Macroscopic Traffic-Flow Modelling Based on Gap-Filling Behavior of Heterogeneous Traffic

Traffic-flow modelling has been of prime interest to traffic engineers and planners since the mid-20th century. Most traffic-flow models were developed for the purpose of characterizing homogeneous traffic flow. Some of these models are extended to characterize the complex interactions involved in heterogeneous traffic flow. Existing heterogeneous traffic-flow models do not characterize the driver behavior leading to gap filling in heterogeneous traffic conditions. This study aimed at explaining the gap-filling behavior in heterogeneous traffic flow by using the effusion model of gas particles. The driver’s behavior leading to gap filling in heterogeneous traffic was characterized through developing analogies between the traffic flow and the Maxwell–Boltzmann equation for effusion of gases. This model was subsequently incorporated into the Payne–Whitham (PW) model by replacing the constant anticipation term. The proposed model was numerically approximated by using Roe’s scheme, and numerical simulation of the proposed model was then carried out by using MATLAB. The results of the proposed and PW models were therefore compared. It is concluded that the new model proposed in this study not only produces better results compared to the PW model, but also better captures the expected reality. The main difference between the behavior of the two models is that the effect of bottleneck in the density of traffic is propagated in the form of a shockwave travelling backwards in time in the new model, while the PW model does not exhibit this effect.