Symmetry Breaking in Car-Following Dynamics: Suppressing Traffic Oscillations via Asymmetric Dynamic Delays

Accurately describing driver response mechanisms is fundamental to microscopic traffic modeling. Traditional car-following models typically assume a fixed reaction time, implying a temporal symmetry where drivers exhibit identical response characteristics during acceleration and deceleration. To address this limitation, this paper proposes a Delay Adaptive Car-following Model that incorporates an asymmetric dynamic delay function to capture the symmetry breaking in driving behavior. Calibrated using empirical trajectory data from the Next Generation Simulation program, the proposed model demonstrates superior accuracy over the conventional Full Velocity Difference Model by effectively reproducing the realistic phenomenon of sluggish acceleration and agile deceleration. Linear stability analysis and numerical simulations reveal that, unlike fixed symmetric delays which often induce instability, the asymmetric dynamic delay acts as a self-adaptive damper. This mechanism suppresses the amplification of disturbances and prevents the formation of stop-and-go waves. The results confirm that incorporating temporal symmetry breaking into delay mechanisms significantly enhances the robustness of traffic flow against oscillations.