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Large deviations without principle: join the shortest queue

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  • Ad Ridder
  • Adam Shwartz

Abstract

We develop a methodology for studying “large deviations type” questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a large class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are routed to the (weighted) shortest queue. It is not known whether the large deviations principle holds for this system. Using the tools developed here we derive large deviations type estimates for the most likely behavior, the most likely path to overflow and the probability of overflow. The analysis applies to any finite number of queues. We show via a counterexample that this system may exhibit unexpected behavior Copyright Springer-Verlag 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:3:p:467-483
    DOI: 10.1007/s00186-005-0037-1
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    References listed on IDEAS

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    1. Adam Shwartz & Alan Weiss, 2005. "Large Deviations with Diminishing Rates," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 281-310, May.
    2. Ad Ridder & Adam Shwartz, 2005. "Large Deviations Methods and the Join-the-Shortest-Queue Model," Tinbergen Institute Discussion Papers 05-016/4, Tinbergen Institute.
    3. 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.
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    Cited by:

    1. Danielle Tibi, 2019. "Martingales and buffer overflow for the symmetric shortest queue model," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 153-190, October.
    2. Plinio S. Dester & Christine Fricker & Danielle Tibi, 2017. "Stationary analysis of the shortest queue problem," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 211-243, December.
    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.

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