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Distributed Selfish Load Balancing

Suppose that a set of $m$ tasks are to be shared as equally as possible among a set of $n$ resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a "selfish agent" and require each agent to select a resource, with the cost of a resource being the...

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Bibliographic Details
Published in:SIAM journal on computing 2007-01, Vol.37 (4), p.1163-1181
Main Authors: Berenbrink, Petra, Friedetzky, Tom, Goldberg, Leslie Ann, Goldberg, Paul W., Hu, Zengjian, Martin, Russell
Format: Article
Language:English
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Summary:Suppose that a set of $m$ tasks are to be shared as equally as possible among a set of $n$ resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a "selfish agent" and require each agent to select a resource, with the cost of a resource being the number of agents that select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced. Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For $m \gg n$, the system becomes approximately balanced (an $\epsilon$-Nash equilibrium) in expected time $O(\log \log m)$. We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time $O(\log \log m + n^4)$. We also give a lower bound of $\Omega(\max\{\log \log m, n\})$ for the convergence time.
ISSN:0097-5397
1095-7111
DOI:10.1137/060660345