On the maximum queue length in the supermarket model
成果类型：
Article
署名作者：
Luczak, Malwina J.; McDiarmid, Colin
署名单位：
University of London; London School Economics & Political Science; University of Oxford
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/00911790500000710
发表日期：
2006
页码：
493-527
关键词：
摘要：
There are n queues, each with a single server. Customers arrive in a Poisson process at rate lambda n, where 0 < lambda < 1. Upon arrival each customer selects d >= 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with probability tending to 1 as n -> infinity the maximum queue length takes at most two values, which are lnlnn/lnd + O(l).
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