A bi-level programming model for the optimal lane reservation problem

This paper studies a discontinuous lane reservation problem considering the heterogeneous traffic demand containing both vehicles with general purposes and vehicles with special tasks. The modeling difference between these two types of vehicles is that only vehicles with special tasks have time budgets for their trip. The objective is to satisfy the target travel time of the vehicles with special tasks through the lane reservation scheme, and to minimize the negative impact on the rest vehicles due to the decrease of the lane number simultaneously. This discontinuous lane reservation problem is formulated as a discrete bi-level programming model, where the upper level determines which road segments could be reserved, while the lower level optimizes the route choices under the given lane reservation scheme. A nested artificial bee colony and Frank-Wolfe algorithm is proposed to solve the model. A numerical experiment with the Sioux-Falls network validates the effectiveness of the proposed model and the efficiency of the solution algorithm.