Strong approximation for the supermarket model

Details Strong approximation for the supermarket model Strong approximation for the supermarket model

2004-05-11

arxiv.org/abs/math/0405183v1

Mathematics

Probability

27 pages

Scientific paper

We prove three strong approximation theorems for the `supermarket' or `join the shortest queue' model -- a law of large numbers, a jump process approximation and a central limit theorem. The estimates are carried through rather explicitly. This allows us to estimate each of the infinitely many components of the process in its own scale and to exhibit a cut-off in the set of active components which grows slowly with the number of servers.

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