Mixed traffic optimization considering road reservation travel based on the bi-level programming model

Reservation travel has gradually become an important strategy to alleviate urban traffic congestion by finely matching traffic supply and demand. In order to quantify the effectiveness of the reservation travel strategy, ordinary vehicles and reservation vehicles are considered, The reservation travel problem is formulated as a Bi-level Programming (BP), where the upper-level objective is to maximize traffic demand, while the lower-level model considers the System Optimal-Stochastic User Equilibrium (SO-SUE) mixed traffic equilibrium. The equivalence of the mixed equilibrium problem and the existence of the solution are proved. On the basis of the WOA algorithm, combined with the lower-level Partan Frank-Wolfe algorithm, the traffic assignment solution process is connected to the upper-level as a function. A Whale Optimization Algorithm (WOA) nested Partan Frank-Wolfe algorithm is proposed to solve the model. Finally, the Sioux-Falls network numerical experiment proves that the reservation travel has a gratifying benefit in alleviating traffic congestion. By comparing the Vehicle-to-Capacity (V/C) ratio and cost before and after the implementation of reservation, it shows the effectiveness of reservation travel for urban traffic congestion management, and discusses the impact of the number of reserved roads and reservation trends on road network capacity, service level and travel cost under the implementation of reservation travel.