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Retaining desirable properties in discretising a travel-time model

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  • Carey, Malachy
  • Ge, Y.E.

Abstract

A recent paper introduced a new whole-link travel time model and showed that it has various desirable properties, including a first-in-first-out (FIFO) property, causality and consistency with the usual static model when flows are constant. The model is formulated as a continuous-time first-order differential equation, which does not have a general analytical solution but can be solved (approximately) numerically by forward or backward discrete-time differencing methods. Here we show that if the step sizes are not arbitrarily small then the solutions obtained by the usual differencing methods do not always preserve FIFO. In view of that, we introduce a new differencing method and prove that it always preserves FIFO and the other desirable properties exhibited by the continuous-time model. In numerical examples we illustrate how the new discrete-time differencing model eliminates FIFO violations, illustrate convergence of a solution process for the new model, and illustrate how various inflow patterns affect FIFO under the old and new differencing methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:41:y:2007:i:5:p:540-553
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    References listed on IDEAS

    as
    1. 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.
    2. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    3. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
    5. 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.
    6. Mounce, Richard & Carey, Malachy, 2011. "Route swapping in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 102-111, January.

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