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Comparing whole-link travel time models

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  • Carey, Malachy
  • Ge, Y. E.

Abstract

In a model commonly used in dynamic traffic assignment the link travel time for a vehicle entering a link at time t is taken as a function of the number of vehicles on the link at time t. In an alternative recently introduced model, the travel time for a vehicle entering a link at time t is taken as a function of an estimate of the flow in the immediate neighbourhood of the vehicle, averaged over the time the vehicle is traversing the link. Here we compare the solutions obtained from these two models when applied to various inflow profiles. We also divide the link into segments, apply each model sequentially to the segments and again compare the results. As the number of segments is increased, the discretisation refined to the continuous limit, the solutions from the two models converge to the same solution, which is the solution of the Lighthill, Whitham, Richards (LWR) model for traffic flow. We illustrate the results for different travel time functions and patterns of inflows to the link. In the numerical examples the solutions from the second of the two models are closer to the limit solutions. We also show that the models converge even when the link segments are not homogeneous, and introduce a correction scheme in the second model to compensate for an approximation error, hence improving the approximation to the LWR model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:37:y:2003:i:10:p:905-926
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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. Rui Ma & Xuegang Ban & Jong-Shi Pang & Henry Liu, 2015. "Submission to the DTA2012 Special Issue: Convergence of Time Discretization Schemes for Continuous-Time Dynamic Network Loading Models," Networks and Spatial Economics, Springer, vol. 15(3), pages 419-441, September.
    4. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Continuous-time point-queue models in dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 360-380.
    5. 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.
    6. Carey, Malachy & Humphreys, Paul & McHugh, Marie & McIvor, Ronan, 2014. "Extending travel-time based models for dynamic network loading and assignment, to achieve adherence to first-in-first-out and link capacities," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 90-104.
    7. 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.
    8. Malachy Carey & Y. E. Ge, 2005. "Alternative Conditions for a Well-Behaved Travel Time Model," Transportation Science, INFORMS, vol. 39(3), pages 417-428, August.
    9. Temelcan, Gizem & Kocken, Hale Gonce & Albayrak, Inci, 2021. "Fuzzy modelling of static system optimum traffic assignment problem having multi origin-destination pair," Socio-Economic Planning Sciences, Elsevier, vol. 77(C).
    10. Zhong, R.X. & Sumalee, A. & Friesz, T.L. & Lam, William H.K., 2011. "Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1035-1061, August.

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