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Large Deviations without Principle: Join the Shortest Queue

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  • Ad Ridder

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

  • Adam Shwartz

    (Electrical Engineering 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-003/4.

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Date of creation: 06 Jan 2004
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Handle: RePEc:dgr:uvatin:20050003

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Web page: http://www.tinbergen.nl

Related research

Keywords: Sample path large deviations; rate function; optimal paths;

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  1. Ad Ridder & Adam Shwartz, 2005. "Large Deviations Methods and the Join-the-Shortest-Queue Model," Tinbergen Institute Discussion Papers 05-016/4, Tinbergen Institute.
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