A macroscopic traffic flow model with gap-controlled driver response and adaptive reaction dynamics

Abstract

Macroscopic traffic flow models play a critical role in analysing and predicting large-scale traffic behaviour. The Payne-Whitham (PW) model has provided a foundational framework in this domain, yet its assumption of instantaneous driver response and fixed desired velocity limits its ability to capture the nuances of real-world traffic dynamics. This paper presents a new macroscopic traffic flow model that extends the PW formulation by integrating gap-controlled driver response and adaptive relaxation behaviour based on forward distance headway. The proposed model modifies the desired velocity and acceleration components to represent spacing-dependent velocity adaptation and relaxation behaviour, thereby enabling a more realistic simulation of flow evolution under varying traffic densities while representing spacing-dependent driver adaptation at the macroscopic level. To assess the model’s effectiveness, simulations were conducted on a 500 m closed-loop roadway containing 50 identical vehicles and an inactive bottleneck. Results demonstrate improved stability, smoother traffic wave propagation, and reduced artificial congestion formations compared to the baseline PW model. These outcomes demonstrate the potential of incorporating gap-controlled driver response and adaptive reaction dynamics to improve numerical stability and produce more physically reasonable traffic evolution under the tested simulation conditions. The findings support further investigation of the proposed formulation through empirical calibration and validation using observed traffic data.