Self-Stabilizing Balls and Bins in Batches

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 modeled 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. Subsequently, 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 * A preliminary version of this paper was published in the proceedings of PODC'16 † The author did some of the research while affiliated with Simon Fraser University. 1 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.

Tight & Simple Load Balancing

“…As it is beyond the scope of this article to provide a complete survey, we focus on results for discrete load balancing on complete graphs and processes with sequential (or at least independent) load balancing actions. For an overview of results on general graphs, processes with multiple correlated load balancing actions (like the so-called diffusion model), and other variants we refer the reader to [1,6]. We should first like to note that the result we prove may almost be considered folklore and variants of it have been proved in different contexts, for example in [4] (who use this to prove results in a specific distributed computational model called population model) or [6] (who study load balancing on general graphs; see below).…”

Infinite Balanced Allocation via Finite Capacities

“…Berenbrink et al [10] study a round-based parallel version of the GREEDY[d] distribution scheme. m = n new balls arrive per round and at the end of the round each non-empty bin deletes one of its balls.…”

“…This effect is commonly referred to as "power of two choices" and it works very well in sequential settings. Not surprisingly, in parallel settings this d-choice process loses some of its powers [2,7,10]. To see this assume the tasks are allocated in batches of size n, one batch after another, but the balls within a batch simultaneously.…”

FairEdge: A Fairness-Oriented Task Offloading Scheme for Iot Applications in Mobile Cloudlet Networks

“…Consider a mobile edge network where user tasks follow an arrival rate λ are allocated into n mobile cloudlets, the ballsinto-bins process perfectly models the distributed computation offloading in a mobile edge cloudlet network. With the random choice in task offloading, the maximum load under an arbitrary round t is [22]:…”

“…As a result, with a fixed arbitrary round t, the theoretical maximum load of any cloudlet becomes as [22]:…”