´??´??´??´??´??This paper describe how saturation flow rates are important in transportation engineering because they underlie current methodologies for estimating roadway intersection capacities, for setting traffic signal timings and for evaluating intersection performance. Early estimates of saturation flow rates were established by Greenshields, and modifications and extensions that refine and modernize these estimates are provided in the current edition of the Highway Capacity Manual (HCM). However, large variations in the measurements of saturation flows have contributed evidence of instabilities in the base rates. Moreover, recent research has produced conflicting findings regarding these rates, particularly for longer queues. Studies reported in the HCM have found the rates as being too high when green phases exceed 40 or 50s. Other recent research studies have found the rates in the HCM as being too low. Following the dispersion of the first few vehicles in a queue, some studies have observed nonlinear and/or irregular queue dispersion tendencies instead of uniform discharge headways between successive vehicles. Nonlinear models of saturation flow are disjointed and have not been adopted in the HCM. This paper synthesizes recent research findings on queue start-up delays, vehicle sizes, queue spacings, acceleration characteristics of starting vehicles and discharge headway observations into a unified theory of saturation flow. Empirical observations are used to calibrate the unified model. Unlike other models that require difficult measurements of speeds or accelerations at precise points for calibration, only average discharge headway times by queue positions are needed. The model substantiates empirical evidence that saturation flow observations may not approach a constant base rate unless vehicles at the trailing end of queues have fully accelerated to their downstream cruising speeds before reaching the stop line, which may not occur at many intersection approaches unless downstream cruising speeds are quite slow and/or green phases are quite long.
Abstract