Large deviations without principle: join the shortest queue |
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Authors: | Ad Ridder Adam Shwartz |
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Institution: | (1) Vrije Universiteit, Amsterdam, The Netherlands;(2) Electrical Engineering, Technion—Israel Institute of Technology, Haifa, Israel |
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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
Work of the first author was performed in part while visiting the Technion. Work of the second author was performed in part
while visiting the Vrije Universiteit, Amsterdam, and was supported in part by Fund for the promotion of research at the Technion. |
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