Analytical approximation and calibration of roundabout capacity: A merging state transition-based modeling approach

This manuscript focuses on the theoretical advancement of causality between entry vehicle dynamics and roundabout capacity modeling, with a merging state transition-based analytical approximation and calibration approach. Gap acceptance models, such as the HCM model, usually ignore roundabout specific operating conditions, whereas empirical models are generally criticized for the lack of fundamental understanding of underlying traffic flow or driving behaviors. The roundabout geometry is firstly extracted into a Y-shaped network, and the traffic movements are illustrated with a state-space-time diagram. Next, we analyze the merging state space for the entry vehicles, and draw the state-transition diagram. The episode of a traffic flow is defined, and we show that the trajectory of an entry vehicle repeats one of four patterns within each episode. Then, state transition-based analytical derivation of roundabout capacity is presented. This is done by estimating the state transition probabilities, followed by an episode-based state transition chain analysis and, finally, finding the solution of state transitions under steady states. Circulating speed is used as a key variable to reflect the operating conditions in the target roundabout. For a special scenario, with all four entry approaches being saturated, we model the interactions between entry flow and circulating flow, and prove that the resulting model can be uniquely solved by classic root-finding algorithms. The accuracy of the proposed model is tested with OpenDD, a real-world high-resolution trajectory dataset collected by drones at four roundabouts. The results of the proposed model are shown to consistently outperform the HCM6 model and another gap acceptance-based model.