Optimal location problem for variable speed limit application areas

Some studies consider variable speed limit (VSL) control as a viable option to prevent traffic breakdown at bottlenecks by limiting the mainline flow with reduced speed limits. However, few studies consider the location of the application area as a design variable of the problem. This paper explains why the location of a VSL control area is crucial to prevent the capacity drop phenomenon at lane drop bottlenecks. We first define two types of stationary states, congested and uncongested, inside a lane drop bottleneck assuming the Lighthill-Whitham Richards model with bounded acceleration. In particular, the characteristics of these stationary states and their admissible conditions are discussed thoroughly. If the speed limit imposed is low enough, the location of the VSL application area is irrelevant to ensure an uncongested stationary state inside the bottleneck. However, for a given range of speed limits, the location of the VSL application area should be designed carefully to allow for uncongested stationary states and prevent the occurrence of the capacity drop. We formulate an optimization problem and show that, contrary to the general belief, the larger the speed limit, the farther the VSL application area should be from the bottleneck. Finally, the results are extended to other types of bottlenecks, such as sag or tunnel bottlenecks. To the best of our knowledge, this is the first study to analytically identify, formulate, and solve the optimal location problem for variable speed limit application areas. It makes fundamental contributions to both traffic flow theory (by analyzing the stationary states for VSL-controlled bottlenecks) and traffic control (by determining the optimal location of a VSL application area). Moreover, the results presented are of practical relevance because they can help to establish some guidelines for practitioners to implement VSL control strategies.