Local Ramp Metering in the Presence of a Distant Downstream Bottleneck: Theoretical Analysis and Simulation Study

The well-known feedback ramp metering algorithm ALINEA can be applied for local ramp metering or used as a key component in a coordinated ramp metering system. ALINEA uses real-time occupancy measurements from the ramp-flow merging area that may be at most few hundred meters downstream of the metered on-ramp nose. In many practical cases, however, bottlenecks with smaller capacity than the merging area may exist further downstream for various reasons, which suggests using measurements from those further downstream bottlenecks rather than from the merging area. This paper addresses the local ramp metering problem in such a downstream bottleneck case. Theoretical analysis indicates that ALINEA may lead to a poorly damped closed-loop behavior in this case, but PI-ALINEA, which is a suitable proportional-integral (PI) extension of ALINEA, can lead to satisfactory control performance. The stability of the closed-loop ramp metering system with PI-ALINEA is rigorously proved by Lyapunov stability arguments. The root locus method is also employed to analyze the linearized closed-loop system performance of ALINEA and PI-ALINEA with and without a downstream bottleneck to provide insights on both controllers' performance. Simulation studies are conducted using a macroscopic traffic flow model to demonstrate that the ramp metering performance of ALINEA indeed deteriorates in the distant downstream bottleneck case, whereas a significant improvement is obtained using PI-ALINEA. Moreover, with its control parameters appropriately tuned, PI-ALINEA is found to be universally applicable to a range of distances between the on-ramp and downstream bottlenecks. This indicates that little fine-tuning would be necessary in field applications.