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Stochastic social optimum traffic assignment

Author

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  • Maher, Mike
  • Stewart, Kathryn
  • Rosa, Andrea

Abstract

This paper formulates a Stochastic Social Optimum (SSO) that relates to the Stochastic User Equilibrium (SUE) in the same way as the Social Optimum (SO) relates to the User Equilibrium (UE) in a deterministic environment. At the SSO solution, the total of the users' perceived costs is minimised. The formulation and analysis is carried out in a general utility-maximising framework, with the probit and logit models being special cases. Conditions for the SSO flow pattern are derived, from which it can be seen that the marginal social costs play the same role in the SSO as the standard costs play in SUE. In particular, it is shown that the SSO solution can be obtained through the use of an algorithm for SUE, but with the marginal costs replacing the standard costs in the stochastic loading and that optimal tolls are the differences between the marginal social costs and the standard costs. For the case of the logit model an explicit path-based objective function is obtained which is of a pleasing symmetrical form when compared with the objective functions for SUE, SO and UE. Additionally, a link-based objective function for the general utility-maximising case is formulated for SSO, which is similar in form to the SUE objective function of Sheffi and Powell.

Suggested Citation

  • Maher, Mike & Stewart, Kathryn & Rosa, Andrea, 2005. "Stochastic social optimum traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 753-767, September.
    • Handle: RePEc:eee:transb:v:39:y:2005:i:8:p:753-767
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    References listed on IDEAS

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    1. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. Maher, M. J. & Hughes, P. C., 1997. "A probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 341-355, August.
    3. Hai Yang, 1999. "System Optimum, Stochastic User Equilibrium, and Optimal Link Tolls," Transportation Science, INFORMS, vol. 33(4), pages 354-360, November.
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    Cited by:

    1. Hai-Jun Huang & Tian-Liang Liu & Xiaolei Guo & Hai Yang, 2011. "Inefficiency of Logit-Based Stochastic User Equilibrium in a Traffic Network Under ATIS," Networks and Spatial Economics, Springer, vol. 11(2), pages 255-269, June.
    2. Sumalee, Agachai & Xu, Wei, 2011. "First-best marginal cost toll for a traffic network with stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 41-59, January.
    3. Stewart, Kathryn, 2007. "Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(7), pages 644-654, August.
    4. Guo, Xiaolei & Yang, Hai & Liu, Tian-Liang, 2010. "Bounding the inefficiency of logit-based stochastic user equilibrium," European Journal of Operational Research, Elsevier, vol. 201(2), pages 463-469, March.
    5. Wu, Di & Yin, Yafeng & Lawphongpanich, Siriphong, 2011. "Pareto-improving congestion pricing on multimodal transportation networks," European Journal of Operational Research, Elsevier, vol. 210(3), pages 660-669, May.
    6. Paul Koster & Erik T. Verhoef & Simon Shepherd & David Watling, 2014. "Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand," Tinbergen Institute Discussion Papers 14-078/VIII, Tinbergen Institute, revised 13 Nov 2014.
    7. Lu, Xiao-Shan & Liu, Tian-Liang & Huang, Hai-Jun, 2015. "Pricing and mode choice based on nested logit model with trip-chain costs," Transport Policy, Elsevier, vol. 44(C), pages 76-88.
    8. Koster, Paul & Verhoef, Erik & Shepherd, Simon & Watling, David, 2018. "Preference heterogeneity and congestion pricing: The two route case revisited," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 137-157.
    9. Canca, David & Zarzo, Alejandro & Algaba, Encarnación & Barrena, Eva, 2013. "Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 428-442.
    10. Liu, Zhiyuan & Wang, Shuaian & Meng, Qiang, 2014. "Optimal joint distance and time toll for cordon-based congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 81-97.
    11. 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.
    12. Hazelton, Martin L., 2022. "The emergence of stochastic user equilibria in day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 102-112.
    13. Qiumin Liu & Vincent A.C. van den Berg & Erik T. Verhoef & Rui Jiang, 2024. "Pricing in the Stochastic Bottleneck Model with Price-Sensitive Demand," Tinbergen Institute Discussion Papers 24-011/VIII, Tinbergen Institute, revised 22 Oct 2024.
    14. Huang, Ruqing & Han, Lee D. & Huang, Zhongxiang, 2022. "A new network equilibrium flow model: User-equilibrium with quantity adjustment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 163(C).
    15. Xie, Chi & Travis Waller, S., 2012. "Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1023-1042.
    16. Watling, D.P. & Shepherd, S.P. & Koh, A., 2015. "Cordon toll competition in a network of two cities: Formulation and sensitivity to traveller route and demand responses," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 93-116.

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