Delay Model of Start-Up Loss Time at Signalized Intersections: Distinguishing Human-Driven and Autonomous Vehicles

To address the travel delay caused by start-up lag in queued traffic at signalized inter-sections and fill the research gap of unseparated start-up loss characteristics between human-driven vehicles (HDVs) and autonomous vehicles (AVs), this study proposes an analytical start-up loss delay model applicable to both unsaturated and saturated traffic states. The model explicitly quantifies queue-length-dependent cascading propagation effects of start-up loss, and integrates vehicle type-specific parameters based on traffic queue theory and mixed traffic flow field observation data. Conventional models are limited by underestimated delay from neglecting platoon-level start-up loss propagation and failure to account for intrinsic HDV-AV start-up mechanism differences; to resolve these, we first distinguished the two vehicle types’ start-up behaviors (reaction time, acceleration, platoon coordination), then decoupled their start-up loss mechanisms and quantified their delay contributions via theoretical derivation, with validation against field test data and comparison with classical Webster and Clayton models. Field results revealed an order-of-magnitude difference in start-up response: HDVs had an average 2.05 s reaction time with large individual variability, while AVs maintained a stable 0.3–0.5 s response; HDV platoons reached saturated flow at the sixth vehicle, versus the third for AV platoons due to consistent acceleration and shorter headways. Model validation showed that under unsaturated conditions, red light duration significantly affects HDV delay, and the AV mix ratio is exponentially negatively correlated with additional delay. Under saturated conditions, green light duration increases start-up loss delay for both vehicle types, yet the growth rate of AVs (3.1–12.3%) is far lower than that of HDVs (18.2–67.5%), and arranging AVs in the leading position of mixed platoons can further reduce delay. The proposed model improves the accuracy of delay estimation in mixed HDV-AV traffic environments, and provides a theoretical basis for the optimized design of signal control strategies and the efficient management of intersection travel delay.