Efficient routing in heavy traffic under partial sampling of service times

Details Efficient routing in heavy traffic under partial sampling of service times Efficient routing in heavy traffic under partial sampling of service times

2007-11-14

arxiv.org/abs/0711.2188v1

Mathematics

Probability

Scientific paper

We consider a queue with renewal arrivals and n exponential servers in the Halfin-Whitt heavy traffic regime, where n and the arrival rate increase without bound, so that a critical loading condition holds. Server k serves at rate $\mu_k $, and the empirical distribution of the $\mu_k $ is assumed to converge weakly. We show that very little information on the service rates is required for a routing mechanism to perform well. More precisely, we construct a routing mechanism that has access to a single sample from the service time distribution of each of $n$ to the power of $1/2 + \epsilon $ randomly selected servers, but not to the actual values of the service rates, the performance of which is asymptotically as good as the best among mechanisms that have the complete information on $ \mu_k $.

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