On the power of two choices: Balls and bins in continuous time

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dc.creatorLuczak, Malwina J.
dc.creatorMcDiarmid, Colin
dc.date2005-08-24
dc.date.accessioned2026-07-07T05:22:37Z
dc.date.available2026-07-07T05:22:37Z
dc.descriptionSuppose that there are n bins, and balls arrive in a Poisson process at rate λn, where λ>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\geq 2, there is an integer-valued function m_d(n)=\ln \ln n/\ln d+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\to \infty. We show also that the maximum load usually does not vary by more than a constant amount from \ln \ln n/\ln d, even over quite long periods of time.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000205 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0508451
dc.identifierhttp://arxiv.org/abs/math/0508451
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 3, 1733-1764
dc.identifierdoi:10.1214/105051605000000205
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76131
dc.subjectProbability
dc.subject60C05 (Primary) 68R05, 90B80, 60K35, 60K30 (Secondary)
dc.titleOn the power of two choices: Balls and bins in continuous time
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