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Large deviations and queueing networks: Methods for rate function identification

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  • Atar, Rami
  • Dupuis, Paul

Abstract

This paper considers the problem of rate function identification for multidimensional queueing models with feedback. A set of techniques are introduced which allow this identification when the model possesses certain structural properties. The main tools used are representation formulas for exponential integrals, weak convergence methods, and the regularity properties of associated Skorokhod Problems. Two examples are treated as special cases of the general theory: the classical Jackson network and a model for processor sharing.

Suggested Citation

  • Atar, Rami & Dupuis, Paul, 1999. "Large deviations and queueing networks: Methods for rate function identification," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 255-296, December.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:2:p:255-296
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    Cited by:

    1. Adam Shwartz & Alan Weiss, 2005. "Large Deviations with Diminishing Rates," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 281-310, May.
    2. Atar, Rami & Shadmi, Yonatan, 2023. "Fluid limits for earliest-deadline-first networks," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 279-307.
    3. Anatolii A. Puhalskii & Alexander A. Vladimirov, 2007. "A Large Deviation Principle for Join the Shortest Queue," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 700-710, August.
    4. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    5. Ad Ridder & Adam Shwartz, 2005. "Large deviations without principle: join the shortest queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 467-483, December.
    6. Ad Ridder & Adam Shwartz, 2005. "Large Deviations Methods and the Join-the-Shortest-Queue Model," Tinbergen Institute Discussion Papers 05-016/4, Tinbergen Institute.
    7. Ad Ridder & Adam Shwartz, 2004. "Large Deviations without Principle: Join the Shortest Queue," Tinbergen Institute Discussion Papers 05-003/4, Tinbergen Institute.

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