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New Linear Program Performance Bounds for Queueing Networks

Author

Listed:
  • J. R. Morrison

    (University of Illinois)

  • P. R. Kumar

    (University of Illinois)

Abstract

We obtain new linear programs for bounding the performance and proving the stability of queueing networks. They exploit the key facts that the transition probabilities of queueing networks are shift invariant on the relative interiors of faces and the cost functions of interest are linear in the state. A systematic procedure for choosing different quadratic functions on the relative interiors of faces to serve as surrogates of the differential costs in an inequality relaxation of the average cost function leads to linear program bounds. These bounds are probably better than earlier known bounds. It is also shown how to incorporate additional features, such as the presence of virtual multi-server stations to further improve the bounds. The approach also extends to provide functional bounds valid for all arrival rates.

Suggested Citation

  • J. R. Morrison & P. R. Kumar, 1999. "New Linear Program Performance Bounds for Queueing Networks," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 575-597, March.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:3:d:10.1023_a:1022638523391
    DOI: 10.1023/A:1022638523391
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    References listed on IDEAS

    as
    1. H. Jin & J. Ou & P. R. Kumar, 1997. "The Throughput of Irreducible Closed Markovian Queueing Networks: Functional Bounds, Asymptotic Loss, Efficiency, and the Harrison-Wein Conjectures," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 886-920, November.
    2. C. Humes & J. Ou & P. R. Kumar, 1997. "The Delay of Open Markovian Queueing Networks: Uniform Functional Bounds, Heavy Traffic Pole Multiplicities, and Stability," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 921-954, November.
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    Citations

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    Cited by:

    1. Dimitris Bertsimas & David Gamarnik & Alexander Anatoliy Rikun, 2011. "Performance Analysis of Queueing Networks via Robust Optimization," Operations Research, INFORMS, vol. 59(2), pages 455-466, April.
    2. Daniela Pucci de Farias & Benjamin Van Roy, 2004. "On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 462-478, August.
    3. Laumer, Simon & Barz, Christiane, 2023. "Reductions of non-separable approximate linear programs for network revenue management," European Journal of Operational Research, Elsevier, vol. 309(1), pages 252-270.
    4. Daniela Pucci de Farias & Benjamin Van Roy, 2006. "A Cost-Shaping Linear Program for Average-Cost Approximate Dynamic Programming with Performance Guarantees," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 597-620, August.
    5. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    6. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    7. Selvaprabu Nadarajah & François Margot & Nicola Secomandi, 2015. "Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage," Management Science, INFORMS, vol. 61(12), pages 3054-3076, December.

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