Impact of VSL Location on Capacity Drop: A Case of Sag and Tunnel Bottlenecks

When there is upstream congestion the discharging flow-rate of a tunnel or sag bottleneck can drop, which leads to additional traffic jams. Therefore, control strategies such as variable speed limit (VSL) have been developed aiming to prevent or mitigate upstream traffic congestion. Understanding traffic dynamics at bottlenecks, especially the mechanism of capacity drop, is critical for developing such models. Many studies are centered on the control algorithm design of VSL. However, there are few studies that systematically anayze the effect that the VSL application area has on the control effectiveness. This paper extends to sag and tunnel bottlenecks the theoretical framework to analytically solve the optimal location of the speed limit application area (first developed in Martínez and Jin (2018)). Moreover, we prove that the optimization formulation can be simplified. Consequently, it can be applied to further bounded acceleration models than the constant one. Finally, for an open-loop control with a constant speed limit for the Kobotonoke tunnel bottleneck, we validate the analytic definition of optimal location by preventing capacity drop in numerical simulations.