# Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles
## 5 Traffic Flow Models
### Microscopic Models
#### 5.2.3 Stimulus-Response Modeling  
Stimulus-response models are a significant component of car-following modeling, focusing particularly on how changes in a leader vehicle's velocity influence the behavior of the following vehicle. These models share similarities with safe-distance models but place a greater emphasis on the sources of changes in the leader's velocity and the subsequent reaction of the follower.  
The foundation of stimulus-response models was laid by [PERSON] et al. [156], who first developed a model where the acceleration of the following vehicle is proportional to the difference in velocity between the leader and the follower, with a time delay accounting for driver reactions. This model posits that the characteristics of the leader vehicle serve as the stimulus, directly influencing the acceleration behavior of the follower.  
This initial model was subsequently refined by [PERSON] et al. [157] and [PERSON] [158] and later summarized by [PERSON] et al. [161], leading to the well-known GHR (Gazis-Herman-Rothery) car-following model. The GHR model, in its most general form, can be expressed as follows:  
\[a(t)=cv^{m}(t)\frac{\Delta v(t-T)}{\Delta x^{l}(t-T)} \tag{21}\]  
where \(a\) and \(v\) are the acceleration and speed of the follower at time \(t\); \(\Delta x\) and \(\Delta v\) are the relative spacing and speeds, respectively, between the leader and follower, assessed at an earlier time (\(t-T\)); \(T\) is the driver reaction time; and \(m\), \(l\), and \(c\) are the constants. This model encapsulates the core idea of stimulus-response dynamics, where the follower's behavior is a direct response to changes in the leader's movement.  
However, as [PERSON] and [PERSON] [178] observed in their comprehensive review of stimulus-response models from 1958 to 1999, these models have been used less frequently in recent years due to inconsistent findings regarding parameter values. Their review highlighted the challenges in applying stimulus-response models across different traffic scenarios, leading to a shift in research focus.  
This shift gave rise to new directions in the car-following theory, such as the development of intelligent driver models [179; 180; 181; 182] and the optimal velocity model [183]. These models were eventually integrated into [PERSON]'s three-phase traffic theory [77; 184], which represents a more holistic approach to understanding traffic dynamics, incorporating elements from both traditional stimulus-response models and more advanced theories that account for the complexities of modern traffic systems.  
In summary, while stimulus-response models were foundational in the development of car-following theories, the evolution of traffic modeling has seen these models being supplemented and, in some cases, replaced by more comprehensive approaches. The relationships between these models and their successors highlight the progression of traffic flow theory from simple reactive models to more sophisticated frameworks that better capture the nuances of driver behaviors and traffic dynamics.