Strong approximation for the supermarket model
成果类型：
Article
署名作者：
Luczak, MJ; Norris, J
署名单位：
University of London; London School Economics & Political Science; University of Cambridge
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051605000000368
发表日期：
2005
页码：
2038-2061
关键词：
摘要：
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.