Impact of Driver Anticipation on Traffic at a Ramp in Foggy Conditions

A new macroscopic traffic model is proposed based on visibility distance and the time to collision (TTC) in foggy conditions. The TTC is obtained from real traffic data. It is shown that the proposed model is hyperbolic and has a well-posed solution. Further, it is string stable. The proposed and Payne–Witham (PW) models are implemented in MATLAB R2019b using the first-order upwind numerical scheme and evaluated over a 3000 m circular road with a ramp at 1500 m. The results show that the proposed model can effectively characterize traffic in poor visibility, while the PW model provides unrealistic results. Thus, the proposed model can be used to accurately predict traffic behavior and alleviate congestion in foggy conditions.