Macroscopic Traffic Modelling on the Impact of Road Surface Potholes: Development and Numerical Solution

In this paper, a second order hyperbolic traffic model is proposed to assess the impact of potholes on traffic evolution. The driver presumption to potholes considers the safe time headway, change in velocity and the changes in potholes width. Further, the traffic alignment is based on the driver reaction to potholes, distance headway and size of potholes. The changes in traffic evolution travel at or below traffic velocity. This rate of changes is impacted by the potholes size, driver reaction, distance headway, time headway and the changes in velocity distributions. Furthermore, the direction of travel during congestion is rearwards, while is in forward direction during smooth flow. The model proposed in this paper can be employed for traffic density below and beyond the critical density. The Gabriel et al. model considers a constant for driver presumptions and is more a fitting parameter, rather than a traffic parameter. This is an inappropriate methodology to employ driver presumptions in second order traffic systems. The Gabriel et al. traffic system is based on the uniform constant velocity for different road conditions, which characterizes traffic evolution unrealistically. The proposed and Gabriel et al. traffic models are assessed over a 4000 m road for changes in the width of a pothole. Both the Gabriel et al. and proposed traffic models are numerically implemented with the conservative scheme in Matlab. The discretization stability of both the models is enforced with the Courant, Friedrich and Levy (CFL) condition. With smaller width of the pothole, the changes in upstream traffic are minor, and the density evolution in forward direction is smoother. While, with larger width of the pothole, the density evolution is slower, resulting congestion in the upstream, and exists for longer period. Moreover, Segment Travel Time (STT) is assessed subject to various sizes of a pothole, and it is observed that the STT significantly increases with the increase in pothole size. Conversely, the Gabriel et al. model characterizes traffic inadequately subject to various sizes of the pothole. The density behavior with this model is almost uniform, thus limiting its performance. The simulation results showed that the traffic evolution with the proposed model is more appropriate than with the Gabriel et al. model.