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Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions


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  • Yang, Hai
  • Meng, Qiang
  • Lee, Der-Horng
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Conventional analysis of optimal congestion pricing relies on three primary elements, namely, the speed-flow relationship, the demand function, and the generalized cost. Analytical demand functions tailed for congestion pricing are, however, difficult to establish in practice even with advanced transport modeling techniques. Inspired and motivated by the recent commentary and analytical works in the literature, this study proposes a trial-and-error implementation scheme of marginal-cost pricing on a general road network when the demand functions are unknown. Given a trial of a set of link tolls, the revealed aggregate link flows can be observed at ease; based on the observed link flows, a new set of link tolls can be determined and used for the next trial. We propose such an iterative toll adjustment procedure based on the method of successive averages, and present a rigorous theoretical proof of its convergence. The iterative procedure presented here allows for a traffic planner to estimate easily the socially optimal congestion tolls in a network without resorting to demand functions.

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Bibliographic Info

Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 38 (2004)
Issue (Month): 6 (July)
Pages: 477-493

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Handle: RePEc:eee:transb:v:38:y:2004:i:6:p:477-493

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  1. Yang, Hai & Iida, Yasunori & Sasaki, Tsuna, 1994. "The equilibrium-based origin-destination matrix estimation problem," Transportation Research Part B: Methodological, Elsevier, vol. 28(1), pages 23-33, February.
  2. Paulley, Neil, 2002. "Recent studies on key issues in road pricing," Transport Policy, Elsevier, vol. 9(3), pages 175-177, July.
  3. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
  4. Yang, Hai & Huang, Hai-Jun, 1998. "Principle of marginal-cost pricing: how does it work in a general road network?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 45-54, January.
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Cited by:
  1. Wada, Kentaro & Akamatsu, Takashi, 2013. "A hybrid implementation mechanism of tradable network permits system which obviates path enumeration: An auction mechanism with day-to-day capacity control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 94-112.
  2. Zhong, R.X. & Sumalee, A. & Friesz, T.L. & Lam, William H.K., 2011. "Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1035-1061, August.
  3. Qiang Meng & Zhiyuan Liu, 2011. "Trial-and-error method for congestion pricing scheme under side-constrained probit-based stochastic user equilibrium conditions," Transportation, Springer, vol. 38(5), pages 819-843, September.
  4. Chung, Byung Do & Yao, Tao & Friesz, Terry L. & Liu, Hongcheng, 2012. "Dynamic congestion pricing with demand uncertainty: A robust optimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1504-1518.
  5. Ferrari, Paolo, 2010. "Willingness to spend and road pricing rates," Transport Policy, Elsevier, vol. 17(3), pages 160-172, May.
  6. Loukas Dimitriou & Theodore Tsekeris, 2009. "Evolutionary game-theoretic model for dynamic congestion pricing in multi-class traffic networks," Netnomics, Springer, vol. 10(1), pages 103-121, April.
  7. Erik T. Verhoef & Andrew Koh & Simon Shepherd, 2008. "Pricing, Capacity and Long-run Cost Functions for First-best and Second-best Network Problems," Tinbergen Institute Discussion Papers 08-056/3, Tinbergen Institute.
  8. Wang, Xiaolei & Yang, Hai, 2012. "Bisection-based trial-and-error implementation of marginal cost pricing and tradable credit scheme," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1085-1096.
  9. Deren Han & Wei Xu & Hai Yang, 2010. "Solving a class of variational inequalities with inexact oracle operators," Computational Statistics, Springer, vol. 71(3), pages 427-452, June.
  10. Yang, Hai & Wang, Xiaolei, 2011. "Managing network mobility with tradable credits," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 580-594, March.
  11. Sheu, Jiuh-Biing & Yang, Hai, 2008. "An integrated toll and ramp control methodology for dynamic freeway congestion management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4327-4348.
  12. Nie, Yu (Marco) & Yin, Yafeng, 2013. "Managing rush hour travel choices with tradable credit scheme," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 1-19.
  13. Zhao, Yong & Kockelman, Kara Maria, 2006. "On-line marginal-cost pricing across networks: Incorporating heterogeneous users and stochastic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 424-435, June.
  14. Zhu, Shanjiang & Du, Longyuan & Zhang, Lei, 2013. "Rationing and pricing strategies for congestion mitigation: Behavioral theory, econometric model, and application in Beijing," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 210-224.


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