# A New Driver Model Based on Driver Response
## 1 Introduction  
Interest in urban traffic modelling has increased in recent years due to the prevalence of congestion, which is a pressing social and economic issue, particularly in developing countries [1]. High density traffic results in slow-moving vehicles and small distances between vehicles. This increases interactions between vehicles and thus the probability of accidents [2]. As urban populations increase, so does the number of vehicles. The number of vehicles has grown from 580 million in 1990 to 816 million in 2010 [3]. The number of vehicles is estimated to reach nearly 3 billion by 2040 [4]. Large numbers of vehicles on the roads result in long traffic queues which dissipate slowly, i.e., traffic takes longer to attain a smooth flow. Traffic queues occur after the flow reaches a maximum. The velocity when the flow is maximum is called the critical velocity and corresponds to the maximum density. Beyond the maximum flow, traffic velocity reduces, and congestion develops. Effective traffic forecasting and management strategies are required to mitigate traffic problems such as congestion and improve road infrastructure utilization [5]. This requires realistic traffic prediction using traffic flow models [6, 7, 8]. The traffic flow is affected by the distance between vehicles and the time required to align to forward conditions. These factors affectdriver response, resulting in velocity variations. Thus, they should be incorporated into traffic models to characterize traffic behaviour accurately and realistically. Three types of models have been used to characterize traffic flow, microscopic, macroscopic, and mesoscopic. Microscopic models consider individual vehicle behaviour and are often based on driver physical and psychological responses [9]. They employ vehicle parameters such as position, velocity, and time and distance headways [10]. Microscopic models are used to predict vehicle dynamics. Macroscopic models deal with aggregate traffic behaviour and are used to determine average density, velocity, and flow [11]. Mesoscopic models take into account both individual and combined vehicle behaviour [12], so vehicles are characterized both individually and as a group. The first microscopic traffic model was proposed by [PERSON] et al. [13]. This model considers driver response to forward vehicles based on the velocity difference. However, it ignores changes in driver behaviour due to traffic conditions; it assumes that in a string of vehicles, a driver adjusts to the speed of forward vehicles with a constant delay of 1.3 s, which is unrealistic and does not follow traffic physics. [PERSON] [14] proposed a microscopic traffic flow model that characterized vehicle behaviour in dense traffic. The distance headway is covered by vehicles while aligning to forward conditions. This is the distance between two consecutive vehicles. In this model, velocity depends on the distance headway. A larger distance headway means a lower traffic density and hence a greater velocity. However, this relationship between velocity and density can result in excessive acceleration, which is unsafe and therefore unrealistic [15]. However, this model was the first to include the time required to align to forward conditions [16]. [PERSON] further suggested that the time to align to forward conditions is a constant [17], but this ignores the differences in driver behaviour. [PERSON] et al. [18] proposed an improvement to the [PERSON] model but neglected the effects of velocity differences resulting in unstable behaviour. Moreover, deviations from the equilibrium velocity can result in high acceleration and deceleration, which is unrealistic. This is because density dependent traffic conditions are not considered. In reality, traffic adjustment is slow when the density is high and quick when the density is low. Further, a constant driver response is employed for all conditions so differences in driver behaviour are ignored. This model is based on data dependent constants, which is not a realistic approach for traffic characterization.