Abstract
Designing a congestion pricing scheme involves a number of complex decisions. Focusing on the quantitative parts of a congestion pricing system with link tolls, the problem involves finding the number of toll links, the link toll locations and their corresponding toll level and schedule. In this paper, we develop and evaluate methods for finding the most efficient design for a congestion pricing scheme in a road network model with elastic demand. The design efficiency is measured by the net social surplus, which is computed as the difference between the social surplus and the collection costs (i.e. setup and operational costs) of the congestion pricing system. The problem of finding such a scheme is stated as a combinatorial bi-level optimization problem. At the upper level, we maximize the net social surplus and at the lower level we solve a user equilibrium problem with elastic demand, given the toll locations and toll levels, to simulate the user response. We modify a known heuristic procedure for finding the optimal locations and toll levels given a fixed number of tolls to locate, to find the optimal number of toll facilities as well. A new heuristic procedure, based on repeated solutions of a continuous approximation of the combinatorial problem is also presented. Numerical results for two small test networks are presented. Both methods perform satisfactorily on the two networks. Comparing the two methods, we find that the continuous approximation procedure is the one which shows the best results.
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Beckmann, M. J., McGuire, C. B., & Winsten, C. B. (1956). Studies in the economics of transportation. New Haven: Yale University Press.
Dafermos, S. C. (1973). Toll patterns for multiclass-user transportation networks. Transportation Science, 7, 211–223.
Daganzo, C. F., & Sheffi, Y. (1977). On stochastic models of traffic assignment. Transportation Science, 11, 253–274.
Gartner, N. H. (1980). Optimal traffic assignment with elastic demands: A review; Part II: Algorithmic approaches. Transportation Science, 14, 192–208.
Hearn, D. W., & Yildirim, M. B. (2002). Toll pricing framework for traffic assignment problems with elastic demand. In M. Gendreau & P. Marcotte (Eds.), Transportation and network analysis: Current trends. Netherlands: Kluwer Academic Publishers.
Larsson, T., & Patriksson, M. (1992). Simplicial decomposition with disaggregated representation for the traffic assignment problem. Transportation Science, 26, 4–17.
Marchand, M. (1968). A note on optimal tolls in an imperfect environment. Econometrica, 36, 575–581.
Maruyama, T., & Sumalee, A. (2007). Efficiency and equity comparison of cordonand area-based road pricing schemes using a trip-chain equilibrium model. Transportation Research Part A, 41, 655–671.
May, A. D., Milne, D. S., Shepherd, S. P., & Sumalee, A. (2002). Specification of optimal cordon pricing locations and charges. Transportation Research Record, 1812, 60–68.
Patriksson, M. (1994). The traffic assignment problem: Models and methods. Utrecht, The Netherlands: VSP.
Patriksson, M., & Rockafellar, R. T. (2003). Sensitivity analysis of aggregated variational inequality problems, with application to traffic equilibria. Transportation Science, 37, 56–68.
Shepherd, S., & Sumalee, A. (2004). A genetic algorithm based approach to optimal toll level and location problems. Network and Spatial Economics, 4, 161–179.
Lawphongpanich, S., & Hearn, D. W. (2004). An MPEC approach to second-best toll pricing. Mathematical Programming Series B, 101, 33–35.
Sumalee, A. (2004). Optimal road user charging cordon design: A heuristic optimization approach. Computer-Aided Civil and Infrastructure Engineering, 19, 377–392.
Verhoef, E., Nijkamp, P., & Rietveld, P. (1996). Second-best congestion pricing: the case of an untolled alternative. Journal of Urban Economics, 40, 279–302.
Verhoef, E. T. (2002). Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points. Transportation Research Part B, 36, 707–729.
Wardrop, J. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers, 1(2), 325–378.
Yang, H., & Lam, W. H. K. (1996). Optimal road tolls under conditions of queueing and congestion. Transportation Research Part A, 30, 319–332.
Zhang, H. M., & Ge, Y. E. (2004). Modeling variable demand equilibrium under second-best road pricing. Transportation Research Part B, 38, 733–749.
Zhang, X., & Yang, H. (2004). The optimal cordon-based network congestion pricing problem. Transportation Research Part B, 38, 517–537.
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Ekström, J., Engelson, L. & Rydergren, C. Heuristic algorithms for a second-best congestion pricing problem. Netnomics 10, 85–102 (2009). https://doi.org/10.1007/s11066-008-9019-9
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DOI: https://doi.org/10.1007/s11066-008-9019-9