# Exploring Safety-Stability Tradeoffs in Cooperative CAV Platoon Controls with Bidirectional Impacts
## 6 Conclusions  
This paper introduces a novel framework based on the concept of phase shift to investigate the influence of bidirectional information flow topology on platoons in terms of both stability and safety. This research sheds light on the effects of phase shift, particularly focusing on two specific cases: the in-phase (IP) effect and the opposite-phase (OP) effect. The IP effect contributes to enhanced platoon safety, while the OP effect significantly increases the risk of rear-end collisions. By employing the proposed framework, the research investigates the impact of different types of dynamics information of vehicles on platoons. Theoretical analyses pertaining to string stability and rear-end collision risk reveal that the integration of diverse information into the models does not universally yield benefits. Specifically, incorporating spacing information can concurrently improve both platoon safety and stability. However, the integration of velocity difference information can only enhance either safety or stability, but not both simultaneously. To validate these theoretical analyses, numerical experiments are conducted on both linear and non-linear car-following models, with simulation results confirming theoretical analyses. There are several potential directions for future research in this field. While this research focuses on uncovering the effects of phase shift on CAV platoons, it primarily  
Figure 21: Minimum TTC variation with respect to \(\gamma_{\
u}\) in the bidirectional IDM. Figure 20: Vehicle speed profile under the bidirectional IDM when \(\gamma_{\
u}=1.5:\) (**a**) 1 st-10 th vehicles, (**b**) 10 th–20 th vehicles. examines the IP and OP effects which represent two extreme cases of phase shift. Other communication factors, such as delay and packet loss, might result in different phase shift effects beyond those already examined. Undertaking a comprehensive investigation of phase shift effects would be a valuable direction to explore. Furthermore, while this research concentrates on the bidirectional communication topology, it is important to consider other communication topologies such as predecessor-leader following topology, multiple predecessor following topology, etc., as well. Exploring different communication architectures and their implications for platoon dynamics could yield valuable findings. In addition, the present study primarily evaluates the impacts of spacing and velocity difference information on CAV platoons. Nevertheless, incorporating other types of information, such as acceleration, traffic jerks, and electronic throttle opening angle, could provide a more comprehensive analysis of communication side impacts on CAV traffic. Moreover, our current analysis is limited to a one-dimensional perspective. Exploring the effects of lateral dynamics, such as left or right turns, on platoon performance represents a promising avenue for future research. Additionally, this research initially concentrated on introducing a theoretical framework. It is essential to expand the studies to include more comprehensive validation processes in subsequent research. Lastly, while this research mainly evaluates traffic performance by examining string stability and rear-end collision risk, there are other aspects that could be explored. Investigating the damping behavior and energy efficiency of CAV platoons, for example, would offer a more holistic assessment of the impacts of communication on CAV traffic. Y.W. : Methodology, Software, Validation, Formal analysis, Investigation, Writing--original draft, Visualization. X.H. : Supervision, Conceptualization, Methodology, Funding acquisition, Investigation, Resources, Writing--review and editing. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the U.S. National Science Foundation under Grant CMMI-2047793. Not applicable. The data that support the findings of this study are available on request from the corresponding author.