IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v48y2013icp67-87.html
   My bibliography  Save this article

Risk-neutral second best toll pricing

Author

Listed:
  • (Jeff) Ban, Xuegang
  • Ferris, Michael C.
  • Tang, Lisa
  • Lu, Shu

Abstract

We propose a risk-neutral second best toll pricing (SBTP) scheme to account for the possible nonuniqueness of user equilibrium solutions. The scheme is designed to optimize for the expected objective value as the UE solution varies within the solution set. We show that such a risk-neutral scheme can be formulated as a stochastic program, which complements the traditional risk-prone SBTP approach and the risk-averse SBTP approach we developed recently. The proposed model can be solved by a simulation-based optimization algorithm that contains three major steps: characterization of the UE solution set, random sampling over the solution set, and a two-phase simulation optimization step. Numerical results illustrate that the proposed risk-neutral design scheme is less aggressive than the risk-prone scheme and less conservative than the risk-averse scheme, and may thus be more preferable from a toll designer’s point of view.

Suggested Citation

  • (Jeff) Ban, Xuegang & Ferris, Michael C. & Tang, Lisa & Lu, Shu, 2013. "Risk-neutral second best toll pricing," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 67-87.
    • Handle: RePEc:eee:transb:v:48:y:2013:i:c:p:67-87
    DOI: 10.1016/j.trb.2012.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261512001531
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2012.11.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Steven A. Gabriel & David Bernstein, 1997. "The Traffic Equilibrium Problem with Nonadditive Path Costs," Transportation Science, INFORMS, vol. 31(4), pages 337-348, November.
    2. Kenneth Button & Erik Verhoef (ed.), 1998. "Road Pricing, Traffic Congestion and the Environment," Books, Edward Elgar Publishing, number 940.
    3. MARCHAND, Maurice, 1968. "A note on optimal tolls in an imperfect environment," LIDAM Reprints CORE 22, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Xuegang Ban & Henry Liu, 2009. "A Link-Node Discrete-Time Dynamic Second Best Toll Pricing Model with a Relaxation Solution Algorithm," Networks and Spatial Economics, Springer, vol. 9(2), pages 243-267, June.
    5. He, Fang & Wu, Di & Yin, Yafeng & Guan, Yongpei, 2013. "Optimal deployment of public charging stations for plug-in hybrid electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 87-101.
    6. 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.
    7. 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.
    8. Bie, Jing & Lo, Hong K., 2010. "Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 90-107, January.
    9. Watling, David, 1999. "Stability of the stochastic equilibrium assignment problem: a dynamical systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 281-312, May.
    10. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    11. Guo, Xiaolei & Liu, Henry X., 2011. "Bounded rationality and irreversible network change," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1606-1618.
    12. Liu, Louie Nan & McDonald, John F., 1999. "Economic efficiency of second-best congestion pricing schemes in urban highway systems," Transportation Research Part B: Methodological, Elsevier, vol. 33(3), pages 157-188, April.
    13. 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.
    14. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    15. Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    16. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    17. Byung Chung & Tao Yao & Chi Xie & Andreas Thorsen, 2011. "Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty," Networks and Spatial Economics, Springer, vol. 11(2), pages 371-389, June.
    18. Lou, Yingyan & Yin, Yafeng & Lawphongpanich, Siriphong, 2010. "Robust congestion pricing under boundedly rational user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 15-28, January.
    19. Arnott, Richard J., 1979. "Unpriced transport congestion," Journal of Economic Theory, Elsevier, vol. 21(2), pages 294-316, October.
    20. 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.
    21. Agdeppa, Rhoda P. & Yamashita, Nobuo & Fukushima, Masao, 2007. "The traffic equilibrium problem with nonadditive costs and its monotone mixed complementarity problem formulation," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 862-874, October.
    22. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    23. Hani S. Mahmassani & Gang-Len Chang, 1987. "On Boundedly Rational User Equilibrium in Transportation Systems," Transportation Science, INFORMS, vol. 21(2), pages 89-99, May.
    24. Penchina, Claude M., 2004. "Minimal-revenue congestion pricing: some more good-news and bad-news," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 559-570, July.
    25. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    26. Verhoef, Erik & Nijkamp, Peter & Rietveld, Piet, 1996. "Second-Best Congestion Pricing: The Case of an Untolled Alternative," Journal of Urban Economics, Elsevier, vol. 40(3), pages 279-302, November.
    27. Xuegang (Jeff)Ban & Shu Lu & Michael Ferris & Henry X. Liu, 2009. "Risk Averse Second Best Toll Pricing," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 197-218, Springer.
    28. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2001. "A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network," Transportation Science, INFORMS, vol. 35(4), pages 345-358, November.
    29. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2004. "Modeling private highways in networks with entry-exit based toll charges," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 191-213, March.
