Micro- and Macroapproach to Modeling Relationship between Control and Stopped Delays at Signalized Intersections

Control delay, the most important measure of effectiveness at signalized intersections, is commonly estimated using analytical models due to the difficulty of field measurements. In analytical models, the uniform component of control delay is derived from an established ratio between control and stopped delays. The Highway Capacity Manual (HCM) delay model utilizes a unique stopped-to-control-delay ($D_s/D_c$) ratio of 0.76. In this paper, the modeling relationship between control and stopped delays is based on empirical data collected on 28 intersection approaches totaling 1,200 individual trajectories with stopped delay. Authors applied analysis on two different levels based on individual vehicle trajectories (microapproach) and on traffic flow (macroapproach). At the micro-level, the authors found a strong linear relationship between control and stopped delays, which exclusively depends on approach speed. It was also found that the average deceleration-acceleration delay of 12.8 s is greater than values cited in the literature. At the macro-level, it was found that the $D_s/D_c$ ratio varies from 0.49 to 0.86 depending on red time and approach speed. The authors concluded that unique $D_s/D_c$ ratio applied in the HCM delay model is not always appropriate for accurate delay estimation and suggested a modified model.