A first-order behavioral model of capacity drop

Abstract

Understanding traffic dynamics at lane-drop bottlenecks, especially the mechanism of capacity drop, is critical for developing and evaluating centralized and decentralized control strategies in a freeway system. In this study, we propose a first-order behavioral model of capacity drop at a continuous lane-drop bottleneck. By extending the theoretical framework for analytically solving the generalized Riemann problem in Jin (2017), we introduce vehicles’ bounded acceleration on the LWR (Lighthill-Whitham-Richards) stationary states inside the lane-drop zone as an additional constraint for the optimization formulation of the entropy condition. We demonstrate that the optimization problem is uniquely solved with well-defined instantaneous continuous standing waves, comprised of the LWR stationary states inside the lane-drop and the bounded acceleration stationary states in the downstream acceleration zones. In the solutions to the generalized Riemann problem, the boundary flux as well as the stationary states and kinematic waves on both upstream and downstream links are the same as those in the phenomenological model of capacity drop proposed in Jin et al. (2015). This is a behavioral model of capacity drop, since both the dropped capacity and the capacity drop ratio are endogenous and can be calculated from the factors related to the fundamental diagram, road geometry, bounded acceleration, and lane changes. We present the Cell Transmission Model for the behavioral and phenomenological models and verify the theoretical results with numerical examples. We calibrate and validate the model with observed stationary speeds at a lane-drop bottleneck. Combined with Jin (2017), this study provides a proof of the conjecture by Hall and Agyemang-Duah (1991) that capacity drop results from the acceleration process when “drivers accelerate away from the (upstream) queue”.