    30. Lo, Hong K. & Chen, Anthony, 2000. "Traffic equilibrium problem with route-specific costs: formulation and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 493-513, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Elaine Chiao Ling & Khoo-Lattimore, Catheryn & Arcodia, Charles, 2017. "A systematic literature review of risk and gender research in tourism," Tourism Management, Elsevier, vol. 58(C), pages 89-100.
    2. Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
    3. Di, Xuan & Liu, Henry X. & Ban, Xuegang (Jeff), 2016. "Second best toll pricing within the framework of bounded rationality," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 74-90.
    4. Wu, Wen-Xiang & Huang, Hai-Jun, 2014. "Finding anonymous tolls to realize target flow pattern in networks with continuously distributed value of time," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 31-46.
    5. Ji, Xiangfeng & Chu, Yanyu, 2020. "A target-oriented bi-attribute user equilibrium model with travelers’ perception errors on the tolled traffic network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    6. Chiou, Suh-Wen, 2015. "A cutting plane projection method for bi-level area traffic control optimization with uncertain travel demand," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 390-403.
    7. Xiangfeng Ji & Xiaoyu Ao, 2021. "Travelers’ Bi-Attribute Decision Making on the Risky Mode Choice with Flow-Dependent Salience Theory," Sustainability, MDPI, vol. 13(7), pages 1-24, April.
    8. Chen, Zhibin & He, Fang & Yin, Yafeng & Du, Yuchuan, 2017. "Optimal design of autonomous vehicle zones in transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 44-61.
    9. (Jeff) Ban, Xuegang & Dessouky, Maged & Pang, Jong-Shi & Fan, Rong, 2019. "A general equilibrium model for transportation systems with e-hailing services and flow congestion," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 273-304.
    10. Omid M. Rouhani, 2016. "Next Generations of Road Pricing: Social Welfare Enhancing," Sustainability, MDPI, vol. 8(3), pages 1-15, March.
    11. Ma, Rui & Ban, Xuegang (Jeff) & Szeto, W.Y., 2017. "Emission modeling and pricing on single-destination dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 255-283.
    12. Xiangfeng Ji & Xuegang (Jeff) Ban & Mengtian Li & Jian Zhang & Bin Ran, 2017. "Non-expected Route Choice Model under Risk on Stochastic Traffic Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 777-807, September.
    13. Qinghui Xu & Xiangfeng Ji, 2020. "User Equilibrium Analysis Considering Travelers’ Context-Dependent Route Choice Behavior on the Risky Traffic Network," Sustainability, MDPI, vol. 12(17), pages 1-25, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Button, Kenneth, 2004. "1. The Rationale For Road Pricing: Standard Theory And Latest Advances," Research in Transportation Economics, Elsevier, vol. 9(1), pages 3-25, January.
    2. 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.
    3. 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.
    4. Kockelman, Kara M. & Lemp, Jason D., 2011. "Anticipating new-highway impacts: Opportunities for welfare analysis and credit-based congestion pricing," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(8), pages 825-838, October.
    5. Tikoudis, Ioannis, 2023. "Revisiting the Pigouvian tax in urban roads: Housing supply restrictions, leaking profits and spatial inequality," Economics of Transportation, Elsevier, vol. 35(C).
    6. Erik T. Verhoef, 1998. "The Implementation of Marginal External Cost Pricing in Road Transport," Tinbergen Institute Discussion Papers 98-091/3, Tinbergen Institute.
    7. Verhoef, Erik Teodoor, 2000. "The Generalized Second-Best Network Congestion Pricing Problem," ERSA conference papers ersa00p336, European Regional Science Association.
    8. Chen, Daqiang & Ignatius, Joshua & Sun, Danzhi & Goh, Mark & Zhan, Shalei, 2018. "Impact of congestion pricing schemes on emissions and temporal shift of freight transport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 77-105.
    9. 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.
    10. 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.
    11. Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
    12. C. Robin Lindsey & Erik T. Verhoef, 2000. "Traffic Congestion and Congestion Pricing," Tinbergen Institute Discussion Papers 00-101/3, Tinbergen Institute.
    13. Holgui­n-Veras, Jose & Cetin, Mecit & Xia, Shuwen, 2006. "A comparative analysis of US toll policy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(10), pages 852-871, December.
    14. Hongli Xu & Hai Yang & Jing Zhou & Yafeng Yin, 2017. "A Route Choice Model with Context-Dependent Value of Time," Transportation Science, INFORMS, vol. 51(2), pages 536-548, May.
    15. Erik T. Verhoef & Kenneth A. Small, 1999. "Product Differentiation on Roads: Second-Best Congestion Pricing with Heterogeneity under Public and Private Ownership," Tinbergen Institute Discussion Papers 99-066/3, Tinbergen Institute.
    16. Xuan Di & Henry Liu & Xuegang Ban & Jeong Yu, 2015. "Submission to the DTA 2012 Special Issue: On the Stability of a Boundedly Rational Day-to-Day Dynamic," Networks and Spatial Economics, Springer, vol. 15(3), pages 537-557, September.
    17. 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.
    18. Georgina Santos & Erik Verhoef, 2011. "Road Congestion Pricing," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 23, Edward Elgar Publishing.
    19. 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.
    20. Holgun-Veras, Jos & Cetin, Mecit, 2009. "Optimal tolls for multi-class traffic: Analytical formulations and policy implications," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(4), pages 445-467, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:48:y:2013:i:c:p:67-87. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.