Abstract
Ramp metering (RM) has been deployed for decades and it is considered an efficient technique to control lane-drop bottlenecks by limiting ramp demand and avoiding the so-called capacity-drop phenomena, drop in the downstream flux that occurs when queues form up- stream of bottleneck. In this study, the authors use a simple link queue model to describe traffic dynamics inside a merge zone with an ordinary differential equation, which combines a capacity drop model and a proportional-integral feedback control algorithm (PI-ALINEA). This enables us to analytically study the system performance and controller design for the ramp metering problem. First they analyze the systemâ??s equilibrium states, their stability, and transition subject to varying demand levels. They consider impacts of both fixed and dynamical metering rates on the equilibrium states of the system and examine the reachability of the system. They further analyze the closed-loop systems and design parameters of PI-ALINEA such that the system can be stabilized at the optimal state at a high demand level. With numerical examples they verify the analytical results with respect to the systemâ??s stability and robustness.