Platooning is considered to be a very effective method for improving traffic efficiency, traffic safety and fuel economy under the connected and automated environment. The prerequisite for realizing these advantages is how to form a platoon without any collisions and how to maintain and optimize the car-following behavior after platoon formation. However, most of the existing studies focus on the platoon configuration and information transmission method, while only a few attempt to address the issue of platoon formation and optimization methods. To this end, this study proposes a novel platoon formation and optimization model combining graph theory and safety potential field (G-SPF) theory for connected and automated vehicles (CAVs) under different vehicle distributions. Compared to previous studies, we innovatively incorporate the concept of the safety potential field to better describe the actual driving risk of vehicles and ensure their absolute safety. A four-step platoon formation and optimization strategy is developed to achieve platoon preliminary formation and platoon driving optimization control. Three traffic scenarios with different CAVs distributions are designed to verify the effectiveness of our proposed platoon formation method based on G-SPF theory, and the simulation results indicate that a collision-free platoon can be formed in a short time. Additionally, the G-SPF-based platoon driving optimization control method is demonstrated by comparing it with two typical control strategies. Compared with the constant spacing and constant time headway control strategies, the simulation results show that our proposed method can improve the traffic capacity by approximately 48.8% and 26.6%, respectively.

Connected vehicle (CV) technologies are changing the form of traditional traffic models. In the CV driving environment, abundant and accurate information is available to vehicles, promoting the development of control strategies and models. Under these circumstances, this paper proposes a bidirectional vehicles information structure (BDVIS) by making use of the acceleration information of one preceding vehicle and one following vehicle to improve the car-following models. Then, we deduced the derived multiple vehicles information structure (DMVIS), including historical movement information of multiple vehicles, without the acceleration information. Next, the paper embeds the four kinds of basic car-following models into the framework to investigate the stability condition of two structures under the small perturbation of traffic flow and explored traffic response properties with different proportions of forward-looking or backward-looking terms. Under the open boundary condition, simulations on a single lane are conducted to validate the theoretical analysis. The results indicated that BDVIS and the DMVIS perform better than the original car-following model in improving the traffic flow stability, but that they have their own advantages for differently positioned vehicles in the platoon. Moreover, increasing the proportions of the preceding and following vehicles presents a benefit to stability, but if traffic is stable, an increase in any of the parameters would extend the influence time, which reveals that neither β₁ or β₂ is the biggest the best for the traffic.