Enhancing transportation network capacity by congestion pricing with simultaneous toll location and toll level optimization |
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Authors: | Xiaoning Zhang Bert van Wee |
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Affiliation: | 1. School of Economics and Management , Tongji University , Siping Road 1239, Shanghai , 200092 , China cexzhang@tongji.edu.cn;3. Faculty of Technology, Policy and Management , Delft University of Technology , The Netherlands |
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Abstract: | In previous studies of congestion pricing, the objective was to minimize total travel time or maximize total social welfare of all travellers in transportation networks. In this article, a new objective function of maximizing the reserve capacity of networks is proposed, and a new bi-level model is formulated for the implementation of congestion pricing, where either link tolls or path tolls are charged. Since the bi-level model is neither convex nor differentiable, the traditional gradient based methods cannot solve the problem for a global optimum. To circumvent the difficulty of computing, the congestion pricing problem of simultaneous toll link and toll level optimization is formulated as a single-level optimization program with equilibrium constraints. Then the equilibrium constraints, the travel time functions, and toll location constraints are all linearized by introducing mixed integer variables. As a result, the overall problem is formulated into a mixed-integer linear program, which can determine the global optimum. Numerical results show that this approach is effective and efficient. |
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Keywords: | bi-level model congestion pricing reserve capacity global optimum user equilibrium mixed integer linear program |
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