Distributed Rate Scaling in Large-Scale Service Systems

We consider a large-scale parallel-server system, where each server dynamically chooses its processing speed in a completely distributed fashion. The goal is to minimize the global cost that is the sum of the average cost of maintaining the respective processing speeds of all servers and a certain non-decreasing function of the sojourn time of tasks. The key challenges arise from the facts that the arrival rate of tasks is unknown and that there is no centralized control or communication among the servers. Using insights from stochastic approximation, we develop a novel rate-scaling algorithm and prove that the cost of the processing rates under our algorithm converges to the globally optimum value as the system size becomes large. En route, we also analyze the performance of a fully heterogeneous parallel-server system (i.e, where each server has a different processing speed), which might be of independent interest.