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Reliability-based stochastic transit assignment: Formulations and capacity paradox

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  • Jiang, Y.
  • Szeto, W.Y.

Abstract

This study develops link-based and approach-based variational inequality (VI) formulations for the frequency-based transit assignment with supply uncertainty, where link flows and flow on each outgoing link from each node are decision variables, respectively. Both the mean and variance of travel cost, including the covariance of in-vehicle travel costs, are captured in both formulations. To address the covariance of in-vehicle travel costs between different links on the same transit line, an augmented route-section network representation is developed, allowing us to apply the dynamic programming method to compute the value of the mapping function of the VI. The approach-based formulation can be solved by an extragradient method that only requires mild assumptions for convergence. It is found that the number of links carrying flow and equilibrium cost can be underestimated if supply uncertainty is not considered.

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  • Jiang, Y. & Szeto, W.Y., 2016. "Reliability-based stochastic transit assignment: Formulations and capacity paradox," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 181-206.
    • Handle: RePEc:eee:transb:v:93:y:2016:i:pa:p:181-206
    DOI: 10.1016/j.trb.2016.06.008
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    1. Hamdouch, Younes & Szeto, W.Y. & Jiang, Y., 2014. "A new schedule-based transit assignment model with travel strategies and supply uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 35-67.
    2. Zhi-Chun Li & William Lam & S. Wong, 2009. "The Optimal Transit Fare Structure under Different Market Regimes with Uncertainty in the Network," Networks and Spatial Economics, Springer, vol. 9(2), pages 191-216, June.
    3. Lam, William H.K. & Shao, Hu & Sumalee, Agachai, 2008. "Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 890-910, December.
    4. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    5. Jia Hao Wu & Michael Florian & Patrice Marcotte, 1994. "Transit Equilibrium Assignment: A Model and Solution Algorithms," Transportation Science, INFORMS, vol. 28(3), pages 193-203, August.
    6. Hamdouch, Younes & Lawphongpanich, Siriphong, 2008. "Schedule-based transit assignment model with travel strategies and capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 663-684, August.
    7. Cepeda, M. & Cominetti, R. & Florian, M., 2006. "A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 437-459, July.
    8. Sumalee, Agachai & Tan, Zhijia & Lam, William H.K., 2009. "Dynamic stochastic transit assignment with explicit seat allocation model," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 895-912, September.
    9. Lozano, Angelica & Storchi, Giovanni, 2001. "Shortest viable path algorithm in multimodal networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(3), pages 225-241, March.
    10. 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.
    11. Cortés, Cristián E. & Jara-Moroni, Pedro & Moreno, Eduardo & Pineda, Cristobal, 2013. "Stochastic transit equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 29-44.
    12. Roberto Cominetti & José Correa, 2001. "Common-Lines and Passenger Assignment in Congested Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 250-267, August.
    13. Lo, Hong K. & Yip, C. W. & Wan, K. H., 2003. "Modeling transfer and non-linear fare structure in multi-modal network," Transportation Research Part B: Methodological, Elsevier, vol. 37(2), pages 149-170, February.
    14. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    15. Chen, Xumei & Yu, Lei & Zhang, Yushi & Guo, Jifu, 2009. "Analyzing urban bus service reliability at the stop, route, and network levels," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(8), pages 722-734, October.
    16. Rasmussen, Thomas Kjær & Watling, David Paul & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 146-165.
    17. Hualing Ren & Ziyou Gao & William H.K. Lam & Jiancheng Long, 2009. "Assessing the benefits of integrated en-route transit information systems and time-varying transit pricing systems in a congested transit network," Transportation Planning and Technology, Taylor & Francis Journals, vol. 32(3), pages 215-237, April.
    18. Fitsum Teklu, 2008. "A Stochastic Process Approach for Frequency-based Transit Assignment with Strict Capacity Constraints," Networks and Spatial Economics, Springer, vol. 8(2), pages 225-240, September.
    19. Lam, William H. K. & Zhou, Jing & Sheng, Zhao-han, 2002. "A capacity restraint transit assignment with elastic line frequency," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 919-938, December.
    20. Schmöcker, Jan-Dirk & Fonzone, Achille & Shimamoto, Hiroshi & Kurauchi, Fumitaka & Bell, Michael G.H., 2011. "Frequency-based transit assignment considering seat capacities," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 392-408, February.
    21. Fosgerau, Mogens & Engelson, Leonid, 2011. "The value of travel time variance," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 1-8, January.
    22. Henry Liu & Xiaozheng He & Bingsheng He, 2009. "Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 9(4), pages 485-503, December.
    23. Lam, W. H. K. & Gao, Z. Y. & Chan, K. S. & Yang, H., 1999. "A stochastic user equilibrium assignment model for congested transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 33(5), pages 351-368, June.
    24. Joaquín de Cea & Enrique Fernández, 1993. "Transit Assignment for Congested Public Transport Systems: An Equilibrium Model," Transportation Science, INFORMS, vol. 27(2), pages 133-147, May.
    25. Nielsen, Otto Anker, 2000. "A stochastic transit assignment model considering differences in passengers utility functions," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 377-402, June.
    26. Claude Chriqui & Pierre Robillard, 1975. "Common Bus Lines," Transportation Science, INFORMS, vol. 9(2), pages 115-121, May.
    27. Yang, Hai & Bell, Michael G. H., 1998. "A capacity paradox in network design and how to avoid it," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 539-545, September.
    28. Sang Nguyen & Stefano Pallottino & Federico Malucelli, 2001. "A Modeling Framework for Passenger Assignment on a Transport Network with Timetables," Transportation Science, INFORMS, vol. 35(3), pages 238-249, August.
    29. Lo, Hong K. & Luo, X.W. & Siu, Barbara W.Y., 2006. "Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 792-806, November.
    30. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 166-181.
    31. Siu, Barbara W.Y. & Lo, Hong K., 2008. "Doubly uncertain transportation network: Degradable capacity and stochastic demand," European Journal of Operational Research, Elsevier, vol. 191(1), pages 166-181, November.
    32. Otto Nielsen & Rasmus Frederiksen, 2006. "Optimisation of timetable-based, stochastic transit assignment models based on MSA," Annals of Operations Research, Springer, vol. 144(1), pages 263-285, April.
    33. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    34. Agostino Nuzzolo & Francesco Russo & Umberto Crisalli, 2001. "A Doubly Dynamic Schedule-based Assignment Model for Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 268-285, August.
    35. Zhi-Chun Li & William H.K. Lam & S.C. Wong, 2009. "Optimization of a Bus and Rail Transit System with Feeder Bus Services under Different Market Regimes," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 495-516, Springer.
    36. W. Burke Jackson & James V. Jucker, 1982. "An Empirical Study of Travel Time Variability and Travel Choice Behavior," Transportation Science, INFORMS, vol. 16(4), pages 460-475, November.
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