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Consistent objectives and solution of dynamic user equilibrium models*

* This paper is a replication of an original study

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  • Han, S.
  • Heydecker, B.G.

Abstract

The aim of this paper is to establish that there exist suitable objective functions for mathematical programming formulations of dynamic user equilibrium assignment in the sense of Wardrop (1952). Recently, Lin and Lo (2000) showed that we cannot necessarily calculate a dynamic user equilibrium assignment by minimising the integral over time of Beckmann's objective function that is widely used to solve for static user equilibrium assignment. In the present paper, two distinct objective functions are presented that result from formulations of assignment either as a variational inequality or as an infinitesimal optimisation: each of these formulations can be solved as a forward dynamic programme. With these formulations and solution approaches, we solve an example based upon Lin and Lo's one correctly.

Suggested Citation

  • Han, S. & Heydecker, B.G., 2006. "Consistent objectives and solution of dynamic user equilibrium models," Transportation Research Part B: Methodological, Elsevier, vol. 40(1), pages 16-34, January.
    • Handle: RePEc:eee:transb:v:40:y:2006:i:1:p:16-34
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    References listed on IDEAS

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    1. 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.
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    Citations

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    Cited by:

    1. Han, Sangjin, 2007. "A route-based solution algorithm for dynamic user equilibrium assignments," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1094-1113, December.
    2. Bates, John, 2007. "Practical modelling of trip re-scheduling under congested conditions," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(9), pages 788-801, November.
    3. 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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    Replication

    This item is a replication of:
  • Lin, Wei-Hua & Lo, Hong K., 2000. "Are the objective and solutions of dynamic user-equilibrium models always consistent?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(2), pages 137-144, February.

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