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Optimal Flows in Stochastic Dynamic Networks with Congestion

Author

Listed:
  • John R. Birge

    (University of Michigan, Ann Arbor, Michigan)

  • James K. Ho

    (University of Illinois, Chicago, Illinois)

Abstract

This paper presents a method for finding optimal flows in a dynamic network with random inputs into the system and congestion limits on flow. This model has been used in deterministic settings to represent dynamic traffic assignment and job shop routing. This paper builds on the deterministic results to show that a globally optimal solution in the stochastic problem may be obtained by a sequence of linear optimizations. A decomposition algorithm for this procedure is presented that efficiently solves problems with large-scale deterministic equivalents of up to 66,000 variables.

Suggested Citation

  • John R. Birge & James K. Ho, 1993. "Optimal Flows in Stochastic Dynamic Networks with Congestion," Operations Research, INFORMS, vol. 41(1), pages 203-216, February.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:1:p:203-216
    DOI: 10.1287/opre.41.1.203
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    Cited by:

    1. Satish Ukkusuri & S. Waller, 2008. "Linear Programming Models for the User and System Optimal Dynamic Network Design Problem: Formulations, Comparisons and Extensions," Networks and Spatial Economics, Springer, vol. 8(4), pages 383-406, December.
    2. Zhao, Chunxue & Fu, Baibai & Wang, Tianming, 2014. "Braess paradox and robustness of traffic networks under stochastic user equilibrium," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 135-141.
    3. Xinhua Mao & Jianwei Wang & Changwei Yuan & Wei Yu & Jiahua Gan, 2018. "A Dynamic Traffic Assignment Model for the Sustainability of Pavement Performance," Sustainability, MDPI, vol. 11(1), pages 1-19, December.

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