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Total unimodularity and decomposition method for large-scale air traffic cell transmission model

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  • Wei, P.
  • Cao, Y.
  • Sun, D.

Abstract

In an earlier work, Sun and Bayen built a Large-Capacity Cell Transmission Model for air traffic flow management. They formulated an integer programming problem of minimizing the total travel time of flights in the National Airspace System of the United States subject to sector capacity constraints. The integer program was relaxed to a linear program for computational efficiency. In this paper the authors formulate the optimization problem in a standard linear programming form. We analyze the total unimodular property of the constraint matrix, and prove that the linear programming relaxation generates an optimal integral solution for the original integer program. It is guaranteed to be optimal and integral if solved by a simplex related method. In order to speed up the computation, we apply the Dantzig–Wolfe Decomposition algorithm, which is shown to preserve the total unimodularity of the constraint matrix. Finally, we evaluate the performances of Sun and Bayen’s relaxation solved by the interior point method and our decomposition algorithm with large-scale air traffic data.

Suggested Citation

  • Wei, P. & Cao, Y. & Sun, D., 2013. "Total unimodularity and decomposition method for large-scale air traffic cell transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 1-16.
    • Handle: RePEc:eee:transb:v:53:y:2013:i:c:p:1-16
    DOI: 10.1016/j.trb.2013.03.004
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    References listed on IDEAS

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    1. Sun, D. & Clinet, A. & Bayen, A.M., 2011. "A dual decomposition method for sector capacity constrained traffic flow optimization," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 880-902, July.
    2. Hanif D. Sherali & Raymond W. Staats & Antonio A. Trani, 2006. "An Airspace-Planning and Collaborative Decision-Making Model: Part II---Cost Model, Data Considerations, and Computations," Transportation Science, INFORMS, vol. 40(2), pages 147-164, May.
    3. 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.
    4. Lisa Navazio & Giorgio Romanin-Jacur, 1998. "The Multiple Connections Multi-Airport Ground Holding Problem: Models and Algorithms," Transportation Science, INFORMS, vol. 32(3), pages 268-276, August.
    5. Mostafa Terrab & Amedeo R. Odoni, 1993. "Strategic Flow Management for Air Traffic Control," Operations Research, INFORMS, vol. 41(1), pages 138-152, February.
    6. Dimitris Bertsimas & Sarah Stock Patterson, 1998. "The Air Traffic Flow Management Problem with Enroute Capacities," Operations Research, INFORMS, vol. 46(3), pages 406-422, June.
    7. Peter B. Vranas & Dimitris J. Bertsimas & Amedeo R. Odoni, 1994. "The Multi-Airport Ground-Holding Problem in Air Traffic Control," Operations Research, INFORMS, vol. 42(2), pages 249-261, April.
    8. Hanif D. Sherali & J. Cole Smith & Antonio A. Trani, 2002. "An Airspace Planning Model for Selecting Flight-plans Under Workload, Safety, and Equity Considerations," Transportation Science, INFORMS, vol. 36(4), pages 378-397, November.
    9. 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.
    10. Thomas W. M. Vossen & Michael O. Ball, 2006. "Slot Trading Opportunities in Collaborative Ground Delay Programs," Transportation Science, INFORMS, vol. 40(1), pages 29-43, February.
    11. Guglielmo Lulli & Amedeo Odoni, 2007. "The European Air Traffic Flow Management Problem," Transportation Science, INFORMS, vol. 41(4), pages 431-443, November.
    12. Robert Hoffman & Michael O. Ball, 2000. "A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints," Operations Research, INFORMS, vol. 48(4), pages 578-590, August.
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    5. Kejun Long & Qin Lin & Jian Gu & Wei Wu & Lee D. Han, 2018. "Exploring Traffic Congestion on Urban Expressways Considering Drivers’ Unreasonable Behavior at Merge/Diverge Sections in China," Sustainability, MDPI, vol. 10(12), pages 1-17, November.

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