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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.

Suggested Citation

  • Yang, Hai & Hai-Jun, Huang, 1997. "Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 425-440, November.
    • Handle: RePEc:eee:transb:v:31:y:1997:i:6:p:425-440
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    1. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    2. Malachy Carey & Ashok Srinivasan, 1993. "Externalities, Average and Marginal Costs, and Tolls on Congested Networks with Time-Varying Flows," Operations Research, INFORMS, vol. 41(1), pages 217-231, February.
    3. Richard Arnott & Andre de Palma & Robin Lindsey, 1987. "Bottleneck Congestion with Elastic Demand," Working Paper 690, Economics Department, Queen's University.
    4. 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.
    5. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    6. 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.
    7. 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.
    8. Arnott, R. & de Palma, A. & Lindsey, R., 1990. "Departure time and route choice for the morning commute," Transportation Research Part B: Methodological, Elsevier, vol. 24(3), pages 209-228, June.
    9. Moshe Ben-Akiva & Andre de Palma & Pavlos Kanaroglou, 1986. "Dynamic Model of Peak Period Traffic Congestion with Elastic Arrival Rates," Transportation Science, INFORMS, vol. 20(3), pages 164-181, August.
    10. 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.
    11. Nathan H. Gartner, 1980. "Optimal Traffic Assignment with Elastic Demands: A Review Part I. Analysis Framework," Transportation Science, INFORMS, vol. 14(2), pages 174-191, May.
    12. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1992. "Route choice with heterogeneous drivers and group-specific congestion costs," Regional Science and Urban Economics, Elsevier, vol. 22(1), pages 71-102, March.
    13. Mun, Se-il, 1994. "Traffic jams and the congestion toll," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 365-375, October.
    14. Henderson, J. V., 1974. "Road congestion : A reconsideration of pricing theory," Journal of Urban Economics, Elsevier, vol. 1(3), pages 346-365, July.
    15. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
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