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The continuous dynamic network loading problem: a mathematical formulation and solution method

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  • Wu, J. H.
  • Chen, Y.
  • Florian, M.

Abstract

The continuous dynamic network loading problem aims to find, on a congested network, temporal arc volumes, arc travel times, and path travel times given time-dependent path flow rates for a given time period. This problem may be considered as a subproblem of a temporal (dynamic) traffic assignment problem. In this paper, we study this problem and formulate it as a system of functional equations. Based on this system, we show that the FIFO (First In, First Out) condition is respected under a reasonable assumption. For computational purposes, we develop a polynomial approximation, which is almost equivalent to the original formulation on a set of finite discrete points. The approximation formulation is a finite dimensional system of equations which is solved as an optimization problem. The optimization problem may or may not be smooth depending on the structure of arc travel times. Several numerical examples are given to illustrate this approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:32:y:1998:i:3:p:173-187
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    References listed on IDEAS

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    1. Deepak K. Merchant & George L. Nemhauser, 1978. "Optimality Conditions for a Dynamic Traffic Assignment Model," Transportation Science, INFORMS, vol. 12(3), pages 200-207, August.
    2. Bin Ran & David E. Boyce & Larry J. LeBlanc, 1993. "A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models," Operations Research, INFORMS, vol. 41(1), pages 192-202, February.
    3. Byung-Wook Wie & Roger L. Tobin & Terry L. Friesz & David Bernstein, 1995. "A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem," Transportation Science, INFORMS, vol. 29(1), pages 79-92, February.
    4. Daganzo, Carlos F., 1995. "Properties of link travel time functions under dynamic loads," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 95-98, April.
    5. MERCHANT, Deepak K. & NEMHAUSER, George L., 1978. "Optimality conditions for a dynamic traffic assignment model," LIDAM Reprints CORE 345, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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