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Efficient routing in heavy traffic under partial sampling of service times

Summary: Efficient routing in heavy traffic
under partial sampling of service times
Rami Atar and Adam Shwartz
Department of Electrical Engineering
Technion­Israel Institute of Technology
March 14, 2008
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 crit-
ical loading condition holds. Server k serves at rate µk, and the empirical distribution of
{µk}k=1,...,n is assumed to converge weakly. We show that very little information on the ser-
vice 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
2 +
randomly selected servers ( > 0), but not to the actual values of the service
rates, the performance of which is asymptotically as good as the best among mechanisms that


Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology


Collections: Engineering