## 2 Related Works
### CF Behavior Modeling  
In the past seventy years, consideration of developing and improving CF behavior modeling, which is one of the foremost fundamental driving behaviors, has been ongoing. Various mapping functions, ranging from simple linear equations to complex sets of nonlinear equations, have been proposed to better understand interactions between following vehicles and leading vehicles in non-free traffic flow. Four fundamental models have been proposed and well-developed and have been demonstrated to be reliable in simulation practices: stimulus-response logic, safety distance logic, desired measures logic, and perceptual-thresholds logic. While attempts based on machine learning techniques have been made, they are beyond the scope of this paper due to limitations in the analysis of human-driven mechanisms, which hinders further applications. First, the stimulus-response CF model is commonly recognized as the foremost classical CF interaction logic. This kind of model takes the interaction characteristics between the CF pair as a \"stimulus\", based on which the following vehicle makes \"responses\" accordingly. Commonly adopted factors that are considered as stimuli include the velocity of the leading vehicle, spacing between the CF pair, and the velocity difference [13]. Numerous upgraded and advanced forms of the original version proposed by [PERSON] et al. [14] have been proposed, such as models with memory [15], or acceleration and deceleration asymmetry [16]. Second, [PERSON] [17] initially defined the safety distance logic. The main hypothesis of this logic is that gaps between the CF pair are more linked to driver response rather than relative velocities. Nonlinear constructs were introduced to fulfil this logic by [PERSON] [18]. There is also a model proposed by [PERSON] [19] that increased the adaptability with several human behavioral parameters considered, such as reaction time and desired velocity, which has been the most popular in its category. Third, models based on the concept of the desired measures were established by [PERSON] [20]. Differing from the logics above, drivers are supposed to achieve expected values of CF characteristics such as time headway. Another famous and well-adopted model is the intelligent driver model (IDM). The IDM is proven to be most accurate and adaptable in reproducing the CF behaviors of drivers, and it remains accurate when applied to different driving styles or different traffic flow facilities [1]. Finally, to avoid neglecting the impact of human psychological reactions, a new concept based on \"perceptual threshold\" was proposed by [PERSON]. It is supposed that not all stimuli from CF pair interactions can lead to subjective operations from the following vehicle. The threshold of perception for a driver is defined as the minimum value of a stimulus that can be detected and elicit a response. Therefore, a dynamic threshold is used to distinguish between free-flow mode or CF mode, which is one of the innovations of this model [13]. In essence, it is one of the few models that can reproduce the following behavior from different driving phases or modes and divide and conquer for each mode. Then, researchers attempted to improve the accuracy of the Wiedemann model by changing the sub-model with the GHR model [21]. However, the driving modes division in these models is relatively subjective and lacks empirical verification. The thresholds that divide different CF modes, such as SDV, BX, SDX, etc. [22], were subjectively proposed based on the theoretical hypothesis, and it is difficult to find empirical evidence to prove that these modes are consistent with realistic driving modes in human CF behavior. Additionally, the Wiedemann model shows disadvantages in the comparison of CF models over the IDM with much more behavioral parameters [1], while the latter only contains free-flow mode and CF mode. Despite the approach of perceptual-thresholds logic, the aforementioned models are based on the assumption of a single mapping function for each driver.