On the power of two choices: Balls and bins in continuous time
成果类型：
Article
署名作者：
Luczak, MJ; McDiarmid, C
署名单位：
University of London; London School Economics & Political Science; University of Oxford
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051605000000205
发表日期：
2005
页码：
1733-1764
关键词：
摘要：
Suppose that there are n bins, and balls arrive in a Poisson process at rate lambda n, where lambda > 0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is placed into one with least load. Balls have independent exponential lifetimes with unit mean. We show that the system converges rapidly to its equilibrium distribution; and when d > 2, there is an integer-valued function m(d)(n) = 1n1nn/1nd + O(1) such that, in the equilibrium distribution, the maximum load of a bin is concentrated on the two values m(d)(n) and m(d)(n) - 1, with probability tending to 1, as n -> infinity. We show also that the maximum load usually does not vary by more than a constant amount from 1n1nn/1nd, even over quite long periods of time.