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A Whole-Link Travel-Time Model with Desirable Properties

Author

Listed:
  • Malachy Carey

    (Faculty of Business and Management, University of Ulster, Northern Ireland, BT37 0QB)

  • Y. E. Ge

    (Faculty of Business and Management, University of Ulster, Northern Ireland, BT37 0QB)

  • Mark McCartney

    (Faculty of Informatics, University of Ulster, Northern Ireland, BT37 0QB)

Abstract

In network models for dynamic traffic assignment the link travel times are often described by “whole-link” models. In particular, they have been expressed as a function of the number of vehicles currently on the link. Such whole-link models are useful approximations and make the network model tractable when flows and travel times are varying over time. Here we propose an alternative whole-link model to approximate travel times. For a vehicle entering a link at time t , we let the link travel time be a function of a weighted average of the inflow rate at the time it enters and the outflow rate at the time it exits. We show that this model ensures first-in-first-out and has other desirable properties. We indicate computational methods for solving the model, apply it to various patterns of inflows, and compare the numerical results with two alternative whole-link models.

Suggested Citation

  • Malachy Carey & Y. E. Ge & Mark McCartney, 2003. "A Whole-Link Travel-Time Model with Desirable Properties," Transportation Science, INFORMS, vol. 37(1), pages 83-96, February.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:1:p:83-96
    DOI: 10.1287/trsc.37.1.83.12819
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jincheng Jiang & Nico Dellaert & Tom Van Woensel & Lixin Wu, 2020. "Modelling traffic flows and estimating road travel times in transportation network under dynamic disturbances," Transportation, Springer, vol. 47(6), pages 2951-2980, December.
    2. Carey, Malachy & Ge, Y.E., 2007. "Retaining desirable properties in discretising a travel-time model," Transportation Research Part B: Methodological, Elsevier, vol. 41(5), pages 540-553, June.
    3. Garcia-Rodenas, Ricardo & Lopez-Garcia, Maria Luz & Nino-Arbelaez, Alejandro & Verastegui-Rayo, Doroteo, 2006. "A continuous whole-link travel time model with occupancy constraint," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1455-1471, December.
    4. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2020. "Reprint of “Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach”," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 117-135.
    5. Satsukawa, Koki & Wada, Kentaro & Watling, David, 2022. "Dynamic system optimal traffic assignment with atomic users: Convergence and stability," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 188-209.
    6. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    7. Long, Jiancheng & Gao, Ziyou & Szeto, W.Y., 2011. "Discretised link travel time models based on cumulative flows: Formulations and properties," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 232-254, January.
    8. M Carey, 2009. "A framework for user equilibrium dynamic traffic assignment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(3), pages 395-410, March.
    9. Georgia Perakis & Guillaume Roels, 2006. "An Analytical Model for Traffic Delays and the Dynamic User Equilibrium Problem," Operations Research, INFORMS, vol. 54(6), pages 1151-1171, December.
    10. Chow, Andy H.F., 2009. "Properties of system optimal traffic assignment with departure time choice and its solution method," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 325-344, March.
    11. Carey, Malachy & Bar-Gera, Hillel & Watling, David & Balijepalli, Chandra, 2014. "Implementing first-in–first-out in the cell transmission model for networks," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 105-118.
    12. Carey, Malachy & Ge, Y. E., 2003. "Comparing whole-link travel time models," Transportation Research Part B: Methodological, Elsevier, vol. 37(10), pages 905-926, December.
    13. Wada, Kentaro & Satsukawa, Koki & Smith, Mike & Akamatsu, Takashi, 2019. "Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 391-413.
    14. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2019. "Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 229-247.
    15. 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.
    16. Hong Zheng & Yi-Chang Chiu & Pitu B. Mirchandani, 2015. "On the System Optimum Dynamic Traffic Assignment and Earliest Arrival Flow Problems," Transportation Science, INFORMS, vol. 49(1), pages 13-27, February.

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