Efficient routing in heavy traffic under partial sampling of service times

TL;DR

This paper demonstrates that in a large-scale queueing system operating under heavy traffic, a routing strategy using minimal partial information about service times can asymptotically match the performance of an optimal mechanism with full knowledge of service rates.

Contribution

It introduces a routing mechanism that requires only a single sample from a subset of servers, achieving near-optimal performance without full knowledge of service rates.

Findings

Routing mechanism performs asymptotically as well as the best with full information.

Minimal partial sampling suffices for near-optimal routing in heavy traffic.

Performance is robust under weak convergence of service rate distribution.

Abstract

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 $.