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Behaviour of a whole-link travel time model used in dynamic traffic assignment

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  • Carey, Malachy
  • McCartney, Mark

Abstract

Whole-link models of traffic flows have been widely used in mathematical programming models for dynamic traffic assignment (DTA). In this paper, we consider a well-known whole-link model in which the link travel time, for traffic entering at time t, is a function of the number of vehicles on the link, and may also be a function of the inflow rate or outflow rate at time t. Instead of considering this in a network context, we examine its behaviour for a single link, for given inflow profiles, so as to distinguish behaviour within a link from network behaviour. We consider steady state solutions, for constant inflows and outflows, note that various model forms can yield the same solution, and that under certain conditions the model may admit multiple values for the link travel time. We derive the complete analytic solution for a model where the travel time depends linearly only on the number of vehicles on the link, and show that the solution exhibits pseudo-periodicity, and converges to a steady state solution. The results indicate that the analytic solution is quite complex even for very simple cases, and that care has to be exercised in the choice of parameters. We illustrate the solutions numerically.

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  • Carey, Malachy & McCartney, Mark, 2002. "Behaviour of a whole-link travel time model used in dynamic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 36(1), pages 83-95, January.
    • Handle: RePEc:eee:transb:v:36:y:2002:i:1:p:83-95
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    References listed on IDEAS

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    Cited by:

    1. Jang, Wonjae & Ran, Bin & Choi, Keechoo, 2005. "A discrete time dynamic flow model and a formulation and solution method for dynamic route choice," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 593-620, August.
    2. 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.
    3. 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.
    4. 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.
    5. Carey, Malachy & McCartney, Mark, 2003. "Pseudo-periodicity in a travel-time model used in dynamic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 769-792, November.
    6. 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.
    7. Yanying Li, 2008. "Short-term prediction of motorway travel time using ANPR and loop data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 507-517.
    8. 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.
    9. Shengneng Hu & Zhen Jia & Anping Yang & Kui Xue & Guoqi He, 2022. "Evaluating the Sustainable Traffic Flow Operational Features of U-turn Design with Advance Left Turn," Sustainability, MDPI, vol. 14(11), pages 1-16, June.
    10. Malachy Carey & Paul Humphreys & Marie McHugh & Ronan McIvor, 2017. "Travel-Time Models With and Without Homogeneity Over Time," Transportation Science, INFORMS, vol. 51(3), pages 882-892, August.
    11. Malachy Carey & Y. E. Ge, 2005. "Convergence of a Discretised Travel-Time Model," Transportation Science, INFORMS, vol. 39(1), pages 25-38, February.
    12. Paipuri, Mahendra & Leclercq, Ludovic, 2020. "Bi-modal macroscopic traffic dynamics in a single region," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 257-290.
    13. Nie, Xiaojian & Zhang, H.M., 2005. "Delay-function-based link models: their properties and computational issues," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 729-751, September.
    14. 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.
    15. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Modeling and solving continuous-time instantaneous dynamic user equilibria: A differential complementarity systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 389-408.
    16. Huang, Y.P. & Xiong, J.H. & Sumalee, A. & Zheng, N. & Lam, W.H.K. & He, Z.B. & Zhong, R.X., 2020. "A dynamic user equilibrium model for multi-region macroscopic fundamental diagram systems with time-varying delays," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 1-25.
    17. 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.
    18. 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.
    19. Ban, Xuegang (Jeff) & Liu, Henry X. & Ferris, Michael C. & Ran, Bin, 2008. "A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 823-842, November.

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