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Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

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  • Han, Lanshan
  • Ukkusuri, Satish
  • Doan, Kien

Abstract

In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.

Suggested Citation

  • Han, Lanshan & Ukkusuri, Satish & Doan, Kien, 2011. "Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1749-1767.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:10:p:1749-1767
    DOI: 10.1016/j.trb.2011.07.007
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    1. Duong Viet Thong & Aviv Gibali & Mathias Staudigl & Phan Tu Vuong, 2021. "Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters," Networks and Spatial Economics, Springer, vol. 21(3), pages 735-768, September.
    2. Ukkusuri, Satish V. & Han, Lanshan & Doan, Kien, 2012. "Dynamic user equilibrium with a path based cell transmission model for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1657-1684.
    3. Li, Xue-yan & Li, Xue-mei & Yang, Lingrun & Li, Jing, 2018. "Dynamic route and departure time choice model based on self-adaptive reference point and reinforcement learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 77-92.
    4. Wang, David Z.W. & Du, Bo, 2016. "Continuum modelling of spatial and dynamic equilibrium in a travel corridor with heterogeneous commuters—A partial differential complementarity system approach," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 1-18.
    5. Han, Ke & Szeto, W.Y. & Friesz, Terry L., 2015. "Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 16-49.
    6. Yan-Qun Jiang & S.C. Wong & Peng Zhang & Keechoo Choi, 2017. "Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City," Transportation Science, INFORMS, vol. 51(3), pages 931-945, August.
    7. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    8. Zhu, Feng & Ukkusuri, Satish V., 2017. "Efficient and fair system states in dynamic transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 272-289.
    9. Doan, Kien & Ukkusuri, Satish V., 2012. "On the holding-back problem in the cell transmission based dynamic traffic assignment models," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1218-1238.
    10. Han, Ke & Friesz, Terry L. & Szeto, W.Y. & Liu, Hongcheng, 2015. "Elastic demand dynamic network user equilibrium: Formulation, existence and computation," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 183-209.
    11. Jonathan D. Hall, 2017. "Improving the fit of structural models of congestion," Working Papers tecipa-590, University of Toronto, Department of Economics.
    12. Liu, Peng & Liao, Feixiong & Huang, Hai-Jun & Timmermans, Harry, 2015. "Dynamic activity-travel assignment in multi-state supernetworks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 656-671.
    13. Wang, Dong & Liao, Feixiong & Gao, Ziyou & Timmermans, Harry, 2019. "Tolerance-based strategies for extending the column generation algorithm to the bounded rational dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 102-121.
    14. Wang, Dong & Liao, Feixiong, 2023. "Incentivized user-based relocation strategies for moderating supply–demand dynamics in one-way car-sharing services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
    15. Babak Javani & Abbas Babazadeh, 2020. "Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning," Networks and Spatial Economics, Springer, vol. 20(2), pages 329-366, June.
    16. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "Existence of simultaneous route and departure choice dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 17-30.
    17. H. M. Abdul Aziz & Satish V. Ukkusuri & Xianyuan Zhan, 2017. "Determining the Impact of Personal Mobility Carbon Allowance Schemes in Transportation Networks," Networks and Spatial Economics, Springer, vol. 17(2), pages 505-545, June.

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