Large Deviations without Principle: Join the Shortest Queue

Ad Ridder () and Adam Shwartz
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Ad Ridder: Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam
Adam Shwartz: Electrical Engineering Technion, Israel Institute of Technology

No 05-003/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Sample path large deviations; rate function; optimal paths (search for similar items in EconPapers)
JEL-codes: C62 C65 (search for similar items in EconPapers)
Date: 2004-01-06
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