versions to create a platform for evaluating CAV performance. Longitudinal movements of CAVs are also commonly depicted using Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC). However, the suitability of the IDM for accurately representing CACC capabilities has been a topic of debate, as discussed by [17]. To address this, the authors developed a CACC vehicle behavior model based on empirical data that accurately represents real-world CACC platoons. Most of the existing studies mainly focus on the influence of the headway settings, MPRs, and car-following models, which are regarded as the most crucial factors to improve road capacity when considering CAVs. Beyond these factors, how CAVs and HVs are clustered or distributed also has a significant impact on the roadway capacity [27; 34; 35]. Consequently, another crucial factor, platoon intensity, which is not widely discussed, should not be ignored. A few studies focus on this point; Ref. [27] defined the concept of platoon intensity and quantified it with certain calibration formulae. However, in most studies, the factor of platoon intensity is regarded as an independent variable that is not affected by other factors. This paper takes this crucial factor together with the MPR into consideration when modeling heterogeneous traffic. Not only the influence of platoon intensity, but also the relationship between platooning intensity and MPR, is evaluated through both numerical analysis and experimental validation. The main contribution of this study is that it reveals the intrinsic relationship between MPR and platooning intensity, which has always been ignored by other studies. On this basis, an improved formula is proposed to calculate the maximum theoretical capacity of mixed flows, taking into account the platooning intensity of CAVs. The remaining sections of this paper are structured as follows. Section 2 presents the proposed theoretical model, providing a detailed explanation of its underlying principles and framework. In Section 3, a numerical analysis is conducted to assess the validity of the proposed theoretical model. The obtained results are compared with findings from the existing literature to evaluate the model's accuracy. Additionally, this section explores the potential relationship between MPR and platooning intensity. Section 4 introduces a case study designed to further validate the numerical analysis results. This case study utilizes a SUMO (version1.10.0) simulation-based approach to examine the maximum theoretical capacity under various CAV penetration rates and speeds. Finally, the paper concludes in the last section (Section 5), summarizing the key findings and contributions of the study.