Balls into non-uniform bins

Balls-into-bins games for uniform bins are widely used to model randomised load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many...

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Vydáno v:Journal of parallel and distributed computing Ročník 74; číslo 2; s. 2065 - 2076
Hlavní autoři: Berenbrink, Petra, Brinkmann, André, Friedetzky, Tom, Nagel, Lars
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Inc 01.02.2014
Elsevier
Témata:
Applied sciences
Balls-into-bins games
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Exact sciences and technology
Inventory control, production control. Distribution
Load balancing
Operational research and scientific management
Operational research. Management science
Randomised algorithms
Software
Randomised algorithms
Load balancing
Balls-into-bins games
Script
Peer to peer
Randomization
Probabilistic approach
Extreme value
Randomized algorithm
Modeling
ISSN:0743-7315, 1096-0848
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Popis
Shrnutí:Balls-into-bins games for uniform bins are widely used to model randomised load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks. In this paper we consider scenarios in which non-uniform selection probabilities help to balance the load among the bins. While previous evaluations try to find strategies for identical bins, we investigate heterogeneous bins where the “capacities” of the bins might differ significantly. We look at the allocation of m balls into n bins of total capacity C where each ball has d random bin choices. For such heterogeneous environments we show that the maximum load remains bounded by lnln(n)/ln(d)+O(1)w.h.p. if the number of balls m equals the total capacity C. Further analytical and simulative results show better bounds and values for the maximum loads in special cases. •This paper investigates randomised multiple-choice balls-into-bins games.•Such a balls-into-bins game models the allocation of tasks to servers of different speeds/capacities.•It is shown that a balanced allocation can be achieved if the number of balls equals the total capacity.•Simulations of other cases suggest that our algorithm works even for a small amount of balls and bins.
ISSN:0743-7315
1096-0848
DOI:10.1016/j.jpdc.2013.10.008