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Toll Patterns for Multiclass-User Transportation Networks

Author

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  • Stella C. Dafermos

    (Brown University, Providence, Rhode Island)

Abstract

In this paper we apply the following general scheme to determine toll patterns for multiclass-user transportation networks: we modify the travel cost as perceived by the individual traveler by charging him a “toll.” Then we try to determine the toll pattern in such a way that the system-optimizing flow pattern becomes at the same time user-optimizing. We discuss two toll policies: (a) Tolls are collected on a link basis, (b) Tolls are collected on a path basis. The study shows that there is a degree of freedom in the path-toll collection policy. Alternative criteria are proposed for the exploitation of the degree of freedom such as: (i) that the tolls collected be nonnegative; (ii) that the personal cost of travelers, before and after the imposition of tolls, remains the same; (iii) that certain classes are treated discriminately in order to attain some social good.

Suggested Citation

  • Stella C. Dafermos, 1973. "Toll Patterns for Multiclass-User Transportation Networks," Transportation Science, INFORMS, vol. 7(3), pages 211-223, August.
    • Handle: RePEc:inm:ortrsc:v:7:y:1973:i:3:p:211-223
    DOI: 10.1287/trsc.7.3.211
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    Cited by:

    1. Zangui, Mahmood & Aashtiani, Hedayat Z. & Lawphongpanich, Siriphong & Yin, Yafeng, 2015. "Path-differentiated pricing in congestion mitigation," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 202-219.
    2. Erik T. Verhoef, 2000. "Second-Best Congestion Pricing in General Networks - Algorithms for Finding Second-Best Optimal Toll Levels and Toll Points," Tinbergen Institute Discussion Papers 00-084/3, Tinbergen Institute.
    3. Verhoef, Erik T., 2002. "Second-best congestion pricing in general static transportation networks with elastic demands," Regional Science and Urban Economics, Elsevier, vol. 32(3), pages 281-310, May.
    4. Jovanović, Radosav & Tošić, Vojin & Čangalović, Mirjana & Stanojević, Milan, 2014. "Anticipatory modulation of air navigation charges to balance the use of airspace network capacities," Transportation Research Part A: Policy and Practice, Elsevier, vol. 61(C), pages 84-99.
    5. Georgia Perakis, 2007. "The “Price of Anarchy” Under Nonlinear and Asymmetric Costs," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 614-628, August.
    6. C. Robin Lindsey & Erik T. Verhoef, 2000. "Traffic Congestion and Congestion Pricing," Tinbergen Institute Discussion Papers 00-101/3, Tinbergen Institute.
    7. Miralinaghi, Mohammad & Peeta, Srinivas, 2016. "Multi-period equilibrium modeling planning framework for tradable credit schemes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 177-198.
    8. Joakim Ekström & Leonid Engelson & Clas Rydergren, 2009. "Heuristic algorithms for a second-best congestion pricing problem," Netnomics, Springer, vol. 10(1), pages 85-102, April.
    9. Viauroux, Christelle, 2011. "Pricing urban congestion: A structural random utility model with traffic anticipation," European Economic Review, Elsevier, vol. 55(7), pages 877-902.
    10. Wie, Byung-Wook & Tobin, Roger L., 1998. "Dynamic congestion pricing models for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 313-327, June.
    11. de Palma, André & Kilani, Moez & Lindsey, Robin, 2005. "Congestion pricing on a road network: A study using the dynamic equilibrium simulator METROPOLIS," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 588-611.
    12. C. Robin Lindsey & Erik T. Verhoef, 1999. "Congestion Modelling," Tinbergen Institute Discussion Papers 99-091/3, Tinbergen Institute.
    13. Verhoef, Erik Teodoor, 2000. "The Generalized Second-Best Network Congestion Pricing Problem," ERSA conference papers ersa00p336, European Regional Science Association.
    14. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    15. Gentile, Guido & Papola, Natale & Persia, Luca, 2005. "Advanced pricing and rationing policies for large scale multimodal networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 612-631.
    16. Yan, Hai & Lam, William H. K., 1996. "Optimal road tolls under conditions of queueing and congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(5), pages 319-332, September.
    17. Farokhi, Farhad & Johansson, Karl H., 2015. "A piecewise-constant congestion taxing policy for repeated routing games," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 123-143.
    18. Verhoef, Erik T. & Koh, Andrew & Shepherd, Simon, 2010. "Pricing, capacity and long-run cost functions for first-best and second-best network problems," Transportation Research Part B: Methodological, Elsevier, vol. 44(7), pages 870-885, August.
    19. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun, 2008. "Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum," European Journal of Operational Research, Elsevier, vol. 189(1), pages 146-158, August.
    20. Bellei, Giuseppe & Gentile, Guido & Papola, Natale, 2002. "Network pricing optimization in multi-user and multimodal context with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(9), pages 779-798, November.
    21. Verhoef, Erik 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: Methodological, Elsevier, vol. 36(8), pages 707-729, September.
    22. Christelle Viauroux, 2007. "Optimal pricing of endogenous congestion: a disaggregated approach," UMBC Economics Department Working Papers 09-107, UMBC Department of Economics, revised 17 Jul 2009.
    23. Yitian Wang & Zixuan Peng & Keming Wang & Xiaolin Song & Baozhen Yao & Tao Feng, 2015. "Research on Urban Road Congestion Pricing Strategy Considering Carbon Dioxide Emissions," Sustainability, MDPI, vol. 7(8), pages 1-20, August.
    24. Zhang, H. M. & Ge, Y. E., 2004. "Modeling variable demand equilibrium under second-best road pricing," Transportation Research Part B: Methodological, Elsevier, vol. 38(8), pages 733-749, September.
    25. Yang, Hai & Zhang, Xiaoning, 2008. "Existence of anonymous link tolls for system optimum on networks with mixed equilibrium behaviors," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 99-112, February.

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