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Bilevel programming applied to optimising urban transportation

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  • Clegg, Janet
  • Smith, Mike
  • Xiang, Yanling
  • Yarrow, Robert

Abstract

This paper outlines a multi-modal, elastic, equilibrium transportation model in which signal green-times and prices charged to traverse a route (public transport fares, parking charges or road-use charges) are explicitly included. An algorithm is specified which, for a fairly general objective function, continually moves current traffic flows, green-times and prices within the model toward locally optimal values while taking account of users' responses. The directions of movement of current traffic flows, green-times and prices are determined by solving linear approximations to the actual problem. The results of applying a simplified form of the algorithm to a small network model with five routes and two signal-controlled junctions are given. It is proved that under realistic conditions the sequence of (traffic flows, green-times, prices) triples generated by the algorithm does indeed approach those triples which possess a reasonable local optimality property. However the optimal control problem discussed here is non-convex and just a Karush-Kuhn-Tucker point is the "answer" sought.

Suggested Citation

  • Clegg, Janet & Smith, Mike & Xiang, Yanling & Yarrow, Robert, 2001. "Bilevel programming applied to optimising urban transportation," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 41-70, January.
    • Handle: RePEc:eee:transb:v:35:y:2001:i:1:p:41-70
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    Cited by:

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    4. Liu, Ronghui & Smith, Mike, 2015. "Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 123-145.
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    6. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    7. Christine Tawfik & Sabine Limbourg, 2018. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects," Sustainability, MDPI, vol. 10(9), pages 1-22, September.
    8. D'Acierno, Luca & Gallo, Mariano & Montella, Bruno, 2006. "Optimisation models for the urban parking pricing problem," Transport Policy, Elsevier, vol. 13(1), pages 34-48, January.
    9. Cantarella, Giulio Erberto & Cartenì, Armando & de Luca, Stefano, 2015. "Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues," European Journal of Operational Research, Elsevier, vol. 241(2), pages 330-347.
    10. 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.
    11. Evers, Ruth & Proost, Stef, 2015. "Optimizing intersections," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 100-119.
    12. Shahriar Afandizadeh & Seyed Ebrahim Abdolmanafi, 2016. "Development of a Model for a Cordon Pricing Scheme Considering Environmental Equity: A Case Study of Tehran," Sustainability, MDPI, vol. 8(2), pages 1-19, February.
    13. Wang, Guangmin & Xu, Meng & Grant-Muller, Susan & Gao, Zaihan, 2020. "Combination of tradable credit scheme and link capacity improvement to balance economic growth and environmental management in sustainable-oriented transport development: A bi-objective bi-level progr," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 459-471.
    14. Senlai Zhu & Jie Ma & Tianpei Tang & Quan Shi, 2020. "A Combined Modal and Route Choice Behavioral Complementarity Equilibrium Model with Users of Vehicles and Electric Bicycles," IJERPH, MDPI, vol. 17(10), pages 1-18, May.
    15. Li Li & Sridhar Tayur, 2005. "Medium-Term Pricing and Operations Planning in Intermodal Transportation," Transportation Science, INFORMS, vol. 39(1), pages 73-86, February.
    16. 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.
    17. Wang, Guangmin & Gao, Ziyou & Xu, Meng & Sun, Huijun, 2014. "Joint link-based credit charging and road capacity improvement in continuous network design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 67(C), pages 1-14.

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