The Power of Two Choices in Randomized Load Balancing
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Computers
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Randomized load balancing is a cost efficient policy for job scheduling in parallel server queueing systems whereby, with every incoming job, a central dispatcher randomly polls some servers and selects the one with the smallest queue. By exactly deriving the jobsâ聙聶 delay distribution in such systems, in explicit and closed form, Mitzenmacher [5] proved the socalled â聙聵power-of-twoâ聙聶 result, which states that by randomly polling only two servers yields an exponential improvement in delay over randomly selecting a single server. Such a fundamental result, however, was obtained in an asymptotic regime in the total number of servers, and does do not necessarily provide accurate estimates for practical finite regimes with small or moderate number of servers. In this paper we obtain stochastic lower and upper bounds on the jobsâ聙聶 average delay in non-asymptotic regimes, by borrowing ideas for analyzing the particular case of the Join-the-Shortest-Queue (JSQ) policy. Numerical illustrations indicate not only that the obtained bounds are remarkably accurate, but also that the existing exact but asymptotic results can be largely misleading in some finite regimes.