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Sensitivity and error analysis of the dual criteria traffic assignment model

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  • Leurent, F.

Abstract

In the dual criteria traffic assignment model, to take into account various trade-offs between travel time and travel cost, the value of time is assumed to be continuously distributed across the trip-makers. This paper presents a sensitivity and error analysis method for the equilibrium solution of a dual criteria model with elastic demand, flow-dependent travel times and side constraints. The method is based on previous work by Tobin and Friesz (Transportation Science 22(4), 242-250, 1988) to bypass the uniqueness requirement in standard sensitivity analysis frameworks for variational inequalities, and exploits the finite-dimensional formulation of the model in terms of path flow variables given by Leurent (Transportation and Traffic Theory, pp. 455-477. Pergamon, Exeter, 1996a). The paper contains three parts. The first demonstrates the usefulness of sensitivity analysis using a two-link network. The second addresses the general network case. Last, the third presents an application to a realistic traffic study.

Suggested Citation

  • Leurent, F., 1998. "Sensitivity and error analysis of the dual criteria traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 189-204, April.
    • Handle: RePEc:eee:transb:v:32:y:1998:i:3:p:189-204
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    References listed on IDEAS

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    1. Marc J. Roberts, 1973. "On Time," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(4), pages 646-650.
    2. Leurent, Fabien, 1993. "Cost versus time equilibrium over a network," European Journal of Operational Research, Elsevier, vol. 71(2), pages 205-221, December.
    3. Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    4. Robert B. Dial, 1996. "Bicriterion Traffic Assignment: Basic Theory and Elementary Algorithms," Transportation Science, INFORMS, vol. 30(2), pages 93-111, May.
    5. 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.
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    Cited by:

    1. Du, Muqing & Chen, Anthony, 2022. "Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 175-202.
    2. Pi, Xidong & Qian, Zhen (Sean), 2017. "A stochastic optimal control approach for real-time traffic routing considering demand uncertainties and travelers’ choice heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 710-732.
    3. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun, 2008. "Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum," European Journal of Operational Research, Elsevier, vol. 189(1), pages 146-158, August.
    4. 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.
    5. Dao-Li Zhu & Hai Yang & Chang-Min Li & Xiao-Lei Wang, 2015. "Properties of the Multiclass Traffic Network Equilibria Under a Tradable Credit Scheme," Transportation Science, INFORMS, vol. 49(3), pages 519-534, August.
    6. Connors, Richard D. & Sumalee, Agachai & Watling, David P., 2007. "Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user-classes," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 593-615, July.
    7. Josefsson, Magnus & Patriksson, Michael, 2007. "Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 4-31, January.
    8. David Watling & Giulio Cantarella, 2015. "Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems," Networks and Spatial Economics, Springer, vol. 15(3), pages 843-882, September.
    9. Aguas, Oriana & Bachmann, Chris, 2022. "Assessing the effects of input uncertainties on the outputs of a freight demand model," Research in Transportation Economics, Elsevier, vol. 95(C).
    10. Michael Patriksson, 2004. "Sensitivity Analysis of Traffic Equilibria," Transportation Science, INFORMS, vol. 38(3), pages 258-281, August.
    11. Yang, Hai & Meng, Qiang, 2001. "Modeling user adoption of advanced traveler information systems: dynamic evolution and stationary equilibrium," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(10), pages 895-912, December.
    12. Huang, Hai-Jun & Li, Zhi-Chun, 2007. "A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1464-1477, February.
    13. Clark, Stephen D. & Watling, David P., 2002. "Sensitivity analysis of the probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 617-635, August.
    14. Yang, Chao & Chen, Anthony & Xu, Xiangdong & Wong, S.C., 2013. "Sensitivity-based uncertainty analysis of a combined travel demand model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 225-244.
    15. Yang, Hai & Tang, Wilson H. & Man Cheung, Wing & Meng, Qiang, 2002. "Profitability and welfare gain of private toll roads in a network with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(6), pages 537-554, July.
    16. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.

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