# A Microscopic Traffic Model Considering Driver Reaction and Sensitivity
## 1 Introduction  
Traffic models are important for vehicle flow characterization [1]. They are used to develop traffic forecasting and control strategies and improve road infrastructure utilization to mitigate congestion [2; 3; 4]. During congestion, stop and go waves cause drivers to vary their speed, which creates poor traffic dynamics [5; 6]. The distances between vehicles and the time required to adjust (align) to conditions ahead affect driver response and can result in significant variations in traffic flow [7]. Time headway, \(\tau\), is the time required to adjust to traffic conditions ahead, and the distance headway is traversed during \(\tau\)[8]. A driver responds slowly with a large distance headway and quickly with a small distance headway [9]. Furthermore, driver response is affected by sensitivity, which is proportional to the change in velocity [9]. Since driver response is not the same for all traffic conditions, it should be considered in a model for accurate and realistic traffic characterization. Three categories of models have been used for traffic flow: microscopic, macroscopic, and mesoscopic. Microscopic models are used to study individual vehicle behavior and employ parameters such as velocity, position, time, and distance headway. They are often based on driver physiological and psychological responses [10] and are employed to predict vehicle dynamics [11; 12; 13]. Macroscopic models are used to study aggregate traffic behavior. Mesoscopic models blend microscopic and macroscopic models and typically involve probability distributions [14]. [PERSON] et al. [15] introduced a microscopic model that considers how drivers respond to forward vehicles using velocity differences. However, this model neglects changes indriver behavior due to traffic conditions. Drivers adjust their speed to forward vehicles with a constant delay of 1.30 s, which can result in poor traffic behavior. [PERSON] [16] developed a microscopic model that characterizes traffic flow during congestion. In this model, velocity is dependent on the distance headway. A larger distance headway reduces congestion so the velocity increases. However, a larger change in velocity results in excessive acceleration, which is not realistic [17]. [PERSON] et al. [18] proposed an improvement to the [PERSON] model, but it ignores velocity differences, which can lead to instability. The equilibrium velocity distribution is density-dependent so the velocity decreases with increasing density. However, deviations from this distribution lead to uniform acceleration, which is unrealistic. Furthermore, driver behavior is the same for all conditions, which does not follow traffic physics. [PERSON] [19] developed a model using regression, but it has many parameters so the complexity is high. [PERSON] and [PERSON] [20] proposed a model that employs velocity differences to characterize velocity and time headway during congestion, but acceleration can be unrealistic. [PERSON] [21] created a model that considers acceleration and driver behavior, but the accuracy is limited to a narrow set of parameters. [PERSON], [PERSON], and [PERSON] [17] developed the Intelligent Driver (ID) model, which incorporates driver reaction and takes into account the velocity and distance headway of preceding vehicles [22; 23; 24]. A limitation of this model is that it employs a fixed acceleration exponent so driver behavior is not considered. This can produce unrealistic results. The ID model was modified in [25] to incorporate driver intent by considering deceleration at intersections. The safe distance between vehicles with the ID model is small at high velocities, which can result in accidents when employed in applications such as Adaptive Cruise Control (ACC). This distance has been adjusted using velocity-based parameters [26]. The ID model has been used to characterize the car-following behavior and stability of Connected and Autonomous Vehicles (CAVs) [27; 28]. However, it fails to capture the characteristics of CAVs in real traffic environments [29].