Präsentation auf PODC: Randomiserte parallele Zuweisung von Jobs auf Server

Auf dem ACM Symposium on Principles of Distributed Computing (PODC) in Chicago wird am 26.7.2016 eine theoretische Arbeit über die Verteilung von Jobs auf Server präsentiert werden.

Titel: Self-stabilizing Balls & Bins in Batches

Autoren: Petra Berenbrink, Tom Friedetzky, Peter Kling, Frederik Mallmann-Trenn, Lars Nagel, Chris Wastell

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 to n bins (servers). In a seminal work, Azar et al. proposed the sequential strategy Greedy[d] for n=m. When thrown, a ball queries the load of d random bins and is allocated to a least loaded of these. Azar et al. showed that d=2 yields an exponential improvement compared to d=1. Berenbrink et al. extended this to m >> n, showing that the maximal load difference is independent of m for d=2 (in contrast to d=1).

We propose a new variant of an infinite balls into bins process. In each round an expected number of c*n 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 c=c(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-c) * log(n/(1-c))) for d=1 and O(log(n/(1-c)))$ for d=2. In particular, Greedy[2] has an exponentially smaller system load for high arrival rates.

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