Effectiveness of variable speed limits considering commuters’ long-term response

• We examine the effectiveness of VSL using Vickrey’s bottleneck model.
• VSL systems avoid or delay capacity drop that arises at activated bottlenecks.
• A continuous VSL system eliminates efficiency loss caused by capacity drop.
• A discrete VSL system also reduces queuing delay, schedule delay and emissions.
• A discrete VSL system unlikely reduces travel time and travel cost in this setting.

This paper examines the effectiveness of variable speed limits (VSLs) on improving traffic flow efficiency and reducing vehicular emissions in a stylized setting of morning commute where a fixed number of individuals commute from home to work through the freeway with a single recurrent bottleneck. The mechanism of interest is for a VSL system to prevent the bottleneck from being activated and thus avoid detrimental capacity drop that arises at the activated bottleneck. We firstly consider a VSL system installed along the freeway towards the bottleneck, which adjusts commuters’ cruising speeds in a continuous fashion and essentially regulates the upstream flow into the bottleneck. By investigating the resulting departure-time equilibrium of commuters, we find the VSL system can eliminate the efficiency loss caused by capacity drop, and further bound its improvements on various performance measures. We then turn to a more practical VSL system, which adjusts commuters’ cruising speeds in a discrete fashion. The conditions for such a system to improve various performance measures are established and its efficiencies are bounded. Based on empirical data, we conclude that the discrete VSL system can avoid or delay capacity drop associated with an active bottleneck and thus reduce queuing delay. It can help reduce the schedule delay cost and total emissions cost. However, it is unlikely for the system to reduce total travel time, individual travel cost and social cost in this particular setting. These results shed light on the effectiveness of VSL systems on realistic freeway networks.