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Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory

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  • Yang, Hai
  • Hai-Jun, Huang

Abstract

In this paper, a time-varying pricing model of a road bottleneck with elastic traffic demand is formulated using the optimal control theory. It is assumed that the optimal use of the bottleneck is achieved when social benefit over the whole time horizon of study is maximized. The necessary conditions for optimal solution are derived and their economic interpretations are given. Different from conventional analyses, queuing is not pre-assumed to be zero when obtaining the optimal time-varying toll, and the exit capacity of the bottleneck is assumed either to be constant or to vary with queue length. An approximate iterative algorithm is proposed for solving the model in a discrete time version. Three numerical examples are presented to demonstrate the applications of the proposed model and algorithm.

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Bibliographic Info

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

Volume (Year): 31 (1997)
Issue (Month): 6 (November)
Pages: 425-440

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Handle: RePEc:eee:transb:v:31:y:1997:i:6:p:425-440

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References

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  1. Mun, Se-il, 1994. "Traffic jams and the congestion toll," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 365-375, October.
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  6. 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.
  7. Richard Arnott & Andre de Palma & Robin Lindsey, 1987. "Bottleneck Congestion with Elastic Demand," Working Papers 690, Queen's University, Department of Economics.
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  9. Byung-Wook Wie, 1995. "A differential game approach to the dynamic mixed behavior traffic network equilibrium problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 117-136, May.
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  11. Braid, Ralph M., 1989. "Uniform versus peak-load pricing of a bottleneck with elastic demand," Journal of Urban Economics, Elsevier, vol. 26(3), pages 320-327, November.
  12. Smith, M. J., 1979. "The marginal cost taxation of a transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 13(3), pages 237-242, September.
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Citations

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Cited by:
  1. Fosgerau, Mogens & Small, Kenneth A., 2013. "Hypercongestion in downtown metropolis," Journal of Urban Economics, Elsevier, vol. 76(C), pages 122-134.
  2. Dung-Ying Lin & Avinash Unnikrishnan & S. Waller, 2011. "A Dual Variable Approximation Based Heuristic for Dynamic Congestion Pricing," Networks and Spatial Economics, Springer, vol. 11(2), pages 271-293, June.
  3. Chen-Hsiu Laih, 2004. "Effects of the optimal step toll scheme on equilibrium commuter behaviour," Applied Economics, Taylor & Francis Journals, vol. 36(1), pages 59-81.
  4. 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.
  5. Watling, David, 2006. "User equilibrium traffic network assignment with stochastic travel times and late arrival penalty," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1539-1556, December.
  6. C. Robin Lindsey & Erik T. Verhoef, 2000. "Traffic Congestion and Congestion Pricing," Tinbergen Institute Discussion Papers 00-101/3, Tinbergen Institute.
  7. Liu, Yang & Nie, Yu (Marco), 2011. "Morning commute problem considering route choice, user heterogeneity and alternative system optima," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 619-642.
  8. Takeshi Nagae & Takashi Akamatsu, 2006. "Dynamic Revenue Management of a Toll Road Project under Transportation Demand Uncertainty," Networks and Spatial Economics, Springer, vol. 6(3), pages 345-357, September.
  9. C. Robin Lindsey & Erik T. Verhoef, 2000. "Traffic Congestion and Congestion Pricing," Tinbergen Institute Discussion Papers 00-101/3, Tinbergen Institute.
  10. Han, S. & Heydecker, B.G., 2006. "Consistent objectives and solution of dynamic user equilibrium models," Transportation Research Part B: Methodological, Elsevier, vol. 40(1), pages 16-34, January.
  11. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun & Zhang, H. Michael, 2005. "Integrated scheduling of daily work activities and morning-evening commutes with bottleneck congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(1), pages 41-60, January.
  12. Huang, Hai-Jun, 2002. "Pricing and logit-based mode choice models of a transit and highway system with elastic demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 562-570, August.
  13. Berg, V.A.C. van den, 2012. "Step tolling with price sensitive demand: Why more steps in the toll makes the consumer better off," Serie Research Memoranda 0003, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  14. Yang, Hai & Meng, Qiang, 1998. "Departure time, route choice and congestion toll in a queuing network with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 247-260, May.
  15. Yang, Hai & Huang, Hai-Jun, 1999. "Carpooling and congestion pricing in a multilane highway with high-occupancy-vehicle lanes," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(2), pages 139-155, February.
  16. van den Berg, Vincent A.C., 2012. "Step-tolling with price-sensitive demand: Why more steps in the toll make the consumer better off," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(10), pages 1608-1622.
  17. 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.
  18. Zhao, Hui & Yan, Xuedong & Gao, Ziyou, 2013. "Transportation serviceability analysis for metropolitan commuting corridors based on modal choice modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 49(C), pages 270-284.
  19. 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.
  20. Yang, Hai & Liu, Wei & Wang, Xiaolei & Zhang, Xiaoning, 2013. "On the morning commute problem with bottleneck congestion and parking space constraints," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 106-118.
  21. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
  22. Ramadurai, Gitakrishnan & Ukkusuri, Satish V. & Zhao, Jinye & Pang, Jong-Shi, 2010. "Linear complementarity formulation for single bottleneck model with heterogeneous commuters," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 193-214, February.

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