Literature review of research progress on car following model

In the past several decades, the car-following model has attracted many experts and scholars from the fields of traffic engineering, computational physics, psychology and so on, these experts and scholars have carried on the thorough research and the exploration to it, causes the model analysis essential factor from simple to rich, from simple to complex. With the continuous improvement of the model, the improved car-following model is more and more in line with the actual traffic conditions. With the development of traffic technology, driver’s car-following behavior will change greatly, which is realized by developing and establishing ITS, driver information guidance system and vehicle automatic intelligent cruise system. Therefore, a lot of car-following models for specific problems have emerged, which is of great practical significance to the further study of car-following theory. In this paper, the research background and significance of car-following model are deeply discussed, the current research status and conclusions are comprehensively analyzed, and the future research direction in this field is prospected.


Research background and meaning
The rapid development of the social economy and science and technology in our country has accelerated the process of urbanization and raised people's living standards remarkably.However, this has also brought severe challenges to urban transportation.With the expansion of the urban scale and population, the number of motor vehicles is increasing rapidly, which leads to serious traffic congestion and frequent traffic accidents.These problems have become one of the bottlenecks that restrict the sustainable and healthy development of the national economy.
With the continuous development of the economy, the field of transportation is also facing a series of urgent problems to be solved.Road traffic is one of the important parts of the modern city, it is related to the normal work, study, and daily life of urban residents, directly affecting the safety of People's life and property and social stability and harmony.Improving the capacity of the road to ensure that the vehicle in the process of driving has a state of low resistance to ensure that people travel more conveniently and comfortably, there is an effective solution to the current traffic problems and promotes sustainable urban development.
Traditional macro-flow assessment methods mainly focus on the impact of flow, density, and other parameters on the total flow.Urban development leads to increasing traffic congestion, especially at road intersections.However, the macroscopic problems of similar problems limit further research on the causes of traffic congestion, vehicle diffusion, and interaction between vehicles.To solve these problems, a micro-model based on car-following behavior is proposed.
Car-following model is a kind of microscopic traffic flow model, which realizes the accurate control of traffic flow by regarding the vehicle as a decentralized influence factor.The car-following model consists of two parts: collision model and tracking control.With the development of tracking theory, we not only have a deeper understanding of the characteristics of vehicle flow but also successfully solve the problems of vehicle dynamics and macro-vehicle flow fluctuation, thus, the challenges which are difficult to deal with in the early stage of vehicle flow theory can be overcome.
To reduce the risk of traffic accidents such as rear-end collisions, the driver needs to adjust the speed of the vehicle in real-time to adapt to the moving state of the vehicle in front and behind, the drivers may lose full control of the vehicle when they are disturbed by other surrounded vehicles.When the continuous vehicle is in a non-free state, the car-following theory presents three remarkable characteristics [1], which are restriction, delay, and transmission.The car-following model uses a mathematical model to analyze and expound the characteristics of vehicle flow in a non-free driving state.It not only reveals the interaction between vehicles but also provides an effective method for the study of traffic flow, which is of great and far-reaching significance for theoretical research.
In the field of transportation engineering, the car-following theory and its model have been recognized by researchers.The main aim of studying vehicle speed control is to explore the nature of traffic flow and to provide a bridge for drivers' micro-behavior by analyzing the distance and speed between vehicles, so as to deal with the macro-phenomenon of traffic flow.The vehicle speed control model has been widely used in many fields, such as mini-traffic simulation, capability analysis, autonomous cruise control, and traffic safety evaluation [2,3].

Current status of international research
Reuschel has been studying car-following theory since the last century.In 1953, Pipes carried on the dynamics research to the car-following phenomenon, and summarized the research content into the classical car-following model.The theory mainly describes the driving behavior by using the change of car-following and the relative position between the person and the target.
In 1958, Chandler developed a General expression, the GM Model, to describe the relative speed, acceleration, and relative distance of the two cars.When the two types of vehicles accelerate at the same time, a new trend will emerge, that is, as the front-to-rear direction of the car changes and gradually increase the value of acceleration [4].
In the 1960s, with the development of cognitive psychology and visual perception theory, carfollowing behavior became more complex.Therefore, from the researchers' perspective, Michaels primarily considered the possibility of applying psychological theory to car-following behavior modeling.In his research, he found that at higher speeds, drivers have a strong perception of the road around them, which leads to a natural attentional mechanism called attentional bias.
In 1981, Gipps proposed two scenarios in the longitudinal model, one was the interaction of vehicles in the free-driving state, in which vehicles showed chasing or decelerating behavior.In the 1990s, a brand-new car-following model, which was composed of several differential equations, had a high degree of complexity and diversity [5].
With the development of intelligent transportation system (ITS) and modern detection technology [6], the car-following model in the ITS environment has become an important research field The focus of these studies is to explore the vehicle-vehicle interaction and coordination model in the"Vehicle-road Synergy" environment, to achieve a more efficient, and more collaborative driving experience.

Current status of domestic research
In 1988, the first highway in our country was built.And in the 1990s, the concept of rapid transit was introduced.Based on this, the research on the car-following situation of these two modes is so rare, and the research content is also relatively scattered.
Zhang Sanle and his team have studied the behavior characteristics of straight-through teams at intersections and proposed a car-following model suitable for this field.In addition, Duan and his colleagues proposed a car-following model that can adapt to the complex traffic environment.These research results lay a foundation for further research on driving characteristics under complex traffic conditions.
In 1996, Xu and other scholars studied the relationship between front and rear vehicle speed and the change of vehicle braking deceleration under the condition of single-lane car-following by using Newton's mechanical principle and established a safe distance model [7].Yang Da and others put forward a car-following model based on the optimal distance, which combined the stimulus-response model [8] with the optimal time distance rule to achieve a more efficient car-following process.
In 2010, some scholars including Chen Cheng-hui proposed a new car-following model.Based on the traditionally expected distance, this method modified the travel time interval between two adjacent lanes by adding an additional parameter, which made the system more stable.
With the rapid development of science and technology, the car-following model is moving in the direction of intelligent driverless, intelligent networks, and so on.

Conclusion
In 1950s, foreign countries began to study the branch of traffic flow based on car-following theory, and came to a lot of important research achievement.Relatively speaking, our domestic research launched late with mainly focusing on the theoretical level.Currently, the domestic car-following research mostly concentrates on the speed-flow relationship.According to the different mathematical properties, carfollowing behavior can be divided into two types: linear and nonlinear [9].
According to the present research progress, the car-following model contains multiple types as shown in figure 1. Hereby we choose some important and widely sued car-following models to be analyzed in this paper.For some typical car-following models, a detailed comparison is given in Table 1 [1].The car-following model has developed for decades, and the exploration of these classical models prove the innovation and advancement of this field.These models are mainly used to predict the movement of traffic flow through studying drivers' reaction process, and then create plural traffic control methods that based on these models.However, due to the tendency and limitations of these abundant models, the applicability of them is limited for dealing with complex real traffic flow.Therefore,it is important to research the modification and improvement of the existing car-following models.In addition, considering the diversity of traffic flow characteristics both domestically and overseas, a widely accepted vehicle following model is still not found.

Research prospect
The research goal of car-following model is to integrate its micro-and macro-level with the real traffic characteristics to achieve more accurate matching effect.As the increase of traffic flow simulation and practical demands, vehicle-following problems have been concentrated much than before.In order to improve the authenticity of and the quality of car-following data, our researchers need to pay attention to multi-objective decision-making and improve the model structure.

To achieve a more comprehensive and multi-dimensional effect, it is necessary to integrate various modeling theories
For the research of car-following behavior modeling, the trend of comprehensive development is more and more obvious [10].Concerning the industrial theories, car-following distance and speed are the most basic and most important two parameters, they have a great impact on driving safety.In order to construct a model that meets different requirements, it is necessary to integrate knowledge from different aspects since the complex characteristics of car-following behavior need to be deeply explored and understood.At present, there are a lot of reports about car-following mechanism, algorithm design and application.However, for some specific problems, such as the drivers' control modes and road conditions, the systematic solution has not been formed and created.

Coordination and unity among people, vehicles, roads and environmental systems are indispensable
In the traffic network, the interaction of people, cars, roads and the environment form an intricate system.For the study of car-following model, any link in the system is very important, because they directly determine the stability and reliability of the system.In different traffic situations, various environmental factors will have a great impact on the system.
Researchers have to comprehensively concern about the impacts on car-following system that brought by different environment in the analysis of car-following model, with considering the influential factors such as the external environment of the vehicle, the dynamic information of the vehicle and the attributes of the driver to ensure the stability and reliability of the car-following model.Through analyzing and optimizing traffic flow, the drivers can evaluate the traffic information and make travel strategies.

For car-following model, its practicability and revisability are very important
The differences in researching car-following model are very apparent between our country and other foreign countries.In specific, the domestic research focuses on the theoretical aspects, while the foreign research focuses on the application.Because of the obvious differences between our country and foreign countries in vehicle dynamic characteristics, traffic composition and driver behavior, the research object of car-following model presents the diversification tendency.
At present, there exists separately strengths and weaknesses of the common car-following models.Since they have no convertibility, the actual traffic flow simulation results are difficult to be accurately predicted.Furthermore, no matter it is domestic or international model, the traffic flow simulation restricts the generality and applicability of the model to some extent, which the calculation results can not fully reflect the actual situation.In practice, the calibration and verification process of these models have some defects, which need to be regulated to improve their accuracy and reliability.

Figure 1 .
Figure 1. 1 car-following model classification under different modeling ideas.

Table 1 .
Comparison of classical car-following models.