Traffic congestion is a challenge that frequently emerges due to changes in the roadways such as tunnels and sags, causing capacity reduction. The capacity drop phenomenon exacerbates traffic congestion, due to decreased queue discharge rates. Among the strategies employed for traffic management, Variable Speed Limit (VSL) control is a common approach to alleviate congestion and mitigate capacity drop. The control is expected to be more powerful when integrated with Connected Vehicles (CVs). However, the intricate interplay between the Market Penetration Rate (MPR) of CVs and the parameters governing VSL remains under-explored.
This study seeks to quantify the relationship between the MPR of CVs and the key VSL parameters, encompassing factors like the optimal acceleration length and speed limits. The VSL control is applied to CVs at the road section upstream of a tunnel bottleneck modelled by a continuum car-following model with bounded acceleration. The findings of this research suggest a minimum MPR of CVs essential for preventing capacity drop and reaching the maximal outflow. Intriguingly, this challenges the conventional notion that regulating solely the leading vehicle suffices to govern the behaviours of all following vehicles. The value of the minimum MPR threshold is affected by the acceleration behaviours vehicles exhibit.
Furthermore, this study underscores the importance of considering the MPR of CVs when devising the optimal speed limit and acceleration length for the VSL. It shows that while a higher speed limit can lead to higher throughput, the optimal acceleration length increases exponentially with the increasing speed limit, particularly in cases with low MPR of CVs. While adopting a relatively lower speed limit, the acceleration length can be reduced to 0m for all levels of MPR of CVs. In summary, it suggests that when implementing VSL in practice, a balance between the resulted throughput, the required acceleration length and the robustness of VSL across different levels of MPR of CVs should be considered.