Research On Distance-based Congestion Pricing Model And Algorithm

All the implemented cordon-based congestion pricing schemes currently use a flat toll-charge method including the daily licensing basis charge and the pay-per-entry basis charge, regardless of the travel distance or time in the pricing cordons. This flat toll charge method is inequitable because it undercharges long journeys and over-restrains short ones. To cope with these drawbacks of flat toll-charge method, the distance-based toll charge method is proposed and studied in depth.This paper firstly assumes that the distance-based toll charge is the nonlinear function of the distance travelled inside the pricing cordon and keeps positive and non-decreasing. Then for the given toll charge function, the tolled user equilibrium model is developed and the existence and uniqueness of model solution are proved thereafter. In view of this unknown specific function, the piecewise linear approximation method is adopted to determine the nonlinear function. The assumption of distance-based nonlinear toll charge function will lead to the non-additive problem, which implies that the Frank-Wolfe algorithm cannot be directly used to solve this non-additive problem. Herein, the path-based algorithm is adopted to solve that and k-shortest algorithm is also embedded into the path-based algorithm to assist in searching for the shortest path with minimal generalized path travel cost.Considering the drivers’path choice behavior under the distance-based toll charge condition, the optimal distance-based toll charge design is formulated by the multi-objective bi-level model. The upper level is set to consider the impact of distance-based toll charge on the multiple objective including the social welfare, environment and equity. The lower level is the traffic assignment with specific toll charge method. Because some of these objectives are conflict in determining the multi-objective optimization problem, the goal programming method is used to solve the multi-objective problem. In addition, the complexity of the proposed multi-objective bi-level model and particularity the distance-based toll charge function also prevent the usage of any gradient-based method for solving the proposed multi-objective bi-level model. Therefore, it would be more straightforward to adopt Genetic Algorithm (GA) as a heuristic for solving the proposed model because GA can ignore the specific mathematical structure of that.Finally a numerical example is presented to verify the proposed models and integrated methodology. The results illustrate that the optimal distance-based toll charge function is highly nonlinear and can achieve the optimality of the network performance.