# Evaluating the Effect of Road Surface Potholes Using a Microscopic Traffic Model
## 1 Introduction  
Road surfaces develop cracks and holes over time which lead to the formation of potholes [1]. Potholes are an important factor in road networks, particularly in developing countries. They affect the smooth flow of traffic and cause discomfort and steering misalignment [2]. Potholes are formed when water penetrates cracks in the road surface commonly caused by wear. This is exacerbated by extreme weather conditions, heavy traffic, and poor drainage [1]. Potholes cause traffic delays and accidents [3]. Thus, it is important to consider the impact of potholes on traffic flow. Potholes cause loss of control and lead to accidents. In 2021, potholes accounted for 0.8% of road accidents resulting in 1.4% of fatalities and 0.6% of injuries [4]. Road surface irregularities have been shown to reduce vehicle speeds by 55% and increase emissions by 2.49% [5]. The Canadian Automobile Association (CAA) reported that potholes increase operating costs by 3 billion dollars annually [6]. In addition, poor road conditions lead to congestion and driver frustration which can result in dangerous driving behavior [7]. Realistic traffic flow models are needed to alleviate these problems. Traffic models can be categorized as microscopic, macroscopic, or mesoscopic. Microscopic models consider individual vehicle behavior and employ parameters such as position, velocity, and time and distance headways [8; 9]. They often incorporate driver psychological and physical responses [10] and are used to predict vehicle dynamics [11]. The first microscopic models were developed by [PERSON] [12] and [PERSON] [13] but cannot accurately characterize traffic flow. Later, [PERSON] [14] created a model based on driver behavior in congested traffic. In this model, a larger distance headway results in higher velocity, and this headway is small during congestion. However, it can produce excessive acceleration which is not realistic [15]. [PERSON] et al. [16] developed a model according to the equilibrium velocity distribution based on density. With this model, a decrease in velocity results in a larger density. However, deviations from this distribution lead to uniformacceleration, which is unrealistic. In addition, traffic behavior can be unstable because velocity differences are not taken into account [17]. [PERSON] and [PERSON] [18] proposed a model which employs velocity differences. However, it only considers aggressive driver behavior as acceleration occurs over a short time. [PERSON] [19] characterized traffic based on driver response but the resulting model is only accurate for a small range of parameters [11]. [PERSON] et al. [15] developed a car following model commonly known as the intelligent driver (ID) model. It can better characterize traffic than previous models [20; 21; 22] as it incorporates practical traffic parameters [11]. Driver behavior is based on the distance headway and velocity of leading vehicles [23; 24; 25]. However, an acceleration exponent is employed which does not capture traffic dynamics, leading to unrealistic behavior. The ID model was improved by incorporating driver reaction to leading vehicles [26], driver safety [27], and the velocity at intersections [28]. However, the velocity can be high when the distance between vehicles is small which can result in accidents. The PTV Vissum model [29] uses field data from eight intersections. Simulated and observed conflicts were employed to determine suitable thresholds for the time to collision. The relationship between simulated and observed conflicts was confirmed in [29]. The accuracy of the PTV Vissum model and Surrogate Safety Assessment Model (SSAM) in estimating pedestrian-vehicle conflicts at signalized intersections was examined in [30]. In addition, partial Crossover Displaced Left-turn intersection (XDL) versus full XDL designs were considered in [31] to optimize intersection control. This resulted in improved capacity, reduced delays, and smaller queues.