Efficient routing in heavy traffic under partial sampling of service times
英文摘要：
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 $μ_k $, and the empirical distribution of the $μ_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 $1/2 + ε$ 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 $ μ_k $.
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