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Large Deviations Methods and the Join-the-Shortest-Queue Model

Author

Listed:
  • Ad Ridder

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

  • Adam Shwartz

    (Technion Israel Institute of Technology)

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 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, 2005. "Large Deviations Methods and the Join-the-Shortest-Queue Model," Tinbergen Institute Discussion Papers 05-016/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050016
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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.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Large Deviations; Queues; Optimal Path to Overflow;
    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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