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Large Deviations without Principle: Join the Shortest Queue

Author

Listed:
  • Ad Ridder

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Adam Shwartz

    (Electrical Engineering Technion, Israel Institute of Technology)

Abstract

This discussion paper resulted in a publication in the Mathematical Methods of Operations Research (2005). Volume 62, issue 3, pages 467-483. 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 larg 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 sytem may exhibit unexpected behavior.

Suggested Citation

  • Ad Ridder & Adam Shwartz, 2004. "Large Deviations without Principle: Join the Shortest Queue," Tinbergen Institute Discussion Papers 05-003/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050003
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    References listed on IDEAS

    as
    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 & 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Sample path large deviations; rate function; optimal paths;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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