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A framework for user equilibrium dynamic traffic assignment

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  • M Carey

    (Queen's University)

Abstract

Several analytic approaches have been developed to describe or predict traffic flows on networks with time-varying (dynamic) travel demands, flows and travel times. A key component of these models lies in modelling the flows and/or travel times on the individual links, but as this is made more realistic or accurate it tends to make the overall model less computationally tractable. To help overcome this, and for other reasons, we develop a bi-level user equilibrium (UE) framework that separates the assignment or loading of flows on the time–space network from the modelling of flows and trip times within individual links. We show that this model or framework satisfies appropriate definitions of UE satisfies a first-in-first-out (FIFO) property of road traffic, and has other desirable properties. The model can be solved by iterating between (a) a linear network-loading model that takes the lengths of time–space links as fixed (within narrow ranges), and (b) a set of link flow sub-models which update the link trip times to construct a new time–space network. This allows links to be processed sequentially or in parallel and avoids having to enumerate paths and compute path flows or travel times. We test and demonstrate the model and algorithms using example networks and find that the algorithm converges quickly and the solutions behave as expected. We show how to extend the model to handle elastic demands, multiple destinations and multiple traffic types, and traffic spillback within links and from link to link.

Suggested Citation

  • 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.
  • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:3:d:10.1057_palgrave.jors.2602543
    DOI: 10.1057/palgrave.jors.2602543
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    References listed on IDEAS

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    1. Rubio-Ardanaz, J. M. & Wu, J. H. & Florian, M., 2003. "Two improved numerical algorithms for the continuous dynamic network loading problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(2), pages 171-190, February.
    2. Chen, Huey-Kuo & Hsueh, Che-Fu, 1998. "A model and an algorithm for the dynamic user-optimal route choice problem," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 219-234, April.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. Lam, William H. K. & Yin, Yafeng, 2001. "An activity-based time-dependent traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 35(6), pages 549-574, July.
    5. Janson, Bruce N., 1991. "Dynamic traffic assignment for urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 25(2-3), pages 143-161.
    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. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    8. Daoli Zhu & Patrice Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem," Transportation Science, INFORMS, vol. 34(4), pages 402-414, November.
    9. Terry L. Friesz & Javier Luque & Roger L. Tobin & Byung-Wook Wie, 1989. "Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem," Operations Research, INFORMS, vol. 37(6), pages 893-901, December.
    10. Wu, J. H. & Chen, Y. & Florian, M., 1998. "The continuous dynamic network loading problem: a mathematical formulation and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 173-187, April.
    11. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    12. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    13. 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.
    14. Lo, Hong K. & Szeto, W. Y., 2002. "A cell-based variational inequality formulation of the dynamic user optimal assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 421-443, June.
    15. Robert E. Bixby, 2002. "Solving Real-World Linear Programs: A Decade and More of Progress," Operations Research, INFORMS, vol. 50(1), pages 3-15, February.
    16. 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.
    17. Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, August.
    18. Daganzo, Carlos F., 1995. "A finite difference approximation of the kinematic wave model of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 261-276, August.
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    Cited by:

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    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.

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