Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/28244

Title: Self-stabilizing balls and bins in batches: The power of leaky bins
Authors: Berenbrink, Petra
Friedetzky, Tom
Kling, Peter
Mallmann-Trenn, Frederik
Nagel, Lars
Wastell, Chris
Keywords: Balls-into-bins
Positive recurrent
Maximum load
Issue Date: 2018
Publisher: © Springer
Citation: BERENBRINK, P. ... et al, 2018. Self-stabilizing balls and bins in batches: The power of leaky bins. Algorithmica, 80 (12), pp.3673–3703.
Abstract: A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modelled as static balls into bins processes, where m balls (tasks) are to be distributed among n bins (servers). In a seminal work, Azar et al. [4] proposed the sequential strategy Greedy[d] for n = m. Each ball queries the load of d random bins and is allocated to a least loaded of them. Azar et al. showed that d = 2 yields an exponential improvement compared to d = 1. Berenbrink et al. [7] extended this to m n, showing that for d = 2 the maximal load difference is independent of m (in contrast to the d = 1 case). We propose a new variant of an infinite balls-into-bins process. In each round an expected number of λn new balls arrive and are distributed (in parallel) to the bins, and each non-empty bin deletes one of its balls. This setting models a set of servers processing incoming requests, where clients can query a server’s current load but receive no information about parallel requests. We study the Greedy[d] distribution scheme in this setting and show a strong self-stabilizing property: for any arrival rate λ = λ(n) < 1, the system load is time-invariant. Moreover, for any (even super-exponential) round t, the maximum system load is (w.h.p.) O 1 1−λ· log n 1−λ for d = 1 and O log n 1−λ for d = 2. In particular, Greedy[2] has an exponentially smaller system load for high arrival rates.
Description: This is a post-peer-review, pre-copyedit version of an article published in Algorithmica. The final authenticated version is available online at: https://doi.org/10.1007/s00453-018-0411-z.
Sponsor: Petra Berenbrink is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Peter Kling is partly supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Pacific Institute for the Mathematical Sciences (PIMS). Lars Nagel is supported by the German Ministry of Education and Research under Grant 01IH13004. Christopher Wastell is supported by EPSRC.
Version: Accepted for publication
DOI: 10.1007/s00453-018-0411-z
URI: https://dspace.lboro.ac.uk/2134/28244
Publisher Link: https://doi.org/10.1007/s00453-018-0411-z
ISSN: 0178-4617
Appears in Collections:Published Articles (Computer Science)

Files associated with this item:

File Description SizeFormat
Submission_Journal.pdfAccepted version481.28 kBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.