Open Access
August 2005 Strong approximation for the supermarket model
Malwina J. Luczak, James Norris
Ann. Appl. Probab. 15(3): 2038-2061 (August 2005). DOI: 10.1214/105051605000000368


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, and rely in part on couplings. This allows us to approximate 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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Malwina J. Luczak. James Norris. "Strong approximation for the supermarket model." Ann. Appl. Probab. 15 (3) 2038 - 2061, August 2005.


Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1080.60086
MathSciNet: MR2152252
Digital Object Identifier: 10.1214/105051605000000368

Primary: 60K25
Secondary: 60F15

Keywords: coupling , diffusion approximation , exponential martingale inequalities , Join the shortest queue , Law of Large Numbers , Supermarket model

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.15 • No. 3 • August 2005
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