  We consider a large-scale parallel-server system, where each server
independently adjusts its processing speed in a decentralized manner. The
objective is to minimize the overall cost, which comprises the average cost of
maintaining the servers' processing speeds and a non-decreasing function of the
tasks' sojourn times. The problem is compounded by the lack of knowledge of the
task arrival rate and the absence of a centralized control or communication
among the servers. We draw on ideas from stochastic approximation and present a
novel rate scaling algorithm that ensures convergence of all server processing
speeds to the globally asymptotically optimum value as the system size
increases. Apart from the algorithm design, a key contribution of our approach
lies in demonstrating how concepts from the stochastic approximation literature
can be leveraged to effectively tackle learning problems in large-scale,
distributed systems. En route, we also analyze the performance of a fully
heterogeneous parallel-server system, where each server has a distinct
processing speed, which might be of independent interest.
