## 1 Introduction
However, by the progress of intelligent transportation systems (ITS), especially for vehicle communication and automatic cruise control (ACC) [25], a vehicle can acquire more information from infrastructures and other vehicles than before, so as to adjust the driving condition. Based on that, some scholars have tried to utilize these messages to build a more adaptable car-following model [26; 27; 28; 29; 30]. [PERSON] et al. found that under the guidance of the forecast information produced by ITS, traffic flow stability would be improved [26]. After analyzing the car-following data, [PERSON] et al. used the ACC strategy to consider relative velocity difference with memory and put forward an extended model to illustrate the transition of traffic congestion [27]. [PERSON] et al. observed that before updating the state information of the leading vehicle a driver will drive according to past memory [28]. Thus, they modified the full velocity difference (FVD) model from the perspective of the backward-looking effect and the memory of the driver. To enhance traffic flow efficiency, [PERSON] et al. established an enhanced cooperative car-following model by combining vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) communications [38]. They mainly focused on mitigating the impact of traffic waves stemming from some realistic communication limitations such as packet loss and probabilistic transmission delay. By adding the consensus control algorithm, the time-varying communication delays are taken into account in the improved model. [PERSON] et al. discussed how to use a car's location information in a V2V communication environment to calculate conflicts between two traffic flows at un-signalized intersections [37]. A modified car-following driving strategy taking into consideration the conflict gap was developed. Herein, we find that most variants of the FVD model only consider the feedback of the driver on adjacent preceding vehicle driving behavior. Explanation of the driver's reaction to the traffic status ahead in the real world is difficult. For example, at a signal-controlled intersection, even when the preceding vehicle is far enough, the driver will decelerate appropriately due to the queuing of the vehicles in front. Conversely, if the average headway of preceding vehicles is large and the velocity of the front cars is high, the driver will still maintain a tight car-following status, even if the space gap to the front vehicle is small. Meanwhile, the preceding vehicle's accelerations will influence the driver's operation. Additionally, when the preceding vehicle brakes, the red stop signal acts as a stimulus that causes the driver to decelerate. Hence, without being concerned about the communication transmission restrictions, this study aims to establish an improved FVD model via considering the traffic flow density in front as associated with the acceleration of the preceding vehicle. Based on the information of the equipped vehicles provided by the V2V communication system, this model can more realistically reflect the driver's feedback when grasping the road conditions ahead. In the next section, a modified version of the car-following model is developed. Section 3 describes linear stability and traffic flow development analyses. Section 4 discusses numerical simulation. Conclusions are drawn in Section 5.