# An Extended Car-Following Model Considering Generalized Preceding Vehicles in V2X Environment
## 1 Introduction  
With the development of urbanization and motorization, the number of vehicles continues to grow, and congestion has become one of the main problems existing in cities around the world. Due to the limitation of urban space, previous methods of reducing traffic jams, such as building more infrastructure, have been producing very little effect. Regarded as an effective technological approach to improve transportation efficiency and alleviate traffic congestion, the intelligent transportation system (ITS) has received increasing attention. As one of the most important parts of ITS, V2X technology, which is the general term for communication and information technologies enabling vehicles to connect to everything [1; 2], can significantly broaden the driver's information perception range, enhance the driver's information perception ability by enabling them to obtain the information about movement state of vehicles on the road. Compared with the ordinary traffic environment, driver's car-following and other driving behavior, as well as traffic flow of following vehicles, will show different characteristics in the V2X environment [3; 4; 5]. The impact of the information mentioned above on car-following behavior and traffic flow was explored by scholars via constructing car-followingmodels. [PERSON] [6] proposed an extended car-following model and explored the impact of the non-neighboring front vehicle position information. [PERSON] et al. [7] and [PERSON] et al. [8] respectively established a car-following model considering the headway of an arbitrary number of vehicles ahead in the current lane. Unlike [PERSON] believed that car-following behavior in the model was the result of multiple optimal velocity functions related to each headway, [PERSON] believed that car-following behavior was the result of one optimal velocity function related to multiple headways. [PERSON] et al. [9] further incorporated the desired following distance and explored the impact of this information by developing an improved car-following model. [PERSON] et al. [10] established an extended car-following model with consideration of the relative velocity of an arbitrary number of vehicles ahead. [PERSON] et al. [11] further considered drivers' reaction delay and extended the car-following model. Instead of drivers' reaction delay, [PERSON] et al. [12] further investigated velocity fluctuation feedback information. [PERSON] et al. [13] presented an improved car-following model based on both headway and relative velocity information of an arbitrary number of preceding vehicles. [PERSON] et al. [14] proposed an extended car-following model to concurrently study headway, relative velocity and acceleration information of an arbitrary number of vehicles ahead in the current lane. Compared with the motion state information of an arbitrary number of vehicles ahead in the current lane, drivers incline to pay more attention to the motion state of vehicles that are in their view. For vehicles outside the field of view, drivers tend to focus on their overall motion state instead of individual motion state. Based on this, [PERSON] et al. [15] established an extended car-following model considering headway of the front vehicle and the average velocity of an arbitrary number of vehicles ahead in the current lane. [PERSON] et al. [16], [PERSON] et al. [17] and [PERSON] et al. [18] presented modified car-following models to explore the information of average headway, average field velocity, the average desired velocity, respectively rather than than than the average velocity. Soon afterward, [PERSON] et al. [19] built an extended car-following model with consideration of average velocity and average desired velocity in the meantime. Results of the above research revealed that providing motion state information of vehicles ahead in the current line to drivers could assist them to optimize car-following behavior and thus enhance the stability of traffic flow